Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90

Contents lists available at ScienceDirect

Physics of the Earth and Planetary Interiors

journal homepage wwwelsevier comlocate pepi

Invited Review

Anisotropy in the deep Earth

httpdxdoiorg101016jpepi2017050050031-9201 2017 Elsevier BV All rights reserved

uArr Corresponding author at Department of Earth and Planetary Science University of California at Berkeley United StatesE-mail address barbaraseismoberkeleyedu (B Romanowicz)

Barbara Romanowicz abuArr Hans-Rudolf Wenk a

aDepartment of Earth and Planetary Science University of California at Berkeley United StatesbCollegravege de France and Institut de Physique du Globe Paris France

a r t i c l e i n f o

Article historyReceived 11 September 2016Received in revised form 30 March 2017Accepted 3 May 2017Available online 6 May 2017

a b s t r a c t

Seismic anisotropy has been found in many regions of the Earthrsquos interior Its presence in the Earthrsquos crusthas been known since the 19th century and is due in part to the alignment of anisotropic crystals inrocks and in part to patterns in the distribution of fractures and pores In the upper mantle seismic ani-sotropy was discovered 50 years ago and can be attributed for the most part to the alignment of intrin-sically anisotropic olivine crystals during large scale deformation associated with convection There issome indication for anisotropy in the transition zone particularly in the vicinity of subducted slabsHere we focus on the deep Earth ndash the lower mantle and core where anisotropy is not yet mapped indetail nor is there consensus on its origin Most of the lower mantle appears largely isotropic exceptin the last 200ndash300 km in the D00 region where evidence for seismic anisotropy has been accumulatingsince the late 1980s mostly from shear wave splitting measurements Recently a picture has beenemerging where strong anisotropy is associated with high shear velocities at the edges of the largelow shear velocity provinces (LLSVPs) in the central Pacific and under Africa These observations are con-sistent with being due to the presence of highly anisotropic MgSiO3 post-perovskite crystals aligned dur-ing the deformation of slabs impinging on the core-mantle boundary and upwelling flow within theLLSVPsWe also discuss mineral physics aspects such as ultrahigh pressure deformation experiments first prin-

ciples calculations to obtain information about elastic properties and derivation of dislocation activitybased on bonding characteristics Polycrystal plasticity simulations can predict anisotropy but modelsare still highly idealized and neglect the complex microstructure of polyphase aggregates with strongand weak components A promising direction for future progress in understanding the origin of seismicanisotropy in the deep mantle and its relation to global mantle circulation is to link macroscopic infor-mation from seismology and microscopic information mineral physics through geodynamics modelingAnisotropy in the inner core was proposed 30 years ago to explain faster P wave propagation along the

direction of the Earthrsquos axis of rotation as well as anomalous splitting of core sensitive free oscillationsThere is still uncertainty about the origin of this anisotropy In particular it is difficult to explain itsstrength based on known elastic properties of iron as it would require almost perfect alignment of ironcrystals Indeed the strongly anomalous P travel times observed on paths from the South SandwichIslands to Alaska may or may not be due to inner core anisotropy and will need to be explained beforeconsensus can be reached on the strength of anisotropy in the inner core and its origin

2017 Elsevier BV All rights reserved

Contents

1 Background and motivation 592 Seismic anisotropy in the deep mantle 60

21 Overview 6022 Accounting for upper mantle anisotropy 6123 Results from array studies 6224 Results from global anisotropic tomography 63

3 Mineral physics perspective on the deep mantle 65

B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90 59

31 Dominant mineral phases in the lower mantle 6532 Some comments on plasticity models and representation of anisotropy 6633 Deformation experiments and rheology 6934 Elastic properties 72

4 Linking seismology and mineral physics through predictions of anisotropy in geodynamic models 73

41 Isotropic geodynamic models for upper mantle convection 7342 Review of upper mantle anisotropic models 7343 Anisotropic models for the lowermost mantle 7444 Isotropic viscosity medium approach for lower mantle anisotropy 7545 Flow calculation based on a global tomographic model 7546 Compositional heterogeneities 7747 Viscosity changes 7748 Active deformation mechanisms 7749 Complications in polyphase systems 77

5 Seismic anisotropy in the inner core 786 Mineral physics of the inner core 80

61 Phase relations 8062 Causes of anisotropy in the inner core 81

7 Conclusions and future directions 82

71 Anisotropy in the deep mantle 8272 Inner core anisotropy 83

Acknowledgements 83References 83

1 Background and motivation

The presence of seismic anisotropy in the crust and in the uppermantle is well documented and there is relatively good consensuson its origins owing to direct observations in the field and labora-tory experiments on mineral crystal structure and deformationproperties in a range of pressures and temperatures that is nowreadily accessible The situation is much less clear for the deepmantle and core due on the one hand to the poor sampling byseismic waves contamination by upper mantle effects and onthe other hand the difficulty for mineral physics deformationexperiments to reach the relevant physical conditions Howeverthere has been significant progress in both fields in the last decadeand a new and promising approach has emerged aiming at com-bining seismic observations of anisotropy in the deep Earth withknowledge from geodynamics modelling and constraints frommineral physics towards understanding deformation patternsrelated to global mantle circulation

Here we review the present state of knowledge on deep mantleand inner core anisotropy in seismology and mineral physicsdescribe current efforts at linking the two through mantle circula-tion modeling and discuss future directions and challenges Firstwe start with some historical background

Anisotropic propagation of sound waves was already describedby Green (1838) who introduced Greenrsquos functions Rudzki (18971911) recognized the importance of anisotropic wave propagationin crustal rocks and developed the framework for seismic explo-ration in the Earthrsquos crust He highlighted the relationship betweenthe orientation of crystals and fractures in rocks On the mineralphysics side it was DrsquoHalloy (1833) who introduced the expressionlsquolsquotexturerdquo to describe directional properties of the rock fabric thatwas further quantified by Naumann (1850) Voigt (1887) firstintroduced a quantitative link between elastic properties of singlecrystals and their orientation with the elastic properties of a tex-tured aggregate In the following century these concepts wererefined and were applied in materials science as well as geo-physics In exploration geophysics eg of oil deposits anisotropybecame a central issue (eg Crampin 1984 Thomsen 1986)

It took considerably longer to recognize anisotropy in the deepEarth At an IUGG meeting in Berkeley Raitt (1963) reported azi-muthal anisotropy below the Moho in the Mendocino escarpment

Similar anisotropy was observed by Morris et al (1969) in Hawaii(Fig 1a) This came at a time when Wegenerrsquos (1915) theory ofcontinental drift was revived by Vine and Matthews (1963) docu-menting magnetic reversals along ridges of upwelling basalts Thestructural geologist Hess (1964) immediately interpreted theseobservations as due to large-scale mantle convection that pro-duced alignment of olivine crystals The alignment was attributedto crystal plasticity Cann (1968) further advanced the mantle con-vection concept (Fig 1b)

With the advent of global seismic tomography it became possi-ble to map the patterns of radial and azimuthal anisotropy in theuppermost mantle using fundamental mode surface wave disper-sion data This pattern of azimuthal anisotropy turned out to bequite regular with an indication of the direction of spreading nearmid-ocean ridges (eg Fig 1c Tanimoto and Anderson 1985Montagner and Tanimoto 1990 1991) while differences in thevelocity of vertically polarized Rayleigh waves and transverselypolarized Love waves could point to the location of rising or sink-ing currents (eg Nataf et al 1984 Montagner 2002)

While it was generally accepted that alignment of olivine crys-tals during mantle convection plays a critical role in the develop-ment of seismic anisotropy the mechanism proposed by Hess(1964) was very simple-minded Olivine crystals do not occur asplatelets or needles that float in a viscous liquid and align relativeto flow plane and flow direction Interest in the mantle startedexperimental research on deformation mechanisms of olivine andassociated crystal preferred orientation (CPO) mainly withpiston-cylinder deformation apparatus (eg Raleigh 1968 and laterKohlstedt and Goetze 1974 Jung and Karato 2001 Jung et al2006) It revealed that depending on conditions different disloca-tion glide mechanisms are active with dominant (010)[100] slipat low stress and water content (A-type) dominant (010)[001]slip at high stress (B-type) and (100)[001] slip at high water con-tent as derived from observations of dislocations by transmissionelectron microscopy and fabric types in aggregates (eg Karatoet al 2008) During dislocation glide crystals in a polycrystallineaggregate rotate and align But the deformation pattern in the con-vecting upper mantle is more complex than a deformation experi-ment most commonly performed in axial compression andsometimes in simple shear and at much higher strain rates thanin the Earth

Fig 1 (a) Azimuthal variation of surface wave velocities in Hawaii (Morris et al 1969) (b) Proposed model for mantle upwelling at an oceanic ridge (Cann 1968) (c)Azimuthal anisotropy in Rayleigh waves at a period of 98s (Montagner and Tanimoto 1990) The lines correspond to fast wave propagation directions and are proportional tothe strength of anisotropy

60 B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90

Geodynamic models are necessary to suggest realistic deforma-tion paths Early models assumed flow in an isotropic medium dri-ven by temperature and density gradients (eg Hager andOrsquoConnell 1981 Tackley 1993 Bunge et al 1996) Also subduc-tion of crustal slabs was explored including rigid slabs (egMcKenzie 1969) as well as more ductile and weak slabs (egGurnis and Hager 1988) The development of seismic anisotropywas considered only later by including polycrystal plasticity toexplain the development of preferred orientation during plasticdeformation (eg Blackman et al 1996 Dawson and Wenk2000 Kaminski and Ribe 2001) We will discuss convection mod-els in more detail below

Seismic observations revealed that the pattern of anisotropy inthe upper mantle is much more complex that the picture in Fig 1cThis has been reviewed recently (eg Long and Becker 2010 Long2013) Here we will focus on anisotropy in the lower mantle andinner core first from what we know from seismology and fromour current knowledge about mineral physics particularly elastic-ity of minerals at deep Earth conditions and deformation mecha-nisms Then we will explain how geodynamics modeling isbrought into the picture Great progress has been made in all threefields over the last 20 years The deep Earth appeared like a simpleimage but the more we learn about it the more complexities ariseIn a concluding section we will highlight some important issuesthat need to be addressed in the future There has been a lot ofinterest in this topic with many publications in prestigious jour-nals such as Science and Nature but still a lot of work remains tobe done to better describe and understand processes that causeseismic anisotropy at deep Earth conditions

The purpose of this review is to establish our current state ofknowledge and to identify some outstanding questions It alsoshould serve as an introduction to the field of deep Earth aniso-tropy for those who are not experts in the field for example forstudent projects

2 Seismic anisotropy in the deep mantle

21 Overview

There is as yet no compelling evidence for the presence of sig-nificant anisotropy in the bulk of the lower mantle at least awayfrom subduction zones (eg Meade et al 1995 Montagner andKennett 1996 Niu and Perez 2004 Panning and Romanowicz2006 Moulik and Ekstroumlm 2014) although a recent study basedon normal mode center frequency observations suggests the pres-ence of anisotropy as expressed in the radial anisotropy parameterg already 1000 km above the core-mantle boundary (de Wit andTrampert 2015) In any case it is now well established that signif-icant seismic anisotropy is present in the D00 region at the base ofthe mantle Here we review the corresponding observational evi-dence which is based on local studies of shear body waves sensi-tive to the deep mantle complemented by global tomographicstudies of radial anisotropy throughout the mantle

The first observations of shear wave splitting attributed to ani-sotropy in the D00 region date back to the late 1980s Vinnik et al(1989) observed elliptically polarized Sdiff waves for paths sam-pling the lowermost mantle in the central Pacific along a direction

Fig 3 Background lsquolsquoVoting maprdquo based on 5 shear wave velocity tomographicmodels modified (from Lekic et al 2012) Locations in D00 where 5 models agreethat Vs is lower than average or higher than average are shown in red and dark bluerespectively White ellipses indicate locations where shear wave splitting observa-tions with Vsh gt Vsv have been attributed to anisotropy in D00 These include regionswhere azimuthal anisotropy has been reported Green ellipses indicate regionswhere strong lateral variations of anisotropy in D00 have been reported at the edgesof the African LLSVP (14 17 21) the Perm anomaly (19) and in the south Pacific(719) Blue ellipses with broken lines indicate regions where Vsv gt Vsh has beenreported andor null splitting See Table 1 for references to numbers and lettersWhite bars and blue broken lines (no splitting) are from Niu and Perez (2004)

B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90 61

for which no splitting was present in SKS Because the absence ofthe latter indicated that the data were not contaminated by uppermantle anisotropy they suggested that the splitting originated inthe deep mantle and could be due to the presence of anisotropyEarlier Mitchell and Helmberger (1973) and Lay and Helmberger(1983) had observed time shifts between the arrival of ScSH andScSV but attributed them to the presence of a high velocity regionat the base of the mantle Many studies followed in the 1990s doc-umenting splitting times of up to 10 s in shear waves such as ScSand Sdiff (Fig 2) that propagate quasi-horizontally in D00 and inter-preted them as indicating the presence of several percent of VTI(Vertical Transverse Isotropy) in the deep mantle (see Lay et al1998 and Kendall and Silver 1998 for early reviews)

As different areas of the world were progressively sampled thepicture that emerged was that globally the vertically polarizedwave (SV) is generally delayed with respect to the horizontallypolarized one (SH) in the circum-pacific ring where isotropic shearwave velocities are higher than average in D00 On the other handintermittent splitting and sometimes delayed SH with respect toSV was observed on paths sampling the large low shear velocityprovinces (LLSVPs) in the central Pacific and under Africa (Fig 3)Additional reports of splitting in ScS and Sdiff have been publishedin the last two decades most of them attributed to anisotropy inD00 A review of observations of shear wave splitting originatingin D00 can be found in Wookey and Kendall (2007) and Nowackiet al (2011) as well as Lay (2015) Here we focus primarily onthe most recent contributions while an updated list of observa-tions is given in Table 1 and Fig 3

Several important challenges affect studies of shear wave split-ting in D00 One is the necessity to account for (or avoid) contamina-tion of seismic waveforms by strong upper mantle anisotropysampled by the body waves considered (Fig 2) Another challengeis the poor azimuthal sampling of D00 at any given location due tothe limited global distribution of earthquake sources and receiversThis makes it difficult to distinguish between different possiblecauses of anisotropy whether due to periodic layering or crystalalignment and whether the nature of the anisotropy is transverseisotropy with a vertical (VTI) or tilted (TTI) axis of symmetry or

SScS

SKKS

SKS

Fig 2 Raypaths through the Earth of the main seismic body wave phases used forstudying anisotropy in the deep mantle Asterisk is earthquake location trianglesare receiver stations

perhaps involves more complex symmetries Also in the case ofSdiff an apparent delay of SVdiff may be due to waveform distorsionin a laterally heterogeneous but isotropic structure due to the factthat the amplitude of SVdiff decays rapidly with distance in regionsof fast isotropic velocity (eg Vinnik et al 1995 Komatitsch et al2010) More generally apparent splitting in S waves sampling theD00 region may sometimes be due to other causes than anisotropysuch as propagation in a complex heterogeneous medium near theboundary between the solid mantle and the liquid core whichrequires more sophisticated modeling than infinite frequency raytheory (Monteiller and Chevrot 2010 Borgeaud et al 2016Nowacki and Wookey 2016) Careful waveform analysis is there-fore necessary before attributing splitting observations to aniso-tropy Some of the splitting results listed in Table 1 may need tobe re-evaluated in that context However consistency in the split-ting results obtained using different types of waves across a num-ber of regions of the world and in some cases detailed waveformmodeling indicates that in general invoking anisotropy as a causefor the observed splitting is a robust result At the present timeinterpretation in terms of layering or CPO requires invoking possi-ble constraints from other fields than seismology and remainsuncertain

22 Accounting for upper mantle anisotropy

In order to account for upper-mantle anisotropy an approachtaken in early studies of Sdiff splitting was to only consider deepearthquakes and paths for which SKS and SKKS do not presentany evidence of splitting (eg Vinnik et al 1989 1995) Selectingobservations for deep earthquakes assures that contamination byanisotropic effects in the upper mantle on the source side can lar-gely be avoided On the station side the paths of Sdiff and SKSSKKSare very close in the upper mantle (Fig 2) while they diverge in thedeep mantle Also only Sdiff spends significant time within D00 Theabsence of splitting in SKSSKKS indicates that either there is noanisotropy in the upper mantle region sampled on the receiverside or the direction of the great circle path is along the null split-ting direction Any splitting observed in Sdiff can thus be attributedto the deep mantle

However such geometries are exceptional Therefore it isimportant to find ways to correct for the widespread and strong

Table 1Summary of local studies of anisotropy in D00

Authors Region Type ofseismicwaves

VSH gt VSV

A Wookey and Kendall (2007)and Refs therein

Caribbean

Kendall and Silver (1996) Caribbean SSdiffDing and Helmberger

(1997)Caribbean ScS

Rokosky et al (2004) Caribbean ScSB Wookey and Kendall (2007)

and Refs thereinAlaska

Lay and Young (1991) Alaska SScSMatzel et al (1996) Alaska SScSSdiffGarnero and Lay (1997) Alaska SScSSdiffWysession et al (1998) Alaska SdiffFouch et al (2001) Alaska SSdiff

E Ritsema (2000) Indian Ocean SF Thomas and Kendall (2002) Siberia SScSSdiffI Usui et al (2008) Antarctic Ocean S1 Kendall and Silver (1998) NW Pacific SScSSdiff3 Vinnik et al (1995 1998b) north central Pacific Sdiff6 Wookey et al (2005b) N Pacific ScS8 Long (2009) East Pacific SKS-SKKS9 Niu and Perez (2004) N America Asia SKSSKKS11 Vanacore and Niu (2011) Caribbean SKS-SKKS12 He and Long (2011) NW Pacific PcSScS SKS

SKKS13 Wookey and Kendall (2008) Caribbean ScS18 Thomas et al (2007) W Pacific ScS20 Fouch et al (2001) North central Pacific SSdiffSV lt SH4 Pulliam and Sen (1998) Central Pacific SC Ritsema et al (1998) Central Pacific SSdiff22 Kawai and Geller (2010) Central Pacific SScSSKSTiltedazimuthallaterally varying5 Russell et al (1998 1999) North Central Pacific ScS7 Ford et al (2006) South Pacific SSdiffA Garnero et al (2004a) Caribbean SScSSdiffA Maupin et al (2005) Caribbean SScSSdiffA Rokosky et al (2004 2006) Caribbean ScSG Wookey et al (2005a) North West Pacific ScS23 Restivo and Helffrich

(2006)North America SKS SKKS

21 Wang and Wen (2007) EastSouth Africa SKSSKKS10 Nowacki et al (2010) Caribbeanwest US ScS14 Lynner and Long (2012) Central Africa SKS-SKKS15 Cottaar and Romanowicz

(2013)South edge of AfricanLLSVP

Sdiff

16 Lynner and Long (2014) EastSouth Africa SKS-SKKS19 Long and Lynner (2015) Near Perm Anomaly SKS-SKKS17 Ford et al (2015) East Africa SKS-SKKSIsotropic or weak anisotropy2 Kendall and Silver (1996) South Pacific SScSSdiffH Garnero et al (2004b) Atlantic SSdiff9 Niu and Perez (2004) South Africa Antarctica

Southeast PacificSKSSKKS

21 Wang and Wen (2007) Eastern Atlantic SKSSKKS

62 B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90

upper mantle anisotropy sampled along the path of deep mantleseismic waves For example Vinnik et al (1998a) proposed a refer-ence event method to correct Sdiff waveforms for unknown uppermantle anisotropy using SKS and SKKS waveforms In the pasttwo decades characterization of upper mantle anisotropy fromSKS splitting data has progressed significantly (see review byLong and Silver 2009) making it possible to apply relatively robustcorrections in 00known00 upper mantle models both on the sourceand receiver sides and thus augment the number of D00 locationsthat can be sampled

Another approach to minimize effects of upper mantle aniso-tropy has been the use of differential measurements on pairs ofphases One such suitable pair is S and ScS which have similarpaths in the upper mantle on the source and station side but at

appropriate distances only ScS samples D00 (Fig 2) while S samplesa portion of the lower mantle which is assumed to be isotropic (egWookey et al 2005a Nowacki et al 2010) Similarly while SKSand SKKS splitting is most strongly acquired during propagationin the upper mantle the paths of SKS and SKKS waves diverge sig-nificantly in the lowermost mantle so that differential splitting ofthese two phases can sometimes be attributed to anisotropy in thedeep mantle (eg Hall et al 2004 Niu and Perez 2004 Restivo andHelffrich 2006 Wang and Wen 2007) Such an approach has beenapplied to several regions of the world (eg Long 2009 He andLong 2011 Vanacore and Niu 2011 Lynner and Long 20122014 Long and Lynner 2015 Ford et al 2015) Results consis-tently show strong and complex anisotropy on the borders of theLLSVPrsquos and interestingly also in the vicinity of the Perm Anomaly(Long and Lynner 2015) a low velocity anomaly seen at the base ofthe mantle in all tomographic models in the vicinity of the town ofPerm (Russia) and of smaller lateral extent ( 900 km) but corre-sponds to a similar reduction in shear velocity as found in theLLSVPs (eg Lekic et al 2012 Fig 3)

23 Results from array studies

Earlier observations and forward modeling studies of D00 aniso-tropy mostly relied on data from isolated stations which made itdifficult to constrain the geometry of anisotropy for lack of sam-pling of the target regions by waves propagating in different direc-tions (eg Maupin 1994) Thus most studies only reported thedifferences in SH and SV propagation times leading to models ofapparent VTI Yet evidence for azimuthal anisotropy has been sug-gested either from waveform complexity (eg Garnero et al2004a Maupin et al 2005) or when the geometry permitted frommeasurements of splitting on paths sampling the target region inat least two directions (eg Wookey and Kendall 2008) With theadvent of denser broadband arrays more detailed studies haveemerged in recent years aiming at the very least to distinguishVTI from radial anisotropy with tilted axis of symmetry (TTI) withimplications for the interpretation of observations in terms ofintrinsic or extrinsic anisotropy (eg Long et al 2006)

Regions of the world where this has been possible so far arecentral America exploiting ScS S data from the dense USArray(Nowacki et al 2010) and the northwest Pacific (He and Long2011) using ScS data from F-net in Japan Studies of Sdiff at thesouthern border of the African LLSVP based on data from the Kaap-val array show lateral variations in anisotropy (To et al 2005Cottaar and Romanowicz 2013) with strong anisotropy in the fastvelocity region outside the LLSVP increasing towards its borderand apparently disappearing inside it Although caution must betaken when interpreting apparent splitting in Sdiff due to isotropicheterogeneity potentially affecting SVdiff in a significant way(Komatitsch et al 2010) the strong elliptical shape of the particlemotion outside of the African LLSVP (Fig 4 and To et al 2005)where isotropic velocities are relatively fast contrasting with thelinear particle motion for paths travelling inside the LLSVP cannotbe accounted for by isotropic heterogeneity This was demon-strated in the follow-up study of Cottaar and Romanowicz(2013) in which the waveforms of Fig 4 and others were modelledusing the spectral element method a numerical method for 3Dseismic wavefield computations which can take effects of 3D iso-tropic heterogeneity into account accurately Differential splittingin S and ScS has also been exploited in the north Pacific (Wookeyet al 2005a) and in east Africa (Ford et al 2015) where remark-ably several azimuths can be sampled

The recent studies have confirmed earlier results with in gen-eral Vshgt Vsv in the ring of faster than average velocities sur-rounding the two LLSVPs and absence of significant splitting orVshltVsv found primarily within the LLSVPs (Fig 3 Table 1)

Fig 4 Example of change of character of particle motion for paths sampling theborder of the African LLSVP (a) Map showing the paths sampled plotted on top of abackground shear wave tomographic model (SAW24B16 Meacutegnin and Romanowicz2000) The portion of path sampling the D00 region is highlighted in yellow (b) and(c) shows particle motions of Sdiff at distances of 120o and at two azimuths In (b)the path in D00 is outside of the LLSVP and in (c) the path in D00 is inside the LLSVP(from To et al 2005) The color indicates the time with respect to predicted Sdiffarrival from PREM Black 35 to 5 s Blue 5 to 20 s Green 20 to 45 s Red 45 to70 s The elliptical particle motion in (B) contrasts with the linear particle motion in(c) This cannot simply be explained by lateral heterogeneity in isotropic velocity asone would expect larger amplitudes in SV for waves propagating inside the lowvelocity LLSVP This interpretation was later confirmed by 3D numerical waveformmodelling (Cottaar and Romanowicz 2013) (For interpretation of the references tocolor in this figure legend the reader is referred to the web version of this article)

B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90 63

The recent results indicate variability of anisotropy at relativelyshort scales with evidence for azimuthal anisotropy with differentorientations of fast velocity axes at least in regions of faster thanaverage isotropic shear velocity Interestingly the studies ofCottaar and Romanowicz (2013) Lynner and Long (2014) andFord et al (2015) consistently show changes in anisotropy acrossthe border of the African LLSVP with stronger anisotropy outsideof it practically disappearing inside it (eg Fig 5) Interestinglythe same trend although less sharply defined because of the chal-lenging geometry is likely present at the northern edge of the Paci-fic LLSVP (Fig 6) Indeed all studies of the latter region considerpaths from Fiji-Tonga sources to stations in north America Differ-ent results are found for different distance ranges with VsvgtVshfor the shorter distances sampling inside the LLSVP (as well asabove D00) and VshgtVsv at longer distances (Sdiff) which samplea significant portion of the fast Vs region outside of the LLSVPVinnik et al (1995 1998b) used Sdiff data and found VSHgtVSV theportion of the corresponding paths inside the LLSVP was smalland Vinnik et al (1998b) showed that splitting only occurred fordistances larger than 102o when paths sampled more of the fastregion outside of the LLSVP Likewise Fouch et al (2001) andRitsema et al (1998) used S Sdiff and found VshgtVsv for larger dis-tance paths while VsvgtVsh for shorter distance paths that samplewithin the LLSVP and above D00 as did Kawai and Geller (2010)Pulliam and Sen (1998) and Russell et al (1998) used S and ScSrespectively at shorter distances sampling inside the LLSVP andfound VsvgtVsh

All these results point in the same direction evidence for signif-icant anisotropy with generally VshgtVsv within the ring of fastvelocities surrounding the Pacific and African LLSVP possiblyincreasing and tilting at their borders but vanishing or changingsign (VsvgtVsh) inside the LLSVPrsquos

24 Results from global anisotropic tomography

Gaining improved understanding of the distribution and natureof seismic anisotropy at the base of the mantle requires better glo-bal sampling with accurate corrections for upper mantle aniso-tropy One possible approach is to construct global whole mantletomographic models of anisotropy Such an approach is attractivebecause a variety of seismic waveforms can be included in partic-ular fundamental and overtone surface waves which provide con-straints on the strong anisotropy in the uppermost mantle (egDebayle and Ricard 2013) Combining surface wave data with var-ious body waveforms that illuminate the entire mantle should ulti-mately allow improved resolution and characterization of deepmantle anisotropy So far this has proven very challenging forthe deep mantle

Indeed most successful has been the tomographic characteriza-tion of shear wave azimuthal anisotropy in the uppermost 200 kmof the mantle at the global scale using Rayleigh wave dispersiondata (eg Tanimoto and Anderson 1984 Montagner andTanimoto 1990 1991 Fig 1) More recent models developed bydifferent groups show broadly consistent trends (eg Trampertand Woodhouse 2003 Ekstroumlm 2011 Debayle and Ricard 2013Yuan and Beghein 2013) On the other hand the robustness of glo-bal scale transition zone azimuthal anisotropy models that utilizesurface wave overtone information (eg Trampert and van Heijst2002 Yuan and Beghein 2013) is still debated This is becausethe anisotropic signal in overtone surface waves is weak the azi-muthal sampling far from ideal and the number of parametersneeded to invert for azimuthal anisotropy at the global scale evenwhen considering only the dominant terms in 2-w (where w is theazimuth) is very large likely resulting in trade-offs with isotropicstructure It is not possible at present to extend this type of studyto the deep mantle as the sensitivity of available long period over-tone data becomes too weak and azimuthal coverage for bodywaves provided by the current geometry of sources and stationsis not sufficient

Thus tomographic imaging of anisotropy in the whole mantlecan at present only hope to resolve the simplest form of aniso-tropy that does not have as strong requirements on azimuthal cov-erage which is VTI (or apparent VTI) Such studies are based onrelatively long period waveforms mostly sensitive to shear veloc-ity combining fundamental mode surface waves surface waveovertones and shear body waves and aim at solving for the distri-bution of only two anisotropic parameters Vsh and Vsv or alter-natively isotropic velocity Vsiso and the anisotropic parameter n =(VshVsv)2 (Panning and Romanowicz 2004 2006 Panning et al2010 Kustowski et al 2008 French and Romanowicz 2014Moulik and Ekstroumlm 2014 Auer et al 2014 Chang et al 20142015) The other three anisotropic parameters that are necessaryto fully describe a VTI medium are scaled to Vsiso and n using scal-ing relations that are appropriate for the upper mantle (egMontagner and Anderson 1989) but may be questionable for thelower mantle However this may not be a significant issue giventhe dominant sensitivity of the waveforms considered to shearvelocities While the resulting models show qualitative agreementat long wavelengths details vary frommodel to model significantlyenough not to be trustworthy for quantitative interpretations

These models do agree on the following observations on aver-age radial anisotropy is strongest in the uppermost mantle andmost of the lower mantle exhibits little radial anisotropy (Fig 7)

Fig 5 a and b Whole mantle depth cross sections through the isotropic Vs part of model SEMUCB_WM1 (French and Romanowicz 2014) at the southern (a) and eastern (b)edge of the African LLSVP where rapid variations in the direction and strength of anisotropy have been reported decreasing from outside (blue) to inside (pink) the LLSVP inc) the map view is from Lynner and Long (2014) with background shear velocity model GyPSuM of Simmons et al (2012) The cross-section location is indicated on the mapby a straight line c and d corresponding cartoons proposed by the authors respectively (c) Cottaar and Romanowicz (2013) (d) Ford and Long (2015)

64 B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90

Inmostmodels there is an indication of an increase in anisotropy inD00 with Vshgt Vsv (n slightly larger than 1) although there is vari-ability among models due to a combination of parametrizationtypes of seismic waves considered and theoretical assumptions

Common 3D features of these models in D00 are a predominanceof Vsh gt Vsv outside of the LLSVPs with patches of Vsh lt Vsv con-fined within the LLSVPs in agreement with local studies (Fig 8)However the current models do not show consistency in theamplitude of the lateral variations in n nor the wavelengths ofthese variations This is partly due to the parametrization chosenFor example Panning and Romanowicz (2004 2006) and Aueret al (2014) allowed relatively short wavelength lateral variationsin n while Moulik and Ekstroumlm (2014) and French andRomanowicz (2014) chose to assign shorter wavelength lateralvariations to isotropic Vs while constraining the anisotropic partof the model to be smooth Theoretical assumptions on wave prop-agation are also important ray theory is not valid for modelling ofSdiff nor is it valid to use the surface wave approximation for mod-elling this phase as shown by Li and Romanowicz (1995) So faronly the Berkeley models are constructed taking into account finitefrequency effects rather than ray theory for body waves (Panningand Romanowicz 2004 2006 French and Romanowicz 2014)

One fundamental issue is that Sdiff and ScSn data (with ngt1) arenecessary to obtain good coverage of D00 at the global scale As dis-cussed previously SVdiff decays rapidly with distance in modelssuch as the reference model PREM (Dziewonski and Anderson1981) where the velocity in D00 is relatively fast The global datasetsare thus necessarily biased although to various degrees depending

on the particular dataset by the predominance of SHdiff introduc-ing trade-offs between isotropic and anisotropic structure (egKustowski et al 2008 Chang et al 2015) and making it only pos-sible to resolve the very longest wavelengths of VTI in D00 withpoor constraints on their amplitude

In summary robustly mapping even the simplest component ofseismic anisotropy apparent VTI at the base of the mantle at highresolution using a tomographic approach is still a challenging openquestion let alone constraining azimuthal anisotropy at the globalscale Still available global models agree with local studies aboutthe prevalence of VshgtVsv in regions of faster than average velocityin D00

As for P wave anisotropy in the deep mantle only few studieshave tried to constrain it so far Several studies have attemptedto retrieve the global average variation with depth of the radiallyanisotropic parameter g = (VphVpv)2 using normal mode data(Montagner and Kennett 1996 Beghein et al 2006) finding someindication that the anisotropy in gmay be anticorrelated with thatof n in the D00 region with however strong trade-offs with density(to which normal mode data are also sensitive) Note that the anti-correlation of isotropic P and S velocities at long wavelengths inthe deep mantle is in contrast better established (eg Su andDziewonski 1997 Kennett and Widyantoro 1998 Masters et al2000 Ishii and Tromp 1999 Romanowicz and Breacuteger 2000) Thepossibility of P wave anisotropy in the deep mantle using P wavedata (mantle and core phases) has been investigated by Boschiand Dziewonski (2000) concluding that anisotropy may be smallwith significant trade-offs with core-mantle boundary topography

Fig 6 Zoom on the northern edge of the Pacific LLSVP The background tomographic model is the isotropic Vs part of model SEMUCB_WM1 (French and Romanowicz 2014)(A) Map view with locations of studies of D00 shear wave splitting suggesting a change of character of anisotropy across the boundary of the LLSVP Green dots indicate thelocation of major hotspots Black line with white and purple dots is the great circle path corresponding to the depth cross section shown in (B) displaying the Hawaian plumeand transition from low to fast velocities in D00 Kawai and Geller (2010) Pulliam and Sen (1998) and Russell et al (1998) find VSV gt VSH while Ritsema et al (1998) Fouch et al(2001) and Vinnik et al (1998) find that Vsh gt Vsv increasingly so for paths sampling the fast region outside of the LLSVP Note that the color saturation of the tomographicmodel is different in (A) and (B)

B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90 65

and outer core structure The possible anticorrelation of P and Sradial anisotropy in the D00 must therefore be considered with cau-tion at the present time when used as a constraint in modeling

Given these difficulties a currently explored possible avenue isto try and combine constraints not only from seismology but alsofrom mineral physics and geodynamics Each of these approachestaken individually involves many assumptions and uncertaintiesbut by combining them the hope is that the space of acceptablemodels for anisotropy and its causes can be further reduced Theidea is to start with the strain field inferred from a mantle circula-tion model compute the corresponding texture development andpredicted seismic anisotropy using available information on crystalplasticity and elasticity for different lower mantle minerals andcompare these predictions with seismic observations This shouldprovide constraints on the mineral physics assumptions as wellas the deep mantle dynamics or at least allow us to rule out someclasses of models Note that in this approach the fundamentalassumption is that anisotropy is due to CPO development resultingfrom large-scale mantle flow

Before describing these efforts in more detail we will reviewcurrent knowledge and capabilities in mineral physics and describehow seismology and mineral physics can be linked through geody-namics modeling

3 Mineral physics perspective on the deep mantle

31 Dominant mineral phases in the lower mantle

Ringwood (1962) speculated about the composition of thelower mantle suggesting that olivine Mg2SiO4 would first breakdown to spinel Mg2SiO4 and then to MgSiO3 with a lsquolsquocorundum-

likerdquo structure and periclase (MgO) Liu (1974) synthesized thisstructure at high temperature and pressure and identified it asMgSiO3 perovskite (which has recently been named bridgmaniteTschauner et al 2014) At high pressure bridgmanite transformsto post-perovskite pPv (eg Murakami et al 2004 Oganov andOno 2004 Tateno et al 2009 Fig 9a) and this may be the mostimportant phase near the core-mantle boundary particularly alonga cold geotherm within subducting slabs (Fig 9b) Thus it appearsthat cubic periclase (Fig 10a) orthorhombic bridgmanite (Fig 10b)and orthorhombic post-perovskite (Fig 10c) are the dominantminerals in the lower mantle Periclase has the same highly sym-metric structure as halite (NaCl) with close-packed MgOVI octahe-dral coordination polyhedra Bridgmanite (spacegroup Pbnm) is adistorted cubic perovskite structure with SiOVI coordination octa-hedra linked over corners and Mg2+ in large interstices Post-perovskite (spacegroup Cmcm) has layers of SiOVI octahedra alter-nating with layers of Mg The layers are parallel to (010) It isisostructural with CaIrO3 (eg Hunt et al 2009) While the pseu-docubic perovskite structure is elastically fairly isotropic the lay-ered post-perovskite structure is highly anisotropic As we willsee post-perovskite is of critical importance for anisotropy in thelower mantle In the following discussion we will use mostly theabbreviation pPv

Most lower mantle minerals (gt660 km) cannot be studied atsurface conditions Even if lower mantle material has reached thesurface by upwelling minerals have undergone phase transitionsThus information about phase diagrams is based on in situ observa-tions in high pressure experiments and ab initio calculations

Irifune and Tsuchiya (2015) have reviewed the mineralogicalcomposition of the lower mantle Different bulk compositions ofthe lower mantle have been proposed Ringwood (1962 1975) sug-gested a peridotitic-lsquolsquopyroliticrdquo composition (Fig 11a) Subducting

Fig 7 Comparison of depth profiles throughout the mantle of global average radialanisotropy parameter n = (VshVsv)2 in 6 recent global shear velocity models n = 1corresponds to isotropy Model S362ANI (Kustowski et al 2008) is isotropic in thelower mantle While there are differences between models all of them agree thatradial anisotropy is strongest in the first 200 km of the mantle and very weak inmost of the lower mantle In D00 on average Vsh is equal of slightly faster than Vsv

66 B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90

slabs may correspond to more siliceous aluminous and Ca-richmid-ocean ridge basalts (MORB eg Irifune and Ringwood 1993Fig 11b) In both cases MgSiO3-perovskite (bridgmanite) domi-nates in large volumes of the lower mantle but for MORB compo-sitions high pressure silica and alumina phases are alsosignificant and there may be no ferropericlase Calcium perovskite(CaSiO3) is cubic (spacegroup Pm3 m) at lower mantle conditions(eg Wang et al 1996 Kawai and Tscuchiya 2015) and is animportant component at depths beyond 750 km It distorts to atetragonal structure at low temperature and high pressure (egShim et al 2002)

As more details about the lower mantle are revealed composi-tional heterogeneities become apparent (eg Badro et al 2003 LiY et al 2014) Higher concentrations of Si Al and Fe add consider-able complexity The diverse composition is in part the result ofsubduction of slabs composed of crust and upper mantle Silica(SiO2) may exist as stishovite with a rutile structure and 6-foldcoordination or at higher pressure as a cubic phase with CaCl2structure and 8-fold coordination (eg Kingma et al 1995) andat even higher pressure as an orthorhombic (Pbcn) a-PbO2 struc-ture (seifertite) (eg Dubrovinsky et al 2004 Grocholski et al2013 Zhang et al 2016) According to first principles calculationsat extreme pressure SiO2 may transform to a pyrite structure(Kuwayama et al 2005) Al2O3 in the form of trigonal corundumor orthorhombic Rh2O3(II) may be present and Fe may exist asnative iron (eg Frost et al 2004 Shi et al 2013)

Of considerable importance is the oxidation state as well as thespin state of iron that have received a lot of attention (egMcCammon 1997 Badro et al 2003 Li et al 2004 Tsuchiya

et al 2006 Fei et al 2007 Lin et al 2008 Catalli et al 2010Saha et al 2011 2012 Vilella et al 2015) With increasing pres-sure there is a transition from a high spin to a low spin configura-tion It may be responsible for the anomalous viscosity structure inthe central part of the lower mantle (900ndash1200 km eg Rudolphet al 2015) although the spin transition is generally thought tooccur deeper (1500 km)

In addition hydrogen may play a significant role (eg Ohtamiand Sakai 2008) A hydrous aluminosilicate is stable at lower man-tle conditions (eg Tsuchiya and Tsuchiya 2008 2011 Pamatoet al 2014) and dehydration may cause melting at the top of thelower mantle (Schmandt et al 2014)

As far as elastic properties and anisotropy are concerned oneshould keep in mind that the major phases over large volumes ofthe lower mantle are bridgmanite ferropericlase pPv and CaSiO3

perovskite These contribute largely to the bulk elastic propertiesbut there may be local deviations

32 Some comments on plasticity models and representation ofanisotropy

What are the sources of seismic anisotropy in the Earth Veryimportant is the alignment of anisotropic crystals called crystalpreferred orientation (CPO) or texture (based on DrsquoHalloy 1833)and universally used in materials science The crystal anisotropyis linked to the crystal structure A second aspect is crystal shapethat produces a shape-preferred orientation (SPO) CPO and SPOare sometimes linked (in mica for example the crystal plane(001) is parallel to the platelet) Often it is not (eg in quartz orin periclase) Also significant is the orientation of flat fracturesand fractures filled with kerogen This is a very important contribu-tion to anisotropy in shales (eg Hornby et al 1994 Sayers 1994Vasin et al 2013) but insignificant in the lower mantle In thelower mantle there is the possibility of partial melt particularlynear the core-mantle boundary (eg Williams and Garnero 1996Lay et al 2004 Shi et al 2013) but this would only give rise to ani-sotropy if melt occurred in parallel thin layers (eg Backus 1962)We will focus here on the development of CPO

Before going into plasticity in the mantle a few words aboutdeformation mechanisms of polycrystalline aggregates are inorder Deformation experiments on minerals have a long historyPfaff (1859) documented mechanical twinning in calcite when astress is applied In the early twentieth century deformation exper-iments at a wide range of temperature and strain conditions wereconducted on metals to explore the deformation behavior (egSchmid 1924) and in this context linear defects called dislocationswere discovered (Polanyi 1934 Taylor 1934) Without disloca-tions it would be very difficult to deform crystals and indeed theyare present in most crystalline materials

Dislocations form in the crystal lattice when a stress is appliedEdge dislocations propagate on a glide plane (hkl) and in a slipdirection [uvw] defined by rational indices relative to crystallo-graphic axes Propagation of dislocations causes crystals to rotaterelative to the applied stress which is conceptually illustrated foran experimentally compressed single crystal in Fig 12 By move-ment of dislocations on glide planes the rectangular crystal attainsa new shape (parallelogram) Since pistons must stay in contactthis results in an effective rotation of b In a polycrystalline aggre-gate neighboring grains play the function of pistons

Based on deformation experiments on metals deformationmechanism maps were established (eg Ashby 1972 Langdonand Mohamed 1978 Frost and Ashby 1982) They define condi-tions such as temperature pressure stress magnitudes strain rateand grain size under which mechanisms such as dislocation glidedislocation climb grain boundary migration and grain boundarysliding are active (Fig 13) Identifying mechanisms is important

Fig 8 Comparison of 6 recent models of lateral variations in the radial anisotropy parameter n = (VshVsv)2 plotted in terms of dlnn referred to isotropy While the modelsdisagree in detail common features are Vsh gt Vsv (blue) in the circum Pacific ring (roughly in agreement with local studies) and pronounced Vsv gt Vsh (orange) in the Fiji-TongaIndonesia region and under southernmost Africa (except SAVANI) Models plotted are (a) SAW642ANb (Panning et al 2010) (b) SAW642AN (Panning andRomanowicz 2006) (c) SAVANI (Auer et al 2014) (d) SGLOBE-rani (Chang et al 2015) (e) S362WANI + M (Moulik and Ekstroumlm 2014) (f) SEMUCB_WM1 (French andRomanowicz 2014)

Fig 9 (a) Experimentally determined PT phase diagram for perovskitebridgmanite (Pv)-post-perovskite (Murakami et al 2004) (b) T-Depth phase diagram plotting the pv-ppv phase boundary and cold and warm geotherms (after Hernlund et al 2005)

B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90 67

because some produce crystal rotations and thus crystallographicpreferred orientation (notably dislocation glide and ndash to someextent ndash dynamic recrystallization) while others generate random

orientations (such as grain boundary sliding in fine-grained mate-rials and dislocation climb) We will return to these issues inSection 48

Fig 10 Crystal structures of (a) periclase (b) bridgmanite and (c) post-perovskite the latter two with octahedrally coordinated silicon

Fig 11 Lower mantle composition for different models (a) pyrolite (b) MORB(from Irifune and Tsuchiya 2015) Pv perovskitebridgmanite Ppv post-perovskiteMw magnesiowuestiteferropericlase Mj majorite Rw ringwoodite SiO2 Ststishovite CC CaCl2 phase AP a-PbO2 phase Al2O Hex CF calcium-ferrite phaseCT calcium-titanate phase

68 B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90

In a polycrystalline aggregate stresses are transmitted acrossgrain boundaries causing heterogeneities even within grains Thisis most realistically approached with finite element methods (egMika and Dawson 1999) but these are still extremely demandingand rarely applied Simpler models have been used in materialsscience for a long time The Taylor (1938) theory developed bythe same Taylor who discovered dislocations (1934) assumeshomogeneous strain All grains undergo the same shape changeirrespective of orientation This leaves grain boundaries intact(Fig 14 left side) The Taylor model is very applicable to cubic met-als with many symmetrically related slip systems Slip on 111h

1 1 0i in fcc metals or cubic periclase has 12 equivalent systemsAnother model (Sachs 1928) assumes stress equilibrium and morefavorably oriented grains deform more than others In the modelthis causes overlaps and gaps at grain boundaries In principle thiswould be more adequate for low symmetry minerals (such asorthorhombic) but of course overlaps and gaps do not exist A com-promise between homogeneous strain and stress equilibrium is aself-consistent model that treats grains as ellipsoidal inclusionsdeforming in an anisotropic viscous medium (Fig 14 centerMolinari et al 1987) It is most widely applied in the Los Alamoscode VPSC (Lebensohn and Tomeacute 1993) and it can be used bothto understand preferred orientation in high pressure experimentsand to predict anisotropy in geodynamic models In the viscoplas-tic self-consistent model grains deform without knowledge of theirneighborhood In a finite element model (Fig 14 right) grains areconstrained by the orientation of neighbors In this sketch it isassumed that each grain has a single orientation In more sophisti-cated FEM models there are strain and orientation gradients devel-oping within grains (eg Mika and Dawson 1999)

When crystals are deformed in a polycrystalline medium theyundergo systematic rotations (Fig 12) and the material attains ananisotropic pattern We need to describe the orientation of a crys-tal relative to the macroscopic sample This is efficiently done byrelating two orthogonal coordinate systems (sample x y z crystal[100] [010] [001]) by three rotations Most frequently the so-called Euler angles are used U is the distance from z to [001]1 is the azimuth of [001] from y (around z) 2 is the azimuthof [100] around [001] (Fig 15) The 3-dimensional crystal orienta-tion distribution (COD) is conventionally described by a continuousorientation distribution function (ODF) The ODF is required to cal-culate anisotropic elastic properties of an aggregate from crystalorientations

For graphical representations of orientation patterns generally2-dimensional spherical projections of the ODF are used Depend-ing on the application one can either use the macroscopic sample xy z as reference and plot crystal directions (pole figures) or use thecrystal as reference and plot sample directions (inverse pole fig-ures) Inverse pole figures are useful if only a single sample direc-tion is of interest eg the compression direction in a compressionexperiment The symmetry of pole figures reflects the symmetry ofthe deformation path In compression experiments pole figures areaxially symmetric The density of poles on the sphere is contouredand then expressed as continuous pole densities usually normal-ized relative to a random distribution and defined as multiples ofa random distribution (mrd) 2ndash5 mrd are moderate CODs20ndash50 mrd very strong CODs The strongest crystal alignmentsin rocks that have been observed are muscovite in slates exceeding100 mrd Fig 16a is a 111 pole figure of rolled copper with roll-

Fig 12 Under stress imposed by pistons a crystal deforms to a new shape by slip of dislocations on a glide plane Since pistons remain in contact with the crystal surfacethere is an effective rotation b In a polycrystal neighboring grains act as effective pistons to transmit the stress

Fig 13 Stress-temperature deformation mechanism map (Langdon and Mohamed1978)

B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90 69

ing R transverse T and normal N sample directions indicatedFig 16b is the corresponding inverse pole figure of the normaldirection Inverse pole figures display the crystal symmetry Bothrepresentations will be used in the following discussion

33 Deformation experiments and rheology

The experiments on plasticity of metals were not applicable tomost minerals because even at elevated temperatures theirdeformation behavior at ambient pressure is generally brittleOne had to wait until high pressure deformation experiments weredeveloped by Griggs (1936) and applied on a wide scale includingolivine (eg Raleigh 1968) Since then sophisticated deformationapparati have been constructed in many laboratories making itpossible to deform rocks at a wide range of pressures and temper-atures They were applied to many minerals and rocks in the crustand upper mantle Studies on olivine (eg Jung and Karato 2001

Hansen et al 2012 Jackson and Faul 2010) documented the com-plex influence of temperature pressure composition (such aswater and iron content) The most sophisticated apparatus wasdeveloped at the Australian National University (Paterson andOlgaard 2000) It allows for deformation experiments on relativelylarge samples (1 cm) in compression tension and torsion Pres-sures are limited to 03 GPa and the limitation in pressure pre-vents these instruments to be used for experiments relevant tothe lower mantle (20ndash150 GPa) and inner core (320ndash360 GPa)

Higher pressure deformation experiments have been reviewedby Weidner and Li (2015) The multi-anvil apparatus called DIAwith three pairs of octahedral pistons (Onodera 1987) has beenmodified to apply stress by preferentially advancing one pistonpair (D-DIA for deformation DIA) The sample can be heated inter-nally Changes in phase structure preferred orientation andmicrostructure can be recorded in situ if the D-DIA apparatus iscombined with a monochromatic synchrotron X-ray beam fordiffraction and imaging (eg Wang et al 2003 2011) The conven-tional D-DIA apparatus has been used to 20 GPa and samples arecylinders 1 mm in diameter (eg Kawazoe et al 2010) A moreadvanced D-DIA (Kawai-type) reaching gt110 GPa with sintereddiamond anvils and smaller samples has been introduced atSPring8 in Japan (Yamazaki et al 2014)

Shear deformation at high pressure can be performed with arotational Drickamer apparatus (RDA) (eg Yamasaki and Karato2001) Shear deformation of a bridgmanite-ferropericlase aggre-gate at 25 GPa and 2100 K has been achieved to large strains(Girard et al 2016) In such torsion experiments the strain variesgreatly as a function of sample radius The experiment documentedthat most of the plastic deformation is accommodated by theweaker ferropericlase

Currently the most accessible method to deform samples atultrahigh pressures (gt500 GPa) is with diamond anvil cells (DAC)where diamonds are used as pistons compressing a small sample(30ndash80 lm in diameter and 50 lm thick) (eg Merkel et al2002 Fig 17) The diamonds are used not only to induce pressurebut also to cause compressive deformation (Fig 17 b c) and theevolution of preferred orientation can be observed in situ if hori-zontal X-rays transmit the sample in radial diffraction geometry(r-DAC) Strong textures have been observed in ferropericlase(eg Merkel et al 2002 Lin et al 2009) perovskitebridgmanite(eg Merkel et al 2003 Wenk et al 2006 Miyagi and Wenk2016 Tsujino et al 2016) and pPv the phase likely to be presentat the core-mantle boundary (eg Merkel et al 2006 2007

Fig 14 2D Sketches of polycrystal plasticity models Gray shades express orien-tation (Left) For the full constraints Taylor model all grains undergo the samedeformation regardless of orientation (Center) The viscoplastic model VPSC treatsgrains as inclusions in an anisotropic viscous medium (Right) In finite elementmodels grains deform differently depending on the orientation of neighbors

Fig 15 Definition of crystal orientation relative to sample coordinates with threerotations (Euler angles) 1 U 2 Projection based on sample coordinate system xy z (pole figure) Crystal coordinate system is defined by axes [100] [010] and[001]

Fig 16 Comparison of (a) 111 pole figure relative to sample coordinates and (b) Ninverse pole figure relative to crystal coordinates for rolled copper Equal areaprojection red colors are high and blue colors are low pole densities N normaldirection R rolling direction and T transverse direction Note the equivalentinformation In the 111 pole figure a maximum in the N direction and in the NDinverse pole figure a maximum in 111

70 B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90

Miyagi et al 2010 2011 Wu et al 2017) Shear deformation canbe induced in rotational DACs (eg Levitas et al 2006) Thismethod has been mainly used to induce phase transformationsand has not yet been applied to study texture evolution at highpressure

In addition to pressure and stress temperature can be inducedin DAC experiments by resistive (eg Liermann et al 2009) andlaser heating (eg Prakapenka et al 2008 Dubrovinsky et al2009) or a combination of the two (Miyagi et al 2013) Tatenoet al (2015) reached temperatures of 6000 K at gt400 GPa on exper-iments on Fe and Fe-Si corresponding to conditions of the Earthrsquos

inner core Obviously there are limitations to DAC experimentssamples are extremely small strain is always compressive andstrain rates are difficult to control

It was surprising to see that silicates and oxides that are brittleat ambient conditions including olivine become ductile at pres-sures of 10GPa even at room temperature and deform by dislo-cation glide (eg Wenk et al 2004) The diffraction image ofMgSiO3 post-perovskite at 150 GPa (Fig 18a) is lsquolsquounrolledrdquo andthe compression direction is indicated by arrows (large 2h smalld Q=1d) (Fig 18b) The elastic lattice distortion (wave-like patternwith azimuth) is related to applied stress and elastic propertiesThe intensity variations with azimuth are indicative of preferredorientation For example there is a strong maximum for 004(fourth order diffraction on the lattice plane 001) in the compres-sion direction This image illustrates why radial diffraction geome-try has to be used to display CPO as function of angle to thecompression direction In axial geometry (X-rays parallel to thediamond axis) Debye-rings have uniform intensity since alldiffracting lattice planes have the same angle to the compressiondirection

A qualitative interpretation of a diffraction image is illustratedin Fig 19 for an experiment with MgGeO3 post-perovskite(Miyagi et al 2011) and used to construct an inverse pole figureof the compression direction (arrow) MgGeO3 is an analog ofMgSiO3 but transforms to pPv at lower pressure There is a maxi-mum for 002 and a minimum for 020 in the compression directionwhich can be plotted in the inverse pole figure (Fig 19 right side)The quantitative deconvolution of diffraction images is not trivialand most often an iterative Rietveld method is applied (egLutterotti et al 2014 Wenk et al 2014) The high pressure syn-chrotron X-ray diffraction deformation images provide quantita-tive information about phases crystal structures density stresselastic properties and preferred orientation

Fig 20a-c shows experimental inverse pole figures of MgSiO3

pPv documenting increasing texture development with pressure-stressndashstrain with a maximum at (001) From the orientation pat-tern active slip systems can be derived by comparing experimentalinverse pole figures with results from polycrystal plasticity calcu-lations that assume certain combinations of slip systems(Fig 20d) Based on the good agreement it can be concluded thatpPv deformed in the experiment by dominant (001)[100] slip(Miyagi et al 2010)

With similar experiments it was suggested that MgSiO3 bridg-manite deforms dominantly by slip on (001) planes in [100][010] and h1 1 0i directions (eg Miyagi and Wenk 2016) but sim-

Fig 18 (a) Diffraction image of MgSiO3 post-perovskite at 150 GPa (b) Unrolled diffractiochanges in Q are due to elastic distortion of the crystal lattice under compression Botquantitative information such as inverse pole figures

Fig 17 Diamond anvil cell for radial diffraction experiments The X-ray beam ishorizontal (a) illustrates the cell and the insert is an enlargement with diamondsand gasket to contain the sample (b c) illustrate that diamonds not only applypressure but also compressive stress that deforms the sample and produces CPO

B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90 71

ple shear experiments in a D-DIA apparatus indicate (100)[001]slip (Tsujino et al 2016) Ferropericlase likely deforms by 110h110i slip (eg Stretton et al 2001 Merkel et al 2002 Linet al 2009) at high pressure conditions For Ca-perovskite domi-nant 110h110i slip was proposed (Miyagi et al 2006 2009)

So far most DAC high-pressure deformation experimentsextracted COD information from intensity variations along Debyerings (eg Fig 18) A new method called multigrain is still underdevelopment It obtains orientation information from individualgrain diffractions (eg Barton and Bernier 2012 Rosa et al2015 Langrand et al 2017) and is especially applicable to coarseraggregates Nisr et al (2012) used information about dislocationsfrom distortion of single crystal diffraction patterns of the post-perovskite analog MgGeO3 and suggested dominant slip on 110and (001) planes

It should be mentioned that information from such high pres-sure experiments is by no means unambiguous Obviously defor-mation conditions in experiments and simulations differconsiderably from those in the deep Earth just to mention temper-ature grain size strain rate interaction of dislocations and interac-tion between grains Furthermore not all CPO patterns that areobserved are due to deformation but could be inherited from orien-tation patterns of precursor phases such as for pPv from perovskite(Dobson et al 2013) or enstatite (Merkel et al 2006 2007 Miyagiet al 2011) Also slip systems may not be the same for pPv phasesof different compositions such as MgGeO3 CaIrO3 NaMgF3 orMn2O3

A different approach has become very important computationof Peierlrsquos stresses and lattice friction for dislocation systems basedon bonding characteristics It was originally developed for metals(eg Kubin et al 1992 Devincre and Kubin 1997) and has morerecently been applied to minerals in the mantle where it allowsto predict slip system activities for a wide range of temperaturendashpressurendashstrain rate conditions (eg Carrez et al 2007Mainprice et al 2008 Cordier et al 2012) Amodeo et al (20122014 2016) propose a switch from 110h010i slip to 100h0 1 1i slip in periclase with pressure Kraych et al (2016) suggest(010)[100] slip in bridgmanite at high pressure According tothese calculations the strength of bridgmanite increases greatlywith pressure and at 60 GPa bridgmanite appears 20 times stron-ger than periclase The critical resolved shear stress decreasesabout 20 from strain rates of 105 s1 (which corresponds to

n image as function of Q (Q = 1d) Intensity variations with azimuth illustrate CPOtom experimental data above fit of the data with the Rietveld method to extract

Fig 19 Explanation of the relationship between DAC diffraction image and inverse pole figure Left Unrolled diffraction image of MgGeO3 post-perovskite Some diffractionlines are labeled The sinusoidal variations are due to imposed stress High stress (high Q low d) is indicated by arrows On the right side is a conceptual construction of theinverse pole figure of the compression axis based on relative diffraction intensities (Miyagi et al 2011)

Fig 20 Inverse pole figures for MgSiO3 post-perovskite (AndashC) experiments (D) Plasticity model with dominant (001) slip equal area projection (Miyagi et al 2010)

72 B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90

experimental values) to 1014 s1 corresponding to likely values atdeep mantle conditions (Fig 21a) The opposite is the case for pPvwhich appears much weaker than periclase at high pressure hightemperature and slow strain rates (Fig 21b Goryaeva et al 20152016) Also the predicted weakest calculated slip system for post-perovskite at deep mantle conditions is (010)[100] correspondingto the layered crystal structure (Fig 21c) but different from thatobserved in DAC experiments (Miyagi et al 2010 Wu et al 2017)

It should be mentioned that a single slip system is not sufficientto deform a polycrystal In the case of the Taylor model at least 5systems have to be active to produce an arbitrary strain (Mises1928) This is relaxed for the self-consistent model but also hereseveral slip systems are active The choice of activity depends onthe crystal orientation relative to the applied stress (Schmid fac-tor) TEM investigations confirm this though some slip systemsusually dominate and the literature refers to the lsquolsquodominantrdquo slipsystem Some dominant slip systems for deep Earth minerals aresummarized in Table 2

34 Elastic properties

Elastic properties of crystals at conditions pertaining to thelower mantle are critical to link microstructural properties of therock with seismic observations The most straightforward experi-mental method that has been applied to many lower mantle min-erals is Brillouin scattering (see review by Speziale et al 2014) andenergy-dispersive X-ray diffraction (eg for calcium silicate per-ovskite Shieh et al 2004) A different approach is with first prin-ciples calculations at high pressure and temperature (for someapplications to bridgmanite CaSiO3 perovskite and pPv see egZhang et al 2013 Wentzcovitch et al 2005 Kawai and

Tsuchiya 2015) First principles results look fairly consistent forminerals at lower mantle conditions but as we will see in Sec-tion 62 predictions for iron at inner core conditions are stillambiguous Furthermore the actual composition of the mineralsparticularly the iron content can be significant (eg Koci et al2007) Values of stiffness coefficients and P-wave anisotropy (An = 200(Pmax Pmin)(Pmax + Pmin) for some low mantle mineralsat lowermost mantle conditions are listed in Table 3 Fig 22 givescorresponding S velocities of single crystals with black lines corre-sponding to the orientation of the fast S-wave polarization As canbe seen in Table 1 periclase and pPv have the highest P-wave ani-sotropy and Ca-perovskite is least anisotropic The S-wave aniso-tropy is considerably higher for pPv and periclase than forbridgmanite and particularly CaSiO3 perovskite

To obtain elastic properties of aggregates one has to averageover all orientations and corresponding elastic tensors takingphase fractions into account Simple averages are upper bound(Voigt 1887) and lower bound (Reuss 1929) Generally an inter-mediate arithmetic mean (Hill 1952) or a geometric mean(Matthies and Humbert 1995) are preferred All these models donot take grain shape into account which is not very significantfor crystalline phases but becomes important for systems withplaty minerals such as graphite or sheet-silicate containing rocksand aggregates with flat oriented pores For such cases a self-consistent (Matthies 2012 Vasin et al 2013) or differential effec-tive medium approach (eg Hornby et al 1994) should be consid-ered It is probably not important for the lower mantle

Note that S-waves passing through anisotropic media have arbi-trary polarization directions in the plane perpendicular to thedirection of propagation as is best displayed for the fast directionof single crystals in Fig 22 but applies also to aggregations of ori-

Fig 21 Critical resolved shear stress CRSS for dislocation glide activities as functionof temperature of (a) bridgmanite at 60 GPa (from Kraych et al 2016) and MgO(from Amodeo et al 2016) at strain rates 105 s1 and 1014 s1 (b) post-perovskiteat 120 GPa at strain rate 1016 s1 (from Goryaeva et al 2016) compared with MgO(from Amodeo et al 2012) Courtesy of P Cordier

B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90 73

ented crystals Seismologists generally consider the projection ofthat polarization direction onto horizontal and vertical axes Thisis convenient because differences in arrival times and waveformsin this representation can be expressed in terms of apparent verti-cal transverse isotropy (VTI) which because of limited azimuthalsampling is often the only anisotropic constraint that can beobtained

4 Linking seismology and mineral physics through predictionsof anisotropy in geodynamic models

41 Isotropic geodynamic models for upper mantle convection

Ever since the concept of plate tectonics became accepted in the1960s convective movements in the Earthrsquos mantle have been pro-posed such as upwelling along oceanic ridges (eg Hess 1964Cann 1968 Fig 1b) The first quantitative models based on hydro-dynamics emerged in the eighties (eg Hager and OrsquoConnell 1981)

Table 2Proposed dominant slip systems in deep Earth minerals

Ferropericlase Lower P 110110High PT also 100011

Bridgmanite Low P (001)[100] [010] 110High P (100)[001](010)[100]

pPv (001)[100](010)[100]

Ca-perovskite 110110e-iron (0001)1120 subordinate 1010

Geodynamic models have been mainly applied to the upper mantleand we will not discuss them here in detail (see eg review by Longand Becker 2010)

Many convection models have been developed to understandthe evolution of the deep Earth Calculations generally assume aviscous fluid and use non-dimensional equations for the conserva-tion of mass momentum and energy applying the Boussineqapproximation Critical parameters are Rayleigh number viscosityboundary temperatures In order to evaluate the strain evolutionduring the convection process tracers are introduced that recordthe velocity gradient tensor at each time step along the path ofthe tracer If the deformation mechanisms are known (eg disloca-tion glide) polycrystal plasticity calculations can be used to calcu-late the evolution of crystal preferred orientation based on thestrain recorded by tracers

Most geodynamic models assume a viscous isotropic mediumwith a smoothly varying viscosity structure and the microstruc-tural processes leading to preferred orientation are introducedpost-mortem Considering an anisotropic medium that constantlychanges its properties greatly increases the complexity of geody-namic calculations However there are models in metallurgy suchas extrusion of an aggregate that illustrate the importance of ananisotropic material behavior (eg Beyerlein et al 2003)

42 Review of upper mantle anisotropic models

We will start the discussion of anisotropic convection byreturning to a simple 2D model (Dawson and Wenk 2000) thatwas originally issued as an educational video by AGU (1999) andcan now be downloaded in digital form (httpepsberkeleyedu~wenkTexturePageMantle-Videohtm) At high Rayleigh number(low viscosity) heat transfer occurs by convection rather than con-duction corresponding to conditions in the Earthrsquos mantle Convec-tion is driven by temperature gradients As aggregates move alongstreamlines the orientation of grains is constantly updated and thelocal texture affects the next deformation step which introducesconsiderable heterogeneities It was surprising to find locallyheterogeneous CPO patterns in the 2D convection cell representingthe upper mantle shown as [100] pole figures of olivine after100 my (Fig 23) Some regions have strong and others very weakpatterns that can be attributed to heterogeneous deformation dueto CPO development and result in lsquolsquoanisotropicrdquo viscosity

Some complexities of different plasticity models for a simplecase of upwelling have been investigated by Blackman et al(1996 2002) and Castelnau et al (2009) If a lower bound behavioris assumed (Sachs 1928) there is very strong CPO developmentFor self-consistent models (Lebensohn and Tomeacute 1993) rotationsare reduced If dislocation glide is combined with dynamic recrys-tallization both grain growth and grain growth combined withnucleation resulting orientation patterns can be very differentRecrystallization is likely in the deep Earth with high temperatureand large strains where grain boundary migration is likely tooccur We will return to the issue of recrystallization in Section 48

Merkel et al (2002) and Lin et al (2009)Amodeo et al (2016)Miyagi and Wenk 2016Tsujino et al (2016)Kraych et al (2016)Miyagi et al (2010) and Wu et al (2017)Goryaeva et al (2016)Miyagi et al (2009) and Ferreacute et al (2009)

Merkel et al (2004) and Miyagi et al (2008)

Fig 1 (a) Azimuthal variation of surface wave velocities in Hawaii (Morris et al 1969) (b) Proposed model for mantle upwelling at an oceanic ridge (Cann 1968) (c)Azimuthal anisotropy in Rayleigh waves at a period of 98s (Montagner and Tanimoto 1990) The lines correspond to fast wave propagation directions and are proportional tothe strength of anisotropy

60 B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90

Geodynamic models are necessary to suggest realistic deforma-tion paths Early models assumed flow in an isotropic medium dri-ven by temperature and density gradients (eg Hager andOrsquoConnell 1981 Tackley 1993 Bunge et al 1996) Also subduc-tion of crustal slabs was explored including rigid slabs (egMcKenzie 1969) as well as more ductile and weak slabs (egGurnis and Hager 1988) The development of seismic anisotropywas considered only later by including polycrystal plasticity toexplain the development of preferred orientation during plasticdeformation (eg Blackman et al 1996 Dawson and Wenk2000 Kaminski and Ribe 2001) We will discuss convection mod-els in more detail below

Seismic observations revealed that the pattern of anisotropy inthe upper mantle is much more complex that the picture in Fig 1cThis has been reviewed recently (eg Long and Becker 2010 Long2013) Here we will focus on anisotropy in the lower mantle andinner core first from what we know from seismology and fromour current knowledge about mineral physics particularly elastic-ity of minerals at deep Earth conditions and deformation mecha-nisms Then we will explain how geodynamics modeling isbrought into the picture Great progress has been made in all threefields over the last 20 years The deep Earth appeared like a simpleimage but the more we learn about it the more complexities ariseIn a concluding section we will highlight some important issuesthat need to be addressed in the future There has been a lot ofinterest in this topic with many publications in prestigious jour-nals such as Science and Nature but still a lot of work remains tobe done to better describe and understand processes that causeseismic anisotropy at deep Earth conditions

The purpose of this review is to establish our current state ofknowledge and to identify some outstanding questions It alsoshould serve as an introduction to the field of deep Earth aniso-tropy for those who are not experts in the field for example forstudent projects

2 Seismic anisotropy in the deep mantle

21 Overview

There is as yet no compelling evidence for the presence of sig-nificant anisotropy in the bulk of the lower mantle at least awayfrom subduction zones (eg Meade et al 1995 Montagner andKennett 1996 Niu and Perez 2004 Panning and Romanowicz2006 Moulik and Ekstroumlm 2014) although a recent study basedon normal mode center frequency observations suggests the pres-ence of anisotropy as expressed in the radial anisotropy parameterg already 1000 km above the core-mantle boundary (de Wit andTrampert 2015) In any case it is now well established that signif-icant seismic anisotropy is present in the D00 region at the base ofthe mantle Here we review the corresponding observational evi-dence which is based on local studies of shear body waves sensi-tive to the deep mantle complemented by global tomographicstudies of radial anisotropy throughout the mantle

The first observations of shear wave splitting attributed to ani-sotropy in the D00 region date back to the late 1980s Vinnik et al(1989) observed elliptically polarized Sdiff waves for paths sam-pling the lowermost mantle in the central Pacific along a direction

Fig 3 Background lsquolsquoVoting maprdquo based on 5 shear wave velocity tomographicmodels modified (from Lekic et al 2012) Locations in D00 where 5 models agreethat Vs is lower than average or higher than average are shown in red and dark bluerespectively White ellipses indicate locations where shear wave splitting observa-tions with Vsh gt Vsv have been attributed to anisotropy in D00 These include regionswhere azimuthal anisotropy has been reported Green ellipses indicate regionswhere strong lateral variations of anisotropy in D00 have been reported at the edgesof the African LLSVP (14 17 21) the Perm anomaly (19) and in the south Pacific(719) Blue ellipses with broken lines indicate regions where Vsv gt Vsh has beenreported andor null splitting See Table 1 for references to numbers and lettersWhite bars and blue broken lines (no splitting) are from Niu and Perez (2004)

B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90 61

for which no splitting was present in SKS Because the absence ofthe latter indicated that the data were not contaminated by uppermantle anisotropy they suggested that the splitting originated inthe deep mantle and could be due to the presence of anisotropyEarlier Mitchell and Helmberger (1973) and Lay and Helmberger(1983) had observed time shifts between the arrival of ScSH andScSV but attributed them to the presence of a high velocity regionat the base of the mantle Many studies followed in the 1990s doc-umenting splitting times of up to 10 s in shear waves such as ScSand Sdiff (Fig 2) that propagate quasi-horizontally in D00 and inter-preted them as indicating the presence of several percent of VTI(Vertical Transverse Isotropy) in the deep mantle (see Lay et al1998 and Kendall and Silver 1998 for early reviews)

As different areas of the world were progressively sampled thepicture that emerged was that globally the vertically polarizedwave (SV) is generally delayed with respect to the horizontallypolarized one (SH) in the circum-pacific ring where isotropic shearwave velocities are higher than average in D00 On the other handintermittent splitting and sometimes delayed SH with respect toSV was observed on paths sampling the large low shear velocityprovinces (LLSVPs) in the central Pacific and under Africa (Fig 3)Additional reports of splitting in ScS and Sdiff have been publishedin the last two decades most of them attributed to anisotropy inD00 A review of observations of shear wave splitting originatingin D00 can be found in Wookey and Kendall (2007) and Nowackiet al (2011) as well as Lay (2015) Here we focus primarily onthe most recent contributions while an updated list of observa-tions is given in Table 1 and Fig 3

Several important challenges affect studies of shear wave split-ting in D00 One is the necessity to account for (or avoid) contamina-tion of seismic waveforms by strong upper mantle anisotropysampled by the body waves considered (Fig 2) Another challengeis the poor azimuthal sampling of D00 at any given location due tothe limited global distribution of earthquake sources and receiversThis makes it difficult to distinguish between different possiblecauses of anisotropy whether due to periodic layering or crystalalignment and whether the nature of the anisotropy is transverseisotropy with a vertical (VTI) or tilted (TTI) axis of symmetry or

SScS

SKKS

SKS

Fig 2 Raypaths through the Earth of the main seismic body wave phases used forstudying anisotropy in the deep mantle Asterisk is earthquake location trianglesare receiver stations

perhaps involves more complex symmetries Also in the case ofSdiff an apparent delay of SVdiff may be due to waveform distorsionin a laterally heterogeneous but isotropic structure due to the factthat the amplitude of SVdiff decays rapidly with distance in regionsof fast isotropic velocity (eg Vinnik et al 1995 Komatitsch et al2010) More generally apparent splitting in S waves sampling theD00 region may sometimes be due to other causes than anisotropysuch as propagation in a complex heterogeneous medium near theboundary between the solid mantle and the liquid core whichrequires more sophisticated modeling than infinite frequency raytheory (Monteiller and Chevrot 2010 Borgeaud et al 2016Nowacki and Wookey 2016) Careful waveform analysis is there-fore necessary before attributing splitting observations to aniso-tropy Some of the splitting results listed in Table 1 may need tobe re-evaluated in that context However consistency in the split-ting results obtained using different types of waves across a num-ber of regions of the world and in some cases detailed waveformmodeling indicates that in general invoking anisotropy as a causefor the observed splitting is a robust result At the present timeinterpretation in terms of layering or CPO requires invoking possi-ble constraints from other fields than seismology and remainsuncertain

22 Accounting for upper mantle anisotropy

In order to account for upper-mantle anisotropy an approachtaken in early studies of Sdiff splitting was to only consider deepearthquakes and paths for which SKS and SKKS do not presentany evidence of splitting (eg Vinnik et al 1989 1995) Selectingobservations for deep earthquakes assures that contamination byanisotropic effects in the upper mantle on the source side can lar-gely be avoided On the station side the paths of Sdiff and SKSSKKSare very close in the upper mantle (Fig 2) while they diverge in thedeep mantle Also only Sdiff spends significant time within D00 Theabsence of splitting in SKSSKKS indicates that either there is noanisotropy in the upper mantle region sampled on the receiverside or the direction of the great circle path is along the null split-ting direction Any splitting observed in Sdiff can thus be attributedto the deep mantle

However such geometries are exceptional Therefore it isimportant to find ways to correct for the widespread and strong

Table 1Summary of local studies of anisotropy in D00

Authors Region Type ofseismicwaves

VSH gt VSV

A Wookey and Kendall (2007)and Refs therein

Caribbean

Kendall and Silver (1996) Caribbean SSdiffDing and Helmberger

(1997)Caribbean ScS

Rokosky et al (2004) Caribbean ScSB Wookey and Kendall (2007)

and Refs thereinAlaska

Lay and Young (1991) Alaska SScSMatzel et al (1996) Alaska SScSSdiffGarnero and Lay (1997) Alaska SScSSdiffWysession et al (1998) Alaska SdiffFouch et al (2001) Alaska SSdiff

E Ritsema (2000) Indian Ocean SF Thomas and Kendall (2002) Siberia SScSSdiffI Usui et al (2008) Antarctic Ocean S1 Kendall and Silver (1998) NW Pacific SScSSdiff3 Vinnik et al (1995 1998b) north central Pacific Sdiff6 Wookey et al (2005b) N Pacific ScS8 Long (2009) East Pacific SKS-SKKS9 Niu and Perez (2004) N America Asia SKSSKKS11 Vanacore and Niu (2011) Caribbean SKS-SKKS12 He and Long (2011) NW Pacific PcSScS SKS

SKKS13 Wookey and Kendall (2008) Caribbean ScS18 Thomas et al (2007) W Pacific ScS20 Fouch et al (2001) North central Pacific SSdiffSV lt SH4 Pulliam and Sen (1998) Central Pacific SC Ritsema et al (1998) Central Pacific SSdiff22 Kawai and Geller (2010) Central Pacific SScSSKSTiltedazimuthallaterally varying5 Russell et al (1998 1999) North Central Pacific ScS7 Ford et al (2006) South Pacific SSdiffA Garnero et al (2004a) Caribbean SScSSdiffA Maupin et al (2005) Caribbean SScSSdiffA Rokosky et al (2004 2006) Caribbean ScSG Wookey et al (2005a) North West Pacific ScS23 Restivo and Helffrich

(2006)North America SKS SKKS

21 Wang and Wen (2007) EastSouth Africa SKSSKKS10 Nowacki et al (2010) Caribbeanwest US ScS14 Lynner and Long (2012) Central Africa SKS-SKKS15 Cottaar and Romanowicz

(2013)South edge of AfricanLLSVP

Sdiff

16 Lynner and Long (2014) EastSouth Africa SKS-SKKS19 Long and Lynner (2015) Near Perm Anomaly SKS-SKKS17 Ford et al (2015) East Africa SKS-SKKSIsotropic or weak anisotropy2 Kendall and Silver (1996) South Pacific SScSSdiffH Garnero et al (2004b) Atlantic SSdiff9 Niu and Perez (2004) South Africa Antarctica

Southeast PacificSKSSKKS

21 Wang and Wen (2007) Eastern Atlantic SKSSKKS

62 B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90

upper mantle anisotropy sampled along the path of deep mantleseismic waves For example Vinnik et al (1998a) proposed a refer-ence event method to correct Sdiff waveforms for unknown uppermantle anisotropy using SKS and SKKS waveforms In the pasttwo decades characterization of upper mantle anisotropy fromSKS splitting data has progressed significantly (see review byLong and Silver 2009) making it possible to apply relatively robustcorrections in 00known00 upper mantle models both on the sourceand receiver sides and thus augment the number of D00 locationsthat can be sampled

Another approach to minimize effects of upper mantle aniso-tropy has been the use of differential measurements on pairs ofphases One such suitable pair is S and ScS which have similarpaths in the upper mantle on the source and station side but at

appropriate distances only ScS samples D00 (Fig 2) while S samplesa portion of the lower mantle which is assumed to be isotropic (egWookey et al 2005a Nowacki et al 2010) Similarly while SKSand SKKS splitting is most strongly acquired during propagationin the upper mantle the paths of SKS and SKKS waves diverge sig-nificantly in the lowermost mantle so that differential splitting ofthese two phases can sometimes be attributed to anisotropy in thedeep mantle (eg Hall et al 2004 Niu and Perez 2004 Restivo andHelffrich 2006 Wang and Wen 2007) Such an approach has beenapplied to several regions of the world (eg Long 2009 He andLong 2011 Vanacore and Niu 2011 Lynner and Long 20122014 Long and Lynner 2015 Ford et al 2015) Results consis-tently show strong and complex anisotropy on the borders of theLLSVPrsquos and interestingly also in the vicinity of the Perm Anomaly(Long and Lynner 2015) a low velocity anomaly seen at the base ofthe mantle in all tomographic models in the vicinity of the town ofPerm (Russia) and of smaller lateral extent ( 900 km) but corre-sponds to a similar reduction in shear velocity as found in theLLSVPs (eg Lekic et al 2012 Fig 3)

23 Results from array studies

Earlier observations and forward modeling studies of D00 aniso-tropy mostly relied on data from isolated stations which made itdifficult to constrain the geometry of anisotropy for lack of sam-pling of the target regions by waves propagating in different direc-tions (eg Maupin 1994) Thus most studies only reported thedifferences in SH and SV propagation times leading to models ofapparent VTI Yet evidence for azimuthal anisotropy has been sug-gested either from waveform complexity (eg Garnero et al2004a Maupin et al 2005) or when the geometry permitted frommeasurements of splitting on paths sampling the target region inat least two directions (eg Wookey and Kendall 2008) With theadvent of denser broadband arrays more detailed studies haveemerged in recent years aiming at the very least to distinguishVTI from radial anisotropy with tilted axis of symmetry (TTI) withimplications for the interpretation of observations in terms ofintrinsic or extrinsic anisotropy (eg Long et al 2006)

Regions of the world where this has been possible so far arecentral America exploiting ScS S data from the dense USArray(Nowacki et al 2010) and the northwest Pacific (He and Long2011) using ScS data from F-net in Japan Studies of Sdiff at thesouthern border of the African LLSVP based on data from the Kaap-val array show lateral variations in anisotropy (To et al 2005Cottaar and Romanowicz 2013) with strong anisotropy in the fastvelocity region outside the LLSVP increasing towards its borderand apparently disappearing inside it Although caution must betaken when interpreting apparent splitting in Sdiff due to isotropicheterogeneity potentially affecting SVdiff in a significant way(Komatitsch et al 2010) the strong elliptical shape of the particlemotion outside of the African LLSVP (Fig 4 and To et al 2005)where isotropic velocities are relatively fast contrasting with thelinear particle motion for paths travelling inside the LLSVP cannotbe accounted for by isotropic heterogeneity This was demon-strated in the follow-up study of Cottaar and Romanowicz(2013) in which the waveforms of Fig 4 and others were modelledusing the spectral element method a numerical method for 3Dseismic wavefield computations which can take effects of 3D iso-tropic heterogeneity into account accurately Differential splittingin S and ScS has also been exploited in the north Pacific (Wookeyet al 2005a) and in east Africa (Ford et al 2015) where remark-ably several azimuths can be sampled

The recent studies have confirmed earlier results with in gen-eral Vshgt Vsv in the ring of faster than average velocities sur-rounding the two LLSVPs and absence of significant splitting orVshltVsv found primarily within the LLSVPs (Fig 3 Table 1)

Fig 4 Example of change of character of particle motion for paths sampling theborder of the African LLSVP (a) Map showing the paths sampled plotted on top of abackground shear wave tomographic model (SAW24B16 Meacutegnin and Romanowicz2000) The portion of path sampling the D00 region is highlighted in yellow (b) and(c) shows particle motions of Sdiff at distances of 120o and at two azimuths In (b)the path in D00 is outside of the LLSVP and in (c) the path in D00 is inside the LLSVP(from To et al 2005) The color indicates the time with respect to predicted Sdiffarrival from PREM Black 35 to 5 s Blue 5 to 20 s Green 20 to 45 s Red 45 to70 s The elliptical particle motion in (B) contrasts with the linear particle motion in(c) This cannot simply be explained by lateral heterogeneity in isotropic velocity asone would expect larger amplitudes in SV for waves propagating inside the lowvelocity LLSVP This interpretation was later confirmed by 3D numerical waveformmodelling (Cottaar and Romanowicz 2013) (For interpretation of the references tocolor in this figure legend the reader is referred to the web version of this article)

B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90 63

The recent results indicate variability of anisotropy at relativelyshort scales with evidence for azimuthal anisotropy with differentorientations of fast velocity axes at least in regions of faster thanaverage isotropic shear velocity Interestingly the studies ofCottaar and Romanowicz (2013) Lynner and Long (2014) andFord et al (2015) consistently show changes in anisotropy acrossthe border of the African LLSVP with stronger anisotropy outsideof it practically disappearing inside it (eg Fig 5) Interestinglythe same trend although less sharply defined because of the chal-lenging geometry is likely present at the northern edge of the Paci-fic LLSVP (Fig 6) Indeed all studies of the latter region considerpaths from Fiji-Tonga sources to stations in north America Differ-ent results are found for different distance ranges with VsvgtVshfor the shorter distances sampling inside the LLSVP (as well asabove D00) and VshgtVsv at longer distances (Sdiff) which samplea significant portion of the fast Vs region outside of the LLSVPVinnik et al (1995 1998b) used Sdiff data and found VSHgtVSV theportion of the corresponding paths inside the LLSVP was smalland Vinnik et al (1998b) showed that splitting only occurred fordistances larger than 102o when paths sampled more of the fastregion outside of the LLSVP Likewise Fouch et al (2001) andRitsema et al (1998) used S Sdiff and found VshgtVsv for larger dis-tance paths while VsvgtVsh for shorter distance paths that samplewithin the LLSVP and above D00 as did Kawai and Geller (2010)Pulliam and Sen (1998) and Russell et al (1998) used S and ScSrespectively at shorter distances sampling inside the LLSVP andfound VsvgtVsh

All these results point in the same direction evidence for signif-icant anisotropy with generally VshgtVsv within the ring of fastvelocities surrounding the Pacific and African LLSVP possiblyincreasing and tilting at their borders but vanishing or changingsign (VsvgtVsh) inside the LLSVPrsquos

24 Results from global anisotropic tomography

Gaining improved understanding of the distribution and natureof seismic anisotropy at the base of the mantle requires better glo-bal sampling with accurate corrections for upper mantle aniso-tropy One possible approach is to construct global whole mantletomographic models of anisotropy Such an approach is attractivebecause a variety of seismic waveforms can be included in partic-ular fundamental and overtone surface waves which provide con-straints on the strong anisotropy in the uppermost mantle (egDebayle and Ricard 2013) Combining surface wave data with var-ious body waveforms that illuminate the entire mantle should ulti-mately allow improved resolution and characterization of deepmantle anisotropy So far this has proven very challenging forthe deep mantle

Indeed most successful has been the tomographic characteriza-tion of shear wave azimuthal anisotropy in the uppermost 200 kmof the mantle at the global scale using Rayleigh wave dispersiondata (eg Tanimoto and Anderson 1984 Montagner andTanimoto 1990 1991 Fig 1) More recent models developed bydifferent groups show broadly consistent trends (eg Trampertand Woodhouse 2003 Ekstroumlm 2011 Debayle and Ricard 2013Yuan and Beghein 2013) On the other hand the robustness of glo-bal scale transition zone azimuthal anisotropy models that utilizesurface wave overtone information (eg Trampert and van Heijst2002 Yuan and Beghein 2013) is still debated This is becausethe anisotropic signal in overtone surface waves is weak the azi-muthal sampling far from ideal and the number of parametersneeded to invert for azimuthal anisotropy at the global scale evenwhen considering only the dominant terms in 2-w (where w is theazimuth) is very large likely resulting in trade-offs with isotropicstructure It is not possible at present to extend this type of studyto the deep mantle as the sensitivity of available long period over-tone data becomes too weak and azimuthal coverage for bodywaves provided by the current geometry of sources and stationsis not sufficient

Thus tomographic imaging of anisotropy in the whole mantlecan at present only hope to resolve the simplest form of aniso-tropy that does not have as strong requirements on azimuthal cov-erage which is VTI (or apparent VTI) Such studies are based onrelatively long period waveforms mostly sensitive to shear veloc-ity combining fundamental mode surface waves surface waveovertones and shear body waves and aim at solving for the distri-bution of only two anisotropic parameters Vsh and Vsv or alter-natively isotropic velocity Vsiso and the anisotropic parameter n =(VshVsv)2 (Panning and Romanowicz 2004 2006 Panning et al2010 Kustowski et al 2008 French and Romanowicz 2014Moulik and Ekstroumlm 2014 Auer et al 2014 Chang et al 20142015) The other three anisotropic parameters that are necessaryto fully describe a VTI medium are scaled to Vsiso and n using scal-ing relations that are appropriate for the upper mantle (egMontagner and Anderson 1989) but may be questionable for thelower mantle However this may not be a significant issue giventhe dominant sensitivity of the waveforms considered to shearvelocities While the resulting models show qualitative agreementat long wavelengths details vary frommodel to model significantlyenough not to be trustworthy for quantitative interpretations

These models do agree on the following observations on aver-age radial anisotropy is strongest in the uppermost mantle andmost of the lower mantle exhibits little radial anisotropy (Fig 7)

Fig 5 a and b Whole mantle depth cross sections through the isotropic Vs part of model SEMUCB_WM1 (French and Romanowicz 2014) at the southern (a) and eastern (b)edge of the African LLSVP where rapid variations in the direction and strength of anisotropy have been reported decreasing from outside (blue) to inside (pink) the LLSVP inc) the map view is from Lynner and Long (2014) with background shear velocity model GyPSuM of Simmons et al (2012) The cross-section location is indicated on the mapby a straight line c and d corresponding cartoons proposed by the authors respectively (c) Cottaar and Romanowicz (2013) (d) Ford and Long (2015)

64 B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90

Inmostmodels there is an indication of an increase in anisotropy inD00 with Vshgt Vsv (n slightly larger than 1) although there is vari-ability among models due to a combination of parametrizationtypes of seismic waves considered and theoretical assumptions

Common 3D features of these models in D00 are a predominanceof Vsh gt Vsv outside of the LLSVPs with patches of Vsh lt Vsv con-fined within the LLSVPs in agreement with local studies (Fig 8)However the current models do not show consistency in theamplitude of the lateral variations in n nor the wavelengths ofthese variations This is partly due to the parametrization chosenFor example Panning and Romanowicz (2004 2006) and Aueret al (2014) allowed relatively short wavelength lateral variationsin n while Moulik and Ekstroumlm (2014) and French andRomanowicz (2014) chose to assign shorter wavelength lateralvariations to isotropic Vs while constraining the anisotropic partof the model to be smooth Theoretical assumptions on wave prop-agation are also important ray theory is not valid for modelling ofSdiff nor is it valid to use the surface wave approximation for mod-elling this phase as shown by Li and Romanowicz (1995) So faronly the Berkeley models are constructed taking into account finitefrequency effects rather than ray theory for body waves (Panningand Romanowicz 2004 2006 French and Romanowicz 2014)

One fundamental issue is that Sdiff and ScSn data (with ngt1) arenecessary to obtain good coverage of D00 at the global scale As dis-cussed previously SVdiff decays rapidly with distance in modelssuch as the reference model PREM (Dziewonski and Anderson1981) where the velocity in D00 is relatively fast The global datasetsare thus necessarily biased although to various degrees depending

on the particular dataset by the predominance of SHdiff introduc-ing trade-offs between isotropic and anisotropic structure (egKustowski et al 2008 Chang et al 2015) and making it only pos-sible to resolve the very longest wavelengths of VTI in D00 withpoor constraints on their amplitude

In summary robustly mapping even the simplest component ofseismic anisotropy apparent VTI at the base of the mantle at highresolution using a tomographic approach is still a challenging openquestion let alone constraining azimuthal anisotropy at the globalscale Still available global models agree with local studies aboutthe prevalence of VshgtVsv in regions of faster than average velocityin D00

As for P wave anisotropy in the deep mantle only few studieshave tried to constrain it so far Several studies have attemptedto retrieve the global average variation with depth of the radiallyanisotropic parameter g = (VphVpv)2 using normal mode data(Montagner and Kennett 1996 Beghein et al 2006) finding someindication that the anisotropy in gmay be anticorrelated with thatof n in the D00 region with however strong trade-offs with density(to which normal mode data are also sensitive) Note that the anti-correlation of isotropic P and S velocities at long wavelengths inthe deep mantle is in contrast better established (eg Su andDziewonski 1997 Kennett and Widyantoro 1998 Masters et al2000 Ishii and Tromp 1999 Romanowicz and Breacuteger 2000) Thepossibility of P wave anisotropy in the deep mantle using P wavedata (mantle and core phases) has been investigated by Boschiand Dziewonski (2000) concluding that anisotropy may be smallwith significant trade-offs with core-mantle boundary topography

Fig 6 Zoom on the northern edge of the Pacific LLSVP The background tomographic model is the isotropic Vs part of model SEMUCB_WM1 (French and Romanowicz 2014)(A) Map view with locations of studies of D00 shear wave splitting suggesting a change of character of anisotropy across the boundary of the LLSVP Green dots indicate thelocation of major hotspots Black line with white and purple dots is the great circle path corresponding to the depth cross section shown in (B) displaying the Hawaian plumeand transition from low to fast velocities in D00 Kawai and Geller (2010) Pulliam and Sen (1998) and Russell et al (1998) find VSV gt VSH while Ritsema et al (1998) Fouch et al(2001) and Vinnik et al (1998) find that Vsh gt Vsv increasingly so for paths sampling the fast region outside of the LLSVP Note that the color saturation of the tomographicmodel is different in (A) and (B)

B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90 65

and outer core structure The possible anticorrelation of P and Sradial anisotropy in the D00 must therefore be considered with cau-tion at the present time when used as a constraint in modeling

Given these difficulties a currently explored possible avenue isto try and combine constraints not only from seismology but alsofrom mineral physics and geodynamics Each of these approachestaken individually involves many assumptions and uncertaintiesbut by combining them the hope is that the space of acceptablemodels for anisotropy and its causes can be further reduced Theidea is to start with the strain field inferred from a mantle circula-tion model compute the corresponding texture development andpredicted seismic anisotropy using available information on crystalplasticity and elasticity for different lower mantle minerals andcompare these predictions with seismic observations This shouldprovide constraints on the mineral physics assumptions as wellas the deep mantle dynamics or at least allow us to rule out someclasses of models Note that in this approach the fundamentalassumption is that anisotropy is due to CPO development resultingfrom large-scale mantle flow

Before describing these efforts in more detail we will reviewcurrent knowledge and capabilities in mineral physics and describehow seismology and mineral physics can be linked through geody-namics modeling

3 Mineral physics perspective on the deep mantle

31 Dominant mineral phases in the lower mantle

Ringwood (1962) speculated about the composition of thelower mantle suggesting that olivine Mg2SiO4 would first breakdown to spinel Mg2SiO4 and then to MgSiO3 with a lsquolsquocorundum-

likerdquo structure and periclase (MgO) Liu (1974) synthesized thisstructure at high temperature and pressure and identified it asMgSiO3 perovskite (which has recently been named bridgmaniteTschauner et al 2014) At high pressure bridgmanite transformsto post-perovskite pPv (eg Murakami et al 2004 Oganov andOno 2004 Tateno et al 2009 Fig 9a) and this may be the mostimportant phase near the core-mantle boundary particularly alonga cold geotherm within subducting slabs (Fig 9b) Thus it appearsthat cubic periclase (Fig 10a) orthorhombic bridgmanite (Fig 10b)and orthorhombic post-perovskite (Fig 10c) are the dominantminerals in the lower mantle Periclase has the same highly sym-metric structure as halite (NaCl) with close-packed MgOVI octahe-dral coordination polyhedra Bridgmanite (spacegroup Pbnm) is adistorted cubic perovskite structure with SiOVI coordination octa-hedra linked over corners and Mg2+ in large interstices Post-perovskite (spacegroup Cmcm) has layers of SiOVI octahedra alter-nating with layers of Mg The layers are parallel to (010) It isisostructural with CaIrO3 (eg Hunt et al 2009) While the pseu-docubic perovskite structure is elastically fairly isotropic the lay-ered post-perovskite structure is highly anisotropic As we willsee post-perovskite is of critical importance for anisotropy in thelower mantle In the following discussion we will use mostly theabbreviation pPv

Most lower mantle minerals (gt660 km) cannot be studied atsurface conditions Even if lower mantle material has reached thesurface by upwelling minerals have undergone phase transitionsThus information about phase diagrams is based on in situ observa-tions in high pressure experiments and ab initio calculations

Irifune and Tsuchiya (2015) have reviewed the mineralogicalcomposition of the lower mantle Different bulk compositions ofthe lower mantle have been proposed Ringwood (1962 1975) sug-gested a peridotitic-lsquolsquopyroliticrdquo composition (Fig 11a) Subducting

Fig 7 Comparison of depth profiles throughout the mantle of global average radialanisotropy parameter n = (VshVsv)2 in 6 recent global shear velocity models n = 1corresponds to isotropy Model S362ANI (Kustowski et al 2008) is isotropic in thelower mantle While there are differences between models all of them agree thatradial anisotropy is strongest in the first 200 km of the mantle and very weak inmost of the lower mantle In D00 on average Vsh is equal of slightly faster than Vsv

66 B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90

slabs may correspond to more siliceous aluminous and Ca-richmid-ocean ridge basalts (MORB eg Irifune and Ringwood 1993Fig 11b) In both cases MgSiO3-perovskite (bridgmanite) domi-nates in large volumes of the lower mantle but for MORB compo-sitions high pressure silica and alumina phases are alsosignificant and there may be no ferropericlase Calcium perovskite(CaSiO3) is cubic (spacegroup Pm3 m) at lower mantle conditions(eg Wang et al 1996 Kawai and Tscuchiya 2015) and is animportant component at depths beyond 750 km It distorts to atetragonal structure at low temperature and high pressure (egShim et al 2002)

As more details about the lower mantle are revealed composi-tional heterogeneities become apparent (eg Badro et al 2003 LiY et al 2014) Higher concentrations of Si Al and Fe add consider-able complexity The diverse composition is in part the result ofsubduction of slabs composed of crust and upper mantle Silica(SiO2) may exist as stishovite with a rutile structure and 6-foldcoordination or at higher pressure as a cubic phase with CaCl2structure and 8-fold coordination (eg Kingma et al 1995) andat even higher pressure as an orthorhombic (Pbcn) a-PbO2 struc-ture (seifertite) (eg Dubrovinsky et al 2004 Grocholski et al2013 Zhang et al 2016) According to first principles calculationsat extreme pressure SiO2 may transform to a pyrite structure(Kuwayama et al 2005) Al2O3 in the form of trigonal corundumor orthorhombic Rh2O3(II) may be present and Fe may exist asnative iron (eg Frost et al 2004 Shi et al 2013)

Of considerable importance is the oxidation state as well as thespin state of iron that have received a lot of attention (egMcCammon 1997 Badro et al 2003 Li et al 2004 Tsuchiya

et al 2006 Fei et al 2007 Lin et al 2008 Catalli et al 2010Saha et al 2011 2012 Vilella et al 2015) With increasing pres-sure there is a transition from a high spin to a low spin configura-tion It may be responsible for the anomalous viscosity structure inthe central part of the lower mantle (900ndash1200 km eg Rudolphet al 2015) although the spin transition is generally thought tooccur deeper (1500 km)

In addition hydrogen may play a significant role (eg Ohtamiand Sakai 2008) A hydrous aluminosilicate is stable at lower man-tle conditions (eg Tsuchiya and Tsuchiya 2008 2011 Pamatoet al 2014) and dehydration may cause melting at the top of thelower mantle (Schmandt et al 2014)

As far as elastic properties and anisotropy are concerned oneshould keep in mind that the major phases over large volumes ofthe lower mantle are bridgmanite ferropericlase pPv and CaSiO3

perovskite These contribute largely to the bulk elastic propertiesbut there may be local deviations

32 Some comments on plasticity models and representation ofanisotropy

What are the sources of seismic anisotropy in the Earth Veryimportant is the alignment of anisotropic crystals called crystalpreferred orientation (CPO) or texture (based on DrsquoHalloy 1833)and universally used in materials science The crystal anisotropyis linked to the crystal structure A second aspect is crystal shapethat produces a shape-preferred orientation (SPO) CPO and SPOare sometimes linked (in mica for example the crystal plane(001) is parallel to the platelet) Often it is not (eg in quartz orin periclase) Also significant is the orientation of flat fracturesand fractures filled with kerogen This is a very important contribu-tion to anisotropy in shales (eg Hornby et al 1994 Sayers 1994Vasin et al 2013) but insignificant in the lower mantle In thelower mantle there is the possibility of partial melt particularlynear the core-mantle boundary (eg Williams and Garnero 1996Lay et al 2004 Shi et al 2013) but this would only give rise to ani-sotropy if melt occurred in parallel thin layers (eg Backus 1962)We will focus here on the development of CPO

Before going into plasticity in the mantle a few words aboutdeformation mechanisms of polycrystalline aggregates are inorder Deformation experiments on minerals have a long historyPfaff (1859) documented mechanical twinning in calcite when astress is applied In the early twentieth century deformation exper-iments at a wide range of temperature and strain conditions wereconducted on metals to explore the deformation behavior (egSchmid 1924) and in this context linear defects called dislocationswere discovered (Polanyi 1934 Taylor 1934) Without disloca-tions it would be very difficult to deform crystals and indeed theyare present in most crystalline materials

Dislocations form in the crystal lattice when a stress is appliedEdge dislocations propagate on a glide plane (hkl) and in a slipdirection [uvw] defined by rational indices relative to crystallo-graphic axes Propagation of dislocations causes crystals to rotaterelative to the applied stress which is conceptually illustrated foran experimentally compressed single crystal in Fig 12 By move-ment of dislocations on glide planes the rectangular crystal attainsa new shape (parallelogram) Since pistons must stay in contactthis results in an effective rotation of b In a polycrystalline aggre-gate neighboring grains play the function of pistons

Based on deformation experiments on metals deformationmechanism maps were established (eg Ashby 1972 Langdonand Mohamed 1978 Frost and Ashby 1982) They define condi-tions such as temperature pressure stress magnitudes strain rateand grain size under which mechanisms such as dislocation glidedislocation climb grain boundary migration and grain boundarysliding are active (Fig 13) Identifying mechanisms is important

Fig 8 Comparison of 6 recent models of lateral variations in the radial anisotropy parameter n = (VshVsv)2 plotted in terms of dlnn referred to isotropy While the modelsdisagree in detail common features are Vsh gt Vsv (blue) in the circum Pacific ring (roughly in agreement with local studies) and pronounced Vsv gt Vsh (orange) in the Fiji-TongaIndonesia region and under southernmost Africa (except SAVANI) Models plotted are (a) SAW642ANb (Panning et al 2010) (b) SAW642AN (Panning andRomanowicz 2006) (c) SAVANI (Auer et al 2014) (d) SGLOBE-rani (Chang et al 2015) (e) S362WANI + M (Moulik and Ekstroumlm 2014) (f) SEMUCB_WM1 (French andRomanowicz 2014)

Fig 9 (a) Experimentally determined PT phase diagram for perovskitebridgmanite (Pv)-post-perovskite (Murakami et al 2004) (b) T-Depth phase diagram plotting the pv-ppv phase boundary and cold and warm geotherms (after Hernlund et al 2005)

B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90 67

because some produce crystal rotations and thus crystallographicpreferred orientation (notably dislocation glide and ndash to someextent ndash dynamic recrystallization) while others generate random

orientations (such as grain boundary sliding in fine-grained mate-rials and dislocation climb) We will return to these issues inSection 48

Fig 10 Crystal structures of (a) periclase (b) bridgmanite and (c) post-perovskite the latter two with octahedrally coordinated silicon

Fig 11 Lower mantle composition for different models (a) pyrolite (b) MORB(from Irifune and Tsuchiya 2015) Pv perovskitebridgmanite Ppv post-perovskiteMw magnesiowuestiteferropericlase Mj majorite Rw ringwoodite SiO2 Ststishovite CC CaCl2 phase AP a-PbO2 phase Al2O Hex CF calcium-ferrite phaseCT calcium-titanate phase

68 B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90

In a polycrystalline aggregate stresses are transmitted acrossgrain boundaries causing heterogeneities even within grains Thisis most realistically approached with finite element methods (egMika and Dawson 1999) but these are still extremely demandingand rarely applied Simpler models have been used in materialsscience for a long time The Taylor (1938) theory developed bythe same Taylor who discovered dislocations (1934) assumeshomogeneous strain All grains undergo the same shape changeirrespective of orientation This leaves grain boundaries intact(Fig 14 left side) The Taylor model is very applicable to cubic met-als with many symmetrically related slip systems Slip on 111h

1 1 0i in fcc metals or cubic periclase has 12 equivalent systemsAnother model (Sachs 1928) assumes stress equilibrium and morefavorably oriented grains deform more than others In the modelthis causes overlaps and gaps at grain boundaries In principle thiswould be more adequate for low symmetry minerals (such asorthorhombic) but of course overlaps and gaps do not exist A com-promise between homogeneous strain and stress equilibrium is aself-consistent model that treats grains as ellipsoidal inclusionsdeforming in an anisotropic viscous medium (Fig 14 centerMolinari et al 1987) It is most widely applied in the Los Alamoscode VPSC (Lebensohn and Tomeacute 1993) and it can be used bothto understand preferred orientation in high pressure experimentsand to predict anisotropy in geodynamic models In the viscoplas-tic self-consistent model grains deform without knowledge of theirneighborhood In a finite element model (Fig 14 right) grains areconstrained by the orientation of neighbors In this sketch it isassumed that each grain has a single orientation In more sophisti-cated FEM models there are strain and orientation gradients devel-oping within grains (eg Mika and Dawson 1999)

When crystals are deformed in a polycrystalline medium theyundergo systematic rotations (Fig 12) and the material attains ananisotropic pattern We need to describe the orientation of a crys-tal relative to the macroscopic sample This is efficiently done byrelating two orthogonal coordinate systems (sample x y z crystal[100] [010] [001]) by three rotations Most frequently the so-called Euler angles are used U is the distance from z to [001]1 is the azimuth of [001] from y (around z) 2 is the azimuthof [100] around [001] (Fig 15) The 3-dimensional crystal orienta-tion distribution (COD) is conventionally described by a continuousorientation distribution function (ODF) The ODF is required to cal-culate anisotropic elastic properties of an aggregate from crystalorientations

For graphical representations of orientation patterns generally2-dimensional spherical projections of the ODF are used Depend-ing on the application one can either use the macroscopic sample xy z as reference and plot crystal directions (pole figures) or use thecrystal as reference and plot sample directions (inverse pole fig-ures) Inverse pole figures are useful if only a single sample direc-tion is of interest eg the compression direction in a compressionexperiment The symmetry of pole figures reflects the symmetry ofthe deformation path In compression experiments pole figures areaxially symmetric The density of poles on the sphere is contouredand then expressed as continuous pole densities usually normal-ized relative to a random distribution and defined as multiples ofa random distribution (mrd) 2ndash5 mrd are moderate CODs20ndash50 mrd very strong CODs The strongest crystal alignmentsin rocks that have been observed are muscovite in slates exceeding100 mrd Fig 16a is a 111 pole figure of rolled copper with roll-

Fig 12 Under stress imposed by pistons a crystal deforms to a new shape by slip of dislocations on a glide plane Since pistons remain in contact with the crystal surfacethere is an effective rotation b In a polycrystal neighboring grains act as effective pistons to transmit the stress

Fig 13 Stress-temperature deformation mechanism map (Langdon and Mohamed1978)

B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90 69

ing R transverse T and normal N sample directions indicatedFig 16b is the corresponding inverse pole figure of the normaldirection Inverse pole figures display the crystal symmetry Bothrepresentations will be used in the following discussion

33 Deformation experiments and rheology

The experiments on plasticity of metals were not applicable tomost minerals because even at elevated temperatures theirdeformation behavior at ambient pressure is generally brittleOne had to wait until high pressure deformation experiments weredeveloped by Griggs (1936) and applied on a wide scale includingolivine (eg Raleigh 1968) Since then sophisticated deformationapparati have been constructed in many laboratories making itpossible to deform rocks at a wide range of pressures and temper-atures They were applied to many minerals and rocks in the crustand upper mantle Studies on olivine (eg Jung and Karato 2001

Hansen et al 2012 Jackson and Faul 2010) documented the com-plex influence of temperature pressure composition (such aswater and iron content) The most sophisticated apparatus wasdeveloped at the Australian National University (Paterson andOlgaard 2000) It allows for deformation experiments on relativelylarge samples (1 cm) in compression tension and torsion Pres-sures are limited to 03 GPa and the limitation in pressure pre-vents these instruments to be used for experiments relevant tothe lower mantle (20ndash150 GPa) and inner core (320ndash360 GPa)

Higher pressure deformation experiments have been reviewedby Weidner and Li (2015) The multi-anvil apparatus called DIAwith three pairs of octahedral pistons (Onodera 1987) has beenmodified to apply stress by preferentially advancing one pistonpair (D-DIA for deformation DIA) The sample can be heated inter-nally Changes in phase structure preferred orientation andmicrostructure can be recorded in situ if the D-DIA apparatus iscombined with a monochromatic synchrotron X-ray beam fordiffraction and imaging (eg Wang et al 2003 2011) The conven-tional D-DIA apparatus has been used to 20 GPa and samples arecylinders 1 mm in diameter (eg Kawazoe et al 2010) A moreadvanced D-DIA (Kawai-type) reaching gt110 GPa with sintereddiamond anvils and smaller samples has been introduced atSPring8 in Japan (Yamazaki et al 2014)

Shear deformation at high pressure can be performed with arotational Drickamer apparatus (RDA) (eg Yamasaki and Karato2001) Shear deformation of a bridgmanite-ferropericlase aggre-gate at 25 GPa and 2100 K has been achieved to large strains(Girard et al 2016) In such torsion experiments the strain variesgreatly as a function of sample radius The experiment documentedthat most of the plastic deformation is accommodated by theweaker ferropericlase

Currently the most accessible method to deform samples atultrahigh pressures (gt500 GPa) is with diamond anvil cells (DAC)where diamonds are used as pistons compressing a small sample(30ndash80 lm in diameter and 50 lm thick) (eg Merkel et al2002 Fig 17) The diamonds are used not only to induce pressurebut also to cause compressive deformation (Fig 17 b c) and theevolution of preferred orientation can be observed in situ if hori-zontal X-rays transmit the sample in radial diffraction geometry(r-DAC) Strong textures have been observed in ferropericlase(eg Merkel et al 2002 Lin et al 2009) perovskitebridgmanite(eg Merkel et al 2003 Wenk et al 2006 Miyagi and Wenk2016 Tsujino et al 2016) and pPv the phase likely to be presentat the core-mantle boundary (eg Merkel et al 2006 2007

Fig 14 2D Sketches of polycrystal plasticity models Gray shades express orien-tation (Left) For the full constraints Taylor model all grains undergo the samedeformation regardless of orientation (Center) The viscoplastic model VPSC treatsgrains as inclusions in an anisotropic viscous medium (Right) In finite elementmodels grains deform differently depending on the orientation of neighbors

Fig 15 Definition of crystal orientation relative to sample coordinates with threerotations (Euler angles) 1 U 2 Projection based on sample coordinate system xy z (pole figure) Crystal coordinate system is defined by axes [100] [010] and[001]

Fig 16 Comparison of (a) 111 pole figure relative to sample coordinates and (b) Ninverse pole figure relative to crystal coordinates for rolled copper Equal areaprojection red colors are high and blue colors are low pole densities N normaldirection R rolling direction and T transverse direction Note the equivalentinformation In the 111 pole figure a maximum in the N direction and in the NDinverse pole figure a maximum in 111

70 B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90

Miyagi et al 2010 2011 Wu et al 2017) Shear deformation canbe induced in rotational DACs (eg Levitas et al 2006) Thismethod has been mainly used to induce phase transformationsand has not yet been applied to study texture evolution at highpressure

In addition to pressure and stress temperature can be inducedin DAC experiments by resistive (eg Liermann et al 2009) andlaser heating (eg Prakapenka et al 2008 Dubrovinsky et al2009) or a combination of the two (Miyagi et al 2013) Tatenoet al (2015) reached temperatures of 6000 K at gt400 GPa on exper-iments on Fe and Fe-Si corresponding to conditions of the Earthrsquos

inner core Obviously there are limitations to DAC experimentssamples are extremely small strain is always compressive andstrain rates are difficult to control

It was surprising to see that silicates and oxides that are brittleat ambient conditions including olivine become ductile at pres-sures of 10GPa even at room temperature and deform by dislo-cation glide (eg Wenk et al 2004) The diffraction image ofMgSiO3 post-perovskite at 150 GPa (Fig 18a) is lsquolsquounrolledrdquo andthe compression direction is indicated by arrows (large 2h smalld Q=1d) (Fig 18b) The elastic lattice distortion (wave-like patternwith azimuth) is related to applied stress and elastic propertiesThe intensity variations with azimuth are indicative of preferredorientation For example there is a strong maximum for 004(fourth order diffraction on the lattice plane 001) in the compres-sion direction This image illustrates why radial diffraction geome-try has to be used to display CPO as function of angle to thecompression direction In axial geometry (X-rays parallel to thediamond axis) Debye-rings have uniform intensity since alldiffracting lattice planes have the same angle to the compressiondirection

A qualitative interpretation of a diffraction image is illustratedin Fig 19 for an experiment with MgGeO3 post-perovskite(Miyagi et al 2011) and used to construct an inverse pole figureof the compression direction (arrow) MgGeO3 is an analog ofMgSiO3 but transforms to pPv at lower pressure There is a maxi-mum for 002 and a minimum for 020 in the compression directionwhich can be plotted in the inverse pole figure (Fig 19 right side)The quantitative deconvolution of diffraction images is not trivialand most often an iterative Rietveld method is applied (egLutterotti et al 2014 Wenk et al 2014) The high pressure syn-chrotron X-ray diffraction deformation images provide quantita-tive information about phases crystal structures density stresselastic properties and preferred orientation

Fig 20a-c shows experimental inverse pole figures of MgSiO3

pPv documenting increasing texture development with pressure-stressndashstrain with a maximum at (001) From the orientation pat-tern active slip systems can be derived by comparing experimentalinverse pole figures with results from polycrystal plasticity calcu-lations that assume certain combinations of slip systems(Fig 20d) Based on the good agreement it can be concluded thatpPv deformed in the experiment by dominant (001)[100] slip(Miyagi et al 2010)

With similar experiments it was suggested that MgSiO3 bridg-manite deforms dominantly by slip on (001) planes in [100][010] and h1 1 0i directions (eg Miyagi and Wenk 2016) but sim-

Fig 18 (a) Diffraction image of MgSiO3 post-perovskite at 150 GPa (b) Unrolled diffractiochanges in Q are due to elastic distortion of the crystal lattice under compression Botquantitative information such as inverse pole figures

Fig 17 Diamond anvil cell for radial diffraction experiments The X-ray beam ishorizontal (a) illustrates the cell and the insert is an enlargement with diamondsand gasket to contain the sample (b c) illustrate that diamonds not only applypressure but also compressive stress that deforms the sample and produces CPO

B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90 71

ple shear experiments in a D-DIA apparatus indicate (100)[001]slip (Tsujino et al 2016) Ferropericlase likely deforms by 110h110i slip (eg Stretton et al 2001 Merkel et al 2002 Linet al 2009) at high pressure conditions For Ca-perovskite domi-nant 110h110i slip was proposed (Miyagi et al 2006 2009)

So far most DAC high-pressure deformation experimentsextracted COD information from intensity variations along Debyerings (eg Fig 18) A new method called multigrain is still underdevelopment It obtains orientation information from individualgrain diffractions (eg Barton and Bernier 2012 Rosa et al2015 Langrand et al 2017) and is especially applicable to coarseraggregates Nisr et al (2012) used information about dislocationsfrom distortion of single crystal diffraction patterns of the post-perovskite analog MgGeO3 and suggested dominant slip on 110and (001) planes

It should be mentioned that information from such high pres-sure experiments is by no means unambiguous Obviously defor-mation conditions in experiments and simulations differconsiderably from those in the deep Earth just to mention temper-ature grain size strain rate interaction of dislocations and interac-tion between grains Furthermore not all CPO patterns that areobserved are due to deformation but could be inherited from orien-tation patterns of precursor phases such as for pPv from perovskite(Dobson et al 2013) or enstatite (Merkel et al 2006 2007 Miyagiet al 2011) Also slip systems may not be the same for pPv phasesof different compositions such as MgGeO3 CaIrO3 NaMgF3 orMn2O3

A different approach has become very important computationof Peierlrsquos stresses and lattice friction for dislocation systems basedon bonding characteristics It was originally developed for metals(eg Kubin et al 1992 Devincre and Kubin 1997) and has morerecently been applied to minerals in the mantle where it allowsto predict slip system activities for a wide range of temperaturendashpressurendashstrain rate conditions (eg Carrez et al 2007Mainprice et al 2008 Cordier et al 2012) Amodeo et al (20122014 2016) propose a switch from 110h010i slip to 100h0 1 1i slip in periclase with pressure Kraych et al (2016) suggest(010)[100] slip in bridgmanite at high pressure According tothese calculations the strength of bridgmanite increases greatlywith pressure and at 60 GPa bridgmanite appears 20 times stron-ger than periclase The critical resolved shear stress decreasesabout 20 from strain rates of 105 s1 (which corresponds to

n image as function of Q (Q = 1d) Intensity variations with azimuth illustrate CPOtom experimental data above fit of the data with the Rietveld method to extract

Fig 19 Explanation of the relationship between DAC diffraction image and inverse pole figure Left Unrolled diffraction image of MgGeO3 post-perovskite Some diffractionlines are labeled The sinusoidal variations are due to imposed stress High stress (high Q low d) is indicated by arrows On the right side is a conceptual construction of theinverse pole figure of the compression axis based on relative diffraction intensities (Miyagi et al 2011)

Fig 20 Inverse pole figures for MgSiO3 post-perovskite (AndashC) experiments (D) Plasticity model with dominant (001) slip equal area projection (Miyagi et al 2010)

72 B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90

experimental values) to 1014 s1 corresponding to likely values atdeep mantle conditions (Fig 21a) The opposite is the case for pPvwhich appears much weaker than periclase at high pressure hightemperature and slow strain rates (Fig 21b Goryaeva et al 20152016) Also the predicted weakest calculated slip system for post-perovskite at deep mantle conditions is (010)[100] correspondingto the layered crystal structure (Fig 21c) but different from thatobserved in DAC experiments (Miyagi et al 2010 Wu et al 2017)

It should be mentioned that a single slip system is not sufficientto deform a polycrystal In the case of the Taylor model at least 5systems have to be active to produce an arbitrary strain (Mises1928) This is relaxed for the self-consistent model but also hereseveral slip systems are active The choice of activity depends onthe crystal orientation relative to the applied stress (Schmid fac-tor) TEM investigations confirm this though some slip systemsusually dominate and the literature refers to the lsquolsquodominantrdquo slipsystem Some dominant slip systems for deep Earth minerals aresummarized in Table 2

34 Elastic properties

Elastic properties of crystals at conditions pertaining to thelower mantle are critical to link microstructural properties of therock with seismic observations The most straightforward experi-mental method that has been applied to many lower mantle min-erals is Brillouin scattering (see review by Speziale et al 2014) andenergy-dispersive X-ray diffraction (eg for calcium silicate per-ovskite Shieh et al 2004) A different approach is with first prin-ciples calculations at high pressure and temperature (for someapplications to bridgmanite CaSiO3 perovskite and pPv see egZhang et al 2013 Wentzcovitch et al 2005 Kawai and

Tsuchiya 2015) First principles results look fairly consistent forminerals at lower mantle conditions but as we will see in Sec-tion 62 predictions for iron at inner core conditions are stillambiguous Furthermore the actual composition of the mineralsparticularly the iron content can be significant (eg Koci et al2007) Values of stiffness coefficients and P-wave anisotropy (An = 200(Pmax Pmin)(Pmax + Pmin) for some low mantle mineralsat lowermost mantle conditions are listed in Table 3 Fig 22 givescorresponding S velocities of single crystals with black lines corre-sponding to the orientation of the fast S-wave polarization As canbe seen in Table 1 periclase and pPv have the highest P-wave ani-sotropy and Ca-perovskite is least anisotropic The S-wave aniso-tropy is considerably higher for pPv and periclase than forbridgmanite and particularly CaSiO3 perovskite

To obtain elastic properties of aggregates one has to averageover all orientations and corresponding elastic tensors takingphase fractions into account Simple averages are upper bound(Voigt 1887) and lower bound (Reuss 1929) Generally an inter-mediate arithmetic mean (Hill 1952) or a geometric mean(Matthies and Humbert 1995) are preferred All these models donot take grain shape into account which is not very significantfor crystalline phases but becomes important for systems withplaty minerals such as graphite or sheet-silicate containing rocksand aggregates with flat oriented pores For such cases a self-consistent (Matthies 2012 Vasin et al 2013) or differential effec-tive medium approach (eg Hornby et al 1994) should be consid-ered It is probably not important for the lower mantle

Note that S-waves passing through anisotropic media have arbi-trary polarization directions in the plane perpendicular to thedirection of propagation as is best displayed for the fast directionof single crystals in Fig 22 but applies also to aggregations of ori-

Fig 21 Critical resolved shear stress CRSS for dislocation glide activities as functionof temperature of (a) bridgmanite at 60 GPa (from Kraych et al 2016) and MgO(from Amodeo et al 2016) at strain rates 105 s1 and 1014 s1 (b) post-perovskiteat 120 GPa at strain rate 1016 s1 (from Goryaeva et al 2016) compared with MgO(from Amodeo et al 2012) Courtesy of P Cordier

B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90 73

ented crystals Seismologists generally consider the projection ofthat polarization direction onto horizontal and vertical axes Thisis convenient because differences in arrival times and waveformsin this representation can be expressed in terms of apparent verti-cal transverse isotropy (VTI) which because of limited azimuthalsampling is often the only anisotropic constraint that can beobtained

4 Linking seismology and mineral physics through predictionsof anisotropy in geodynamic models

41 Isotropic geodynamic models for upper mantle convection

Ever since the concept of plate tectonics became accepted in the1960s convective movements in the Earthrsquos mantle have been pro-posed such as upwelling along oceanic ridges (eg Hess 1964Cann 1968 Fig 1b) The first quantitative models based on hydro-dynamics emerged in the eighties (eg Hager and OrsquoConnell 1981)

Table 2Proposed dominant slip systems in deep Earth minerals

Ferropericlase Lower P 110110High PT also 100011

Bridgmanite Low P (001)[100] [010] 110High P (100)[001](010)[100]

pPv (001)[100](010)[100]

Ca-perovskite 110110e-iron (0001)1120 subordinate 1010

Geodynamic models have been mainly applied to the upper mantleand we will not discuss them here in detail (see eg review by Longand Becker 2010)

Many convection models have been developed to understandthe evolution of the deep Earth Calculations generally assume aviscous fluid and use non-dimensional equations for the conserva-tion of mass momentum and energy applying the Boussineqapproximation Critical parameters are Rayleigh number viscosityboundary temperatures In order to evaluate the strain evolutionduring the convection process tracers are introduced that recordthe velocity gradient tensor at each time step along the path ofthe tracer If the deformation mechanisms are known (eg disloca-tion glide) polycrystal plasticity calculations can be used to calcu-late the evolution of crystal preferred orientation based on thestrain recorded by tracers

Most geodynamic models assume a viscous isotropic mediumwith a smoothly varying viscosity structure and the microstruc-tural processes leading to preferred orientation are introducedpost-mortem Considering an anisotropic medium that constantlychanges its properties greatly increases the complexity of geody-namic calculations However there are models in metallurgy suchas extrusion of an aggregate that illustrate the importance of ananisotropic material behavior (eg Beyerlein et al 2003)

42 Review of upper mantle anisotropic models

We will start the discussion of anisotropic convection byreturning to a simple 2D model (Dawson and Wenk 2000) thatwas originally issued as an educational video by AGU (1999) andcan now be downloaded in digital form (httpepsberkeleyedu~wenkTexturePageMantle-Videohtm) At high Rayleigh number(low viscosity) heat transfer occurs by convection rather than con-duction corresponding to conditions in the Earthrsquos mantle Convec-tion is driven by temperature gradients As aggregates move alongstreamlines the orientation of grains is constantly updated and thelocal texture affects the next deformation step which introducesconsiderable heterogeneities It was surprising to find locallyheterogeneous CPO patterns in the 2D convection cell representingthe upper mantle shown as [100] pole figures of olivine after100 my (Fig 23) Some regions have strong and others very weakpatterns that can be attributed to heterogeneous deformation dueto CPO development and result in lsquolsquoanisotropicrdquo viscosity

Some complexities of different plasticity models for a simplecase of upwelling have been investigated by Blackman et al(1996 2002) and Castelnau et al (2009) If a lower bound behavioris assumed (Sachs 1928) there is very strong CPO developmentFor self-consistent models (Lebensohn and Tomeacute 1993) rotationsare reduced If dislocation glide is combined with dynamic recrys-tallization both grain growth and grain growth combined withnucleation resulting orientation patterns can be very differentRecrystallization is likely in the deep Earth with high temperatureand large strains where grain boundary migration is likely tooccur We will return to the issue of recrystallization in Section 48

Merkel et al (2002) and Lin et al (2009)Amodeo et al (2016)Miyagi and Wenk 2016Tsujino et al (2016)Kraych et al (2016)Miyagi et al (2010) and Wu et al (2017)Goryaeva et al (2016)Miyagi et al (2009) and Ferreacute et al (2009)

Merkel et al (2004) and Miyagi et al (2008)

Fig 3 Background lsquolsquoVoting maprdquo based on 5 shear wave velocity tomographicmodels modified (from Lekic et al 2012) Locations in D00 where 5 models agreethat Vs is lower than average or higher than average are shown in red and dark bluerespectively White ellipses indicate locations where shear wave splitting observa-tions with Vsh gt Vsv have been attributed to anisotropy in D00 These include regionswhere azimuthal anisotropy has been reported Green ellipses indicate regionswhere strong lateral variations of anisotropy in D00 have been reported at the edgesof the African LLSVP (14 17 21) the Perm anomaly (19) and in the south Pacific(719) Blue ellipses with broken lines indicate regions where Vsv gt Vsh has beenreported andor null splitting See Table 1 for references to numbers and lettersWhite bars and blue broken lines (no splitting) are from Niu and Perez (2004)

B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90 61

for which no splitting was present in SKS Because the absence ofthe latter indicated that the data were not contaminated by uppermantle anisotropy they suggested that the splitting originated inthe deep mantle and could be due to the presence of anisotropyEarlier Mitchell and Helmberger (1973) and Lay and Helmberger(1983) had observed time shifts between the arrival of ScSH andScSV but attributed them to the presence of a high velocity regionat the base of the mantle Many studies followed in the 1990s doc-umenting splitting times of up to 10 s in shear waves such as ScSand Sdiff (Fig 2) that propagate quasi-horizontally in D00 and inter-preted them as indicating the presence of several percent of VTI(Vertical Transverse Isotropy) in the deep mantle (see Lay et al1998 and Kendall and Silver 1998 for early reviews)

As different areas of the world were progressively sampled thepicture that emerged was that globally the vertically polarizedwave (SV) is generally delayed with respect to the horizontallypolarized one (SH) in the circum-pacific ring where isotropic shearwave velocities are higher than average in D00 On the other handintermittent splitting and sometimes delayed SH with respect toSV was observed on paths sampling the large low shear velocityprovinces (LLSVPs) in the central Pacific and under Africa (Fig 3)Additional reports of splitting in ScS and Sdiff have been publishedin the last two decades most of them attributed to anisotropy inD00 A review of observations of shear wave splitting originatingin D00 can be found in Wookey and Kendall (2007) and Nowackiet al (2011) as well as Lay (2015) Here we focus primarily onthe most recent contributions while an updated list of observa-tions is given in Table 1 and Fig 3

Several important challenges affect studies of shear wave split-ting in D00 One is the necessity to account for (or avoid) contamina-tion of seismic waveforms by strong upper mantle anisotropysampled by the body waves considered (Fig 2) Another challengeis the poor azimuthal sampling of D00 at any given location due tothe limited global distribution of earthquake sources and receiversThis makes it difficult to distinguish between different possiblecauses of anisotropy whether due to periodic layering or crystalalignment and whether the nature of the anisotropy is transverseisotropy with a vertical (VTI) or tilted (TTI) axis of symmetry or

SScS

SKKS

SKS

Fig 2 Raypaths through the Earth of the main seismic body wave phases used forstudying anisotropy in the deep mantle Asterisk is earthquake location trianglesare receiver stations

perhaps involves more complex symmetries Also in the case ofSdiff an apparent delay of SVdiff may be due to waveform distorsionin a laterally heterogeneous but isotropic structure due to the factthat the amplitude of SVdiff decays rapidly with distance in regionsof fast isotropic velocity (eg Vinnik et al 1995 Komatitsch et al2010) More generally apparent splitting in S waves sampling theD00 region may sometimes be due to other causes than anisotropysuch as propagation in a complex heterogeneous medium near theboundary between the solid mantle and the liquid core whichrequires more sophisticated modeling than infinite frequency raytheory (Monteiller and Chevrot 2010 Borgeaud et al 2016Nowacki and Wookey 2016) Careful waveform analysis is there-fore necessary before attributing splitting observations to aniso-tropy Some of the splitting results listed in Table 1 may need tobe re-evaluated in that context However consistency in the split-ting results obtained using different types of waves across a num-ber of regions of the world and in some cases detailed waveformmodeling indicates that in general invoking anisotropy as a causefor the observed splitting is a robust result At the present timeinterpretation in terms of layering or CPO requires invoking possi-ble constraints from other fields than seismology and remainsuncertain

22 Accounting for upper mantle anisotropy

In order to account for upper-mantle anisotropy an approachtaken in early studies of Sdiff splitting was to only consider deepearthquakes and paths for which SKS and SKKS do not presentany evidence of splitting (eg Vinnik et al 1989 1995) Selectingobservations for deep earthquakes assures that contamination byanisotropic effects in the upper mantle on the source side can lar-gely be avoided On the station side the paths of Sdiff and SKSSKKSare very close in the upper mantle (Fig 2) while they diverge in thedeep mantle Also only Sdiff spends significant time within D00 Theabsence of splitting in SKSSKKS indicates that either there is noanisotropy in the upper mantle region sampled on the receiverside or the direction of the great circle path is along the null split-ting direction Any splitting observed in Sdiff can thus be attributedto the deep mantle

However such geometries are exceptional Therefore it isimportant to find ways to correct for the widespread and strong

Table 1Summary of local studies of anisotropy in D00

Authors Region Type ofseismicwaves

VSH gt VSV

A Wookey and Kendall (2007)and Refs therein

Caribbean

Kendall and Silver (1996) Caribbean SSdiffDing and Helmberger

(1997)Caribbean ScS

Rokosky et al (2004) Caribbean ScSB Wookey and Kendall (2007)

and Refs thereinAlaska

Lay and Young (1991) Alaska SScSMatzel et al (1996) Alaska SScSSdiffGarnero and Lay (1997) Alaska SScSSdiffWysession et al (1998) Alaska SdiffFouch et al (2001) Alaska SSdiff

E Ritsema (2000) Indian Ocean SF Thomas and Kendall (2002) Siberia SScSSdiffI Usui et al (2008) Antarctic Ocean S1 Kendall and Silver (1998) NW Pacific SScSSdiff3 Vinnik et al (1995 1998b) north central Pacific Sdiff6 Wookey et al (2005b) N Pacific ScS8 Long (2009) East Pacific SKS-SKKS9 Niu and Perez (2004) N America Asia SKSSKKS11 Vanacore and Niu (2011) Caribbean SKS-SKKS12 He and Long (2011) NW Pacific PcSScS SKS

SKKS13 Wookey and Kendall (2008) Caribbean ScS18 Thomas et al (2007) W Pacific ScS20 Fouch et al (2001) North central Pacific SSdiffSV lt SH4 Pulliam and Sen (1998) Central Pacific SC Ritsema et al (1998) Central Pacific SSdiff22 Kawai and Geller (2010) Central Pacific SScSSKSTiltedazimuthallaterally varying5 Russell et al (1998 1999) North Central Pacific ScS7 Ford et al (2006) South Pacific SSdiffA Garnero et al (2004a) Caribbean SScSSdiffA Maupin et al (2005) Caribbean SScSSdiffA Rokosky et al (2004 2006) Caribbean ScSG Wookey et al (2005a) North West Pacific ScS23 Restivo and Helffrich

(2006)North America SKS SKKS

21 Wang and Wen (2007) EastSouth Africa SKSSKKS10 Nowacki et al (2010) Caribbeanwest US ScS14 Lynner and Long (2012) Central Africa SKS-SKKS15 Cottaar and Romanowicz

(2013)South edge of AfricanLLSVP

Sdiff

16 Lynner and Long (2014) EastSouth Africa SKS-SKKS19 Long and Lynner (2015) Near Perm Anomaly SKS-SKKS17 Ford et al (2015) East Africa SKS-SKKSIsotropic or weak anisotropy2 Kendall and Silver (1996) South Pacific SScSSdiffH Garnero et al (2004b) Atlantic SSdiff9 Niu and Perez (2004) South Africa Antarctica

Southeast PacificSKSSKKS

21 Wang and Wen (2007) Eastern Atlantic SKSSKKS

62 B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90

upper mantle anisotropy sampled along the path of deep mantleseismic waves For example Vinnik et al (1998a) proposed a refer-ence event method to correct Sdiff waveforms for unknown uppermantle anisotropy using SKS and SKKS waveforms In the pasttwo decades characterization of upper mantle anisotropy fromSKS splitting data has progressed significantly (see review byLong and Silver 2009) making it possible to apply relatively robustcorrections in 00known00 upper mantle models both on the sourceand receiver sides and thus augment the number of D00 locationsthat can be sampled

Another approach to minimize effects of upper mantle aniso-tropy has been the use of differential measurements on pairs ofphases One such suitable pair is S and ScS which have similarpaths in the upper mantle on the source and station side but at

appropriate distances only ScS samples D00 (Fig 2) while S samplesa portion of the lower mantle which is assumed to be isotropic (egWookey et al 2005a Nowacki et al 2010) Similarly while SKSand SKKS splitting is most strongly acquired during propagationin the upper mantle the paths of SKS and SKKS waves diverge sig-nificantly in the lowermost mantle so that differential splitting ofthese two phases can sometimes be attributed to anisotropy in thedeep mantle (eg Hall et al 2004 Niu and Perez 2004 Restivo andHelffrich 2006 Wang and Wen 2007) Such an approach has beenapplied to several regions of the world (eg Long 2009 He andLong 2011 Vanacore and Niu 2011 Lynner and Long 20122014 Long and Lynner 2015 Ford et al 2015) Results consis-tently show strong and complex anisotropy on the borders of theLLSVPrsquos and interestingly also in the vicinity of the Perm Anomaly(Long and Lynner 2015) a low velocity anomaly seen at the base ofthe mantle in all tomographic models in the vicinity of the town ofPerm (Russia) and of smaller lateral extent ( 900 km) but corre-sponds to a similar reduction in shear velocity as found in theLLSVPs (eg Lekic et al 2012 Fig 3)

23 Results from array studies

Earlier observations and forward modeling studies of D00 aniso-tropy mostly relied on data from isolated stations which made itdifficult to constrain the geometry of anisotropy for lack of sam-pling of the target regions by waves propagating in different direc-tions (eg Maupin 1994) Thus most studies only reported thedifferences in SH and SV propagation times leading to models ofapparent VTI Yet evidence for azimuthal anisotropy has been sug-gested either from waveform complexity (eg Garnero et al2004a Maupin et al 2005) or when the geometry permitted frommeasurements of splitting on paths sampling the target region inat least two directions (eg Wookey and Kendall 2008) With theadvent of denser broadband arrays more detailed studies haveemerged in recent years aiming at the very least to distinguishVTI from radial anisotropy with tilted axis of symmetry (TTI) withimplications for the interpretation of observations in terms ofintrinsic or extrinsic anisotropy (eg Long et al 2006)

Regions of the world where this has been possible so far arecentral America exploiting ScS S data from the dense USArray(Nowacki et al 2010) and the northwest Pacific (He and Long2011) using ScS data from F-net in Japan Studies of Sdiff at thesouthern border of the African LLSVP based on data from the Kaap-val array show lateral variations in anisotropy (To et al 2005Cottaar and Romanowicz 2013) with strong anisotropy in the fastvelocity region outside the LLSVP increasing towards its borderand apparently disappearing inside it Although caution must betaken when interpreting apparent splitting in Sdiff due to isotropicheterogeneity potentially affecting SVdiff in a significant way(Komatitsch et al 2010) the strong elliptical shape of the particlemotion outside of the African LLSVP (Fig 4 and To et al 2005)where isotropic velocities are relatively fast contrasting with thelinear particle motion for paths travelling inside the LLSVP cannotbe accounted for by isotropic heterogeneity This was demon-strated in the follow-up study of Cottaar and Romanowicz(2013) in which the waveforms of Fig 4 and others were modelledusing the spectral element method a numerical method for 3Dseismic wavefield computations which can take effects of 3D iso-tropic heterogeneity into account accurately Differential splittingin S and ScS has also been exploited in the north Pacific (Wookeyet al 2005a) and in east Africa (Ford et al 2015) where remark-ably several azimuths can be sampled

The recent studies have confirmed earlier results with in gen-eral Vshgt Vsv in the ring of faster than average velocities sur-rounding the two LLSVPs and absence of significant splitting orVshltVsv found primarily within the LLSVPs (Fig 3 Table 1)

Fig 4 Example of change of character of particle motion for paths sampling theborder of the African LLSVP (a) Map showing the paths sampled plotted on top of abackground shear wave tomographic model (SAW24B16 Meacutegnin and Romanowicz2000) The portion of path sampling the D00 region is highlighted in yellow (b) and(c) shows particle motions of Sdiff at distances of 120o and at two azimuths In (b)the path in D00 is outside of the LLSVP and in (c) the path in D00 is inside the LLSVP(from To et al 2005) The color indicates the time with respect to predicted Sdiffarrival from PREM Black 35 to 5 s Blue 5 to 20 s Green 20 to 45 s Red 45 to70 s The elliptical particle motion in (B) contrasts with the linear particle motion in(c) This cannot simply be explained by lateral heterogeneity in isotropic velocity asone would expect larger amplitudes in SV for waves propagating inside the lowvelocity LLSVP This interpretation was later confirmed by 3D numerical waveformmodelling (Cottaar and Romanowicz 2013) (For interpretation of the references tocolor in this figure legend the reader is referred to the web version of this article)

B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90 63

The recent results indicate variability of anisotropy at relativelyshort scales with evidence for azimuthal anisotropy with differentorientations of fast velocity axes at least in regions of faster thanaverage isotropic shear velocity Interestingly the studies ofCottaar and Romanowicz (2013) Lynner and Long (2014) andFord et al (2015) consistently show changes in anisotropy acrossthe border of the African LLSVP with stronger anisotropy outsideof it practically disappearing inside it (eg Fig 5) Interestinglythe same trend although less sharply defined because of the chal-lenging geometry is likely present at the northern edge of the Paci-fic LLSVP (Fig 6) Indeed all studies of the latter region considerpaths from Fiji-Tonga sources to stations in north America Differ-ent results are found for different distance ranges with VsvgtVshfor the shorter distances sampling inside the LLSVP (as well asabove D00) and VshgtVsv at longer distances (Sdiff) which samplea significant portion of the fast Vs region outside of the LLSVPVinnik et al (1995 1998b) used Sdiff data and found VSHgtVSV theportion of the corresponding paths inside the LLSVP was smalland Vinnik et al (1998b) showed that splitting only occurred fordistances larger than 102o when paths sampled more of the fastregion outside of the LLSVP Likewise Fouch et al (2001) andRitsema et al (1998) used S Sdiff and found VshgtVsv for larger dis-tance paths while VsvgtVsh for shorter distance paths that samplewithin the LLSVP and above D00 as did Kawai and Geller (2010)Pulliam and Sen (1998) and Russell et al (1998) used S and ScSrespectively at shorter distances sampling inside the LLSVP andfound VsvgtVsh

All these results point in the same direction evidence for signif-icant anisotropy with generally VshgtVsv within the ring of fastvelocities surrounding the Pacific and African LLSVP possiblyincreasing and tilting at their borders but vanishing or changingsign (VsvgtVsh) inside the LLSVPrsquos

24 Results from global anisotropic tomography

Gaining improved understanding of the distribution and natureof seismic anisotropy at the base of the mantle requires better glo-bal sampling with accurate corrections for upper mantle aniso-tropy One possible approach is to construct global whole mantletomographic models of anisotropy Such an approach is attractivebecause a variety of seismic waveforms can be included in partic-ular fundamental and overtone surface waves which provide con-straints on the strong anisotropy in the uppermost mantle (egDebayle and Ricard 2013) Combining surface wave data with var-ious body waveforms that illuminate the entire mantle should ulti-mately allow improved resolution and characterization of deepmantle anisotropy So far this has proven very challenging forthe deep mantle

Indeed most successful has been the tomographic characteriza-tion of shear wave azimuthal anisotropy in the uppermost 200 kmof the mantle at the global scale using Rayleigh wave dispersiondata (eg Tanimoto and Anderson 1984 Montagner andTanimoto 1990 1991 Fig 1) More recent models developed bydifferent groups show broadly consistent trends (eg Trampertand Woodhouse 2003 Ekstroumlm 2011 Debayle and Ricard 2013Yuan and Beghein 2013) On the other hand the robustness of glo-bal scale transition zone azimuthal anisotropy models that utilizesurface wave overtone information (eg Trampert and van Heijst2002 Yuan and Beghein 2013) is still debated This is becausethe anisotropic signal in overtone surface waves is weak the azi-muthal sampling far from ideal and the number of parametersneeded to invert for azimuthal anisotropy at the global scale evenwhen considering only the dominant terms in 2-w (where w is theazimuth) is very large likely resulting in trade-offs with isotropicstructure It is not possible at present to extend this type of studyto the deep mantle as the sensitivity of available long period over-tone data becomes too weak and azimuthal coverage for bodywaves provided by the current geometry of sources and stationsis not sufficient

Thus tomographic imaging of anisotropy in the whole mantlecan at present only hope to resolve the simplest form of aniso-tropy that does not have as strong requirements on azimuthal cov-erage which is VTI (or apparent VTI) Such studies are based onrelatively long period waveforms mostly sensitive to shear veloc-ity combining fundamental mode surface waves surface waveovertones and shear body waves and aim at solving for the distri-bution of only two anisotropic parameters Vsh and Vsv or alter-natively isotropic velocity Vsiso and the anisotropic parameter n =(VshVsv)2 (Panning and Romanowicz 2004 2006 Panning et al2010 Kustowski et al 2008 French and Romanowicz 2014Moulik and Ekstroumlm 2014 Auer et al 2014 Chang et al 20142015) The other three anisotropic parameters that are necessaryto fully describe a VTI medium are scaled to Vsiso and n using scal-ing relations that are appropriate for the upper mantle (egMontagner and Anderson 1989) but may be questionable for thelower mantle However this may not be a significant issue giventhe dominant sensitivity of the waveforms considered to shearvelocities While the resulting models show qualitative agreementat long wavelengths details vary frommodel to model significantlyenough not to be trustworthy for quantitative interpretations

These models do agree on the following observations on aver-age radial anisotropy is strongest in the uppermost mantle andmost of the lower mantle exhibits little radial anisotropy (Fig 7)

Fig 5 a and b Whole mantle depth cross sections through the isotropic Vs part of model SEMUCB_WM1 (French and Romanowicz 2014) at the southern (a) and eastern (b)edge of the African LLSVP where rapid variations in the direction and strength of anisotropy have been reported decreasing from outside (blue) to inside (pink) the LLSVP inc) the map view is from Lynner and Long (2014) with background shear velocity model GyPSuM of Simmons et al (2012) The cross-section location is indicated on the mapby a straight line c and d corresponding cartoons proposed by the authors respectively (c) Cottaar and Romanowicz (2013) (d) Ford and Long (2015)

64 B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90

Inmostmodels there is an indication of an increase in anisotropy inD00 with Vshgt Vsv (n slightly larger than 1) although there is vari-ability among models due to a combination of parametrizationtypes of seismic waves considered and theoretical assumptions

Common 3D features of these models in D00 are a predominanceof Vsh gt Vsv outside of the LLSVPs with patches of Vsh lt Vsv con-fined within the LLSVPs in agreement with local studies (Fig 8)However the current models do not show consistency in theamplitude of the lateral variations in n nor the wavelengths ofthese variations This is partly due to the parametrization chosenFor example Panning and Romanowicz (2004 2006) and Aueret al (2014) allowed relatively short wavelength lateral variationsin n while Moulik and Ekstroumlm (2014) and French andRomanowicz (2014) chose to assign shorter wavelength lateralvariations to isotropic Vs while constraining the anisotropic partof the model to be smooth Theoretical assumptions on wave prop-agation are also important ray theory is not valid for modelling ofSdiff nor is it valid to use the surface wave approximation for mod-elling this phase as shown by Li and Romanowicz (1995) So faronly the Berkeley models are constructed taking into account finitefrequency effects rather than ray theory for body waves (Panningand Romanowicz 2004 2006 French and Romanowicz 2014)

One fundamental issue is that Sdiff and ScSn data (with ngt1) arenecessary to obtain good coverage of D00 at the global scale As dis-cussed previously SVdiff decays rapidly with distance in modelssuch as the reference model PREM (Dziewonski and Anderson1981) where the velocity in D00 is relatively fast The global datasetsare thus necessarily biased although to various degrees depending

on the particular dataset by the predominance of SHdiff introduc-ing trade-offs between isotropic and anisotropic structure (egKustowski et al 2008 Chang et al 2015) and making it only pos-sible to resolve the very longest wavelengths of VTI in D00 withpoor constraints on their amplitude

In summary robustly mapping even the simplest component ofseismic anisotropy apparent VTI at the base of the mantle at highresolution using a tomographic approach is still a challenging openquestion let alone constraining azimuthal anisotropy at the globalscale Still available global models agree with local studies aboutthe prevalence of VshgtVsv in regions of faster than average velocityin D00

As for P wave anisotropy in the deep mantle only few studieshave tried to constrain it so far Several studies have attemptedto retrieve the global average variation with depth of the radiallyanisotropic parameter g = (VphVpv)2 using normal mode data(Montagner and Kennett 1996 Beghein et al 2006) finding someindication that the anisotropy in gmay be anticorrelated with thatof n in the D00 region with however strong trade-offs with density(to which normal mode data are also sensitive) Note that the anti-correlation of isotropic P and S velocities at long wavelengths inthe deep mantle is in contrast better established (eg Su andDziewonski 1997 Kennett and Widyantoro 1998 Masters et al2000 Ishii and Tromp 1999 Romanowicz and Breacuteger 2000) Thepossibility of P wave anisotropy in the deep mantle using P wavedata (mantle and core phases) has been investigated by Boschiand Dziewonski (2000) concluding that anisotropy may be smallwith significant trade-offs with core-mantle boundary topography

Fig 6 Zoom on the northern edge of the Pacific LLSVP The background tomographic model is the isotropic Vs part of model SEMUCB_WM1 (French and Romanowicz 2014)(A) Map view with locations of studies of D00 shear wave splitting suggesting a change of character of anisotropy across the boundary of the LLSVP Green dots indicate thelocation of major hotspots Black line with white and purple dots is the great circle path corresponding to the depth cross section shown in (B) displaying the Hawaian plumeand transition from low to fast velocities in D00 Kawai and Geller (2010) Pulliam and Sen (1998) and Russell et al (1998) find VSV gt VSH while Ritsema et al (1998) Fouch et al(2001) and Vinnik et al (1998) find that Vsh gt Vsv increasingly so for paths sampling the fast region outside of the LLSVP Note that the color saturation of the tomographicmodel is different in (A) and (B)

B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90 65

and outer core structure The possible anticorrelation of P and Sradial anisotropy in the D00 must therefore be considered with cau-tion at the present time when used as a constraint in modeling

Given these difficulties a currently explored possible avenue isto try and combine constraints not only from seismology but alsofrom mineral physics and geodynamics Each of these approachestaken individually involves many assumptions and uncertaintiesbut by combining them the hope is that the space of acceptablemodels for anisotropy and its causes can be further reduced Theidea is to start with the strain field inferred from a mantle circula-tion model compute the corresponding texture development andpredicted seismic anisotropy using available information on crystalplasticity and elasticity for different lower mantle minerals andcompare these predictions with seismic observations This shouldprovide constraints on the mineral physics assumptions as wellas the deep mantle dynamics or at least allow us to rule out someclasses of models Note that in this approach the fundamentalassumption is that anisotropy is due to CPO development resultingfrom large-scale mantle flow

Before describing these efforts in more detail we will reviewcurrent knowledge and capabilities in mineral physics and describehow seismology and mineral physics can be linked through geody-namics modeling

3 Mineral physics perspective on the deep mantle

31 Dominant mineral phases in the lower mantle

Ringwood (1962) speculated about the composition of thelower mantle suggesting that olivine Mg2SiO4 would first breakdown to spinel Mg2SiO4 and then to MgSiO3 with a lsquolsquocorundum-

likerdquo structure and periclase (MgO) Liu (1974) synthesized thisstructure at high temperature and pressure and identified it asMgSiO3 perovskite (which has recently been named bridgmaniteTschauner et al 2014) At high pressure bridgmanite transformsto post-perovskite pPv (eg Murakami et al 2004 Oganov andOno 2004 Tateno et al 2009 Fig 9a) and this may be the mostimportant phase near the core-mantle boundary particularly alonga cold geotherm within subducting slabs (Fig 9b) Thus it appearsthat cubic periclase (Fig 10a) orthorhombic bridgmanite (Fig 10b)and orthorhombic post-perovskite (Fig 10c) are the dominantminerals in the lower mantle Periclase has the same highly sym-metric structure as halite (NaCl) with close-packed MgOVI octahe-dral coordination polyhedra Bridgmanite (spacegroup Pbnm) is adistorted cubic perovskite structure with SiOVI coordination octa-hedra linked over corners and Mg2+ in large interstices Post-perovskite (spacegroup Cmcm) has layers of SiOVI octahedra alter-nating with layers of Mg The layers are parallel to (010) It isisostructural with CaIrO3 (eg Hunt et al 2009) While the pseu-docubic perovskite structure is elastically fairly isotropic the lay-ered post-perovskite structure is highly anisotropic As we willsee post-perovskite is of critical importance for anisotropy in thelower mantle In the following discussion we will use mostly theabbreviation pPv

Most lower mantle minerals (gt660 km) cannot be studied atsurface conditions Even if lower mantle material has reached thesurface by upwelling minerals have undergone phase transitionsThus information about phase diagrams is based on in situ observa-tions in high pressure experiments and ab initio calculations

Irifune and Tsuchiya (2015) have reviewed the mineralogicalcomposition of the lower mantle Different bulk compositions ofthe lower mantle have been proposed Ringwood (1962 1975) sug-gested a peridotitic-lsquolsquopyroliticrdquo composition (Fig 11a) Subducting

Fig 7 Comparison of depth profiles throughout the mantle of global average radialanisotropy parameter n = (VshVsv)2 in 6 recent global shear velocity models n = 1corresponds to isotropy Model S362ANI (Kustowski et al 2008) is isotropic in thelower mantle While there are differences between models all of them agree thatradial anisotropy is strongest in the first 200 km of the mantle and very weak inmost of the lower mantle In D00 on average Vsh is equal of slightly faster than Vsv

66 B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90

slabs may correspond to more siliceous aluminous and Ca-richmid-ocean ridge basalts (MORB eg Irifune and Ringwood 1993Fig 11b) In both cases MgSiO3-perovskite (bridgmanite) domi-nates in large volumes of the lower mantle but for MORB compo-sitions high pressure silica and alumina phases are alsosignificant and there may be no ferropericlase Calcium perovskite(CaSiO3) is cubic (spacegroup Pm3 m) at lower mantle conditions(eg Wang et al 1996 Kawai and Tscuchiya 2015) and is animportant component at depths beyond 750 km It distorts to atetragonal structure at low temperature and high pressure (egShim et al 2002)

As more details about the lower mantle are revealed composi-tional heterogeneities become apparent (eg Badro et al 2003 LiY et al 2014) Higher concentrations of Si Al and Fe add consider-able complexity The diverse composition is in part the result ofsubduction of slabs composed of crust and upper mantle Silica(SiO2) may exist as stishovite with a rutile structure and 6-foldcoordination or at higher pressure as a cubic phase with CaCl2structure and 8-fold coordination (eg Kingma et al 1995) andat even higher pressure as an orthorhombic (Pbcn) a-PbO2 struc-ture (seifertite) (eg Dubrovinsky et al 2004 Grocholski et al2013 Zhang et al 2016) According to first principles calculationsat extreme pressure SiO2 may transform to a pyrite structure(Kuwayama et al 2005) Al2O3 in the form of trigonal corundumor orthorhombic Rh2O3(II) may be present and Fe may exist asnative iron (eg Frost et al 2004 Shi et al 2013)

Of considerable importance is the oxidation state as well as thespin state of iron that have received a lot of attention (egMcCammon 1997 Badro et al 2003 Li et al 2004 Tsuchiya

et al 2006 Fei et al 2007 Lin et al 2008 Catalli et al 2010Saha et al 2011 2012 Vilella et al 2015) With increasing pres-sure there is a transition from a high spin to a low spin configura-tion It may be responsible for the anomalous viscosity structure inthe central part of the lower mantle (900ndash1200 km eg Rudolphet al 2015) although the spin transition is generally thought tooccur deeper (1500 km)

In addition hydrogen may play a significant role (eg Ohtamiand Sakai 2008) A hydrous aluminosilicate is stable at lower man-tle conditions (eg Tsuchiya and Tsuchiya 2008 2011 Pamatoet al 2014) and dehydration may cause melting at the top of thelower mantle (Schmandt et al 2014)

As far as elastic properties and anisotropy are concerned oneshould keep in mind that the major phases over large volumes ofthe lower mantle are bridgmanite ferropericlase pPv and CaSiO3

perovskite These contribute largely to the bulk elastic propertiesbut there may be local deviations

32 Some comments on plasticity models and representation ofanisotropy

What are the sources of seismic anisotropy in the Earth Veryimportant is the alignment of anisotropic crystals called crystalpreferred orientation (CPO) or texture (based on DrsquoHalloy 1833)and universally used in materials science The crystal anisotropyis linked to the crystal structure A second aspect is crystal shapethat produces a shape-preferred orientation (SPO) CPO and SPOare sometimes linked (in mica for example the crystal plane(001) is parallel to the platelet) Often it is not (eg in quartz orin periclase) Also significant is the orientation of flat fracturesand fractures filled with kerogen This is a very important contribu-tion to anisotropy in shales (eg Hornby et al 1994 Sayers 1994Vasin et al 2013) but insignificant in the lower mantle In thelower mantle there is the possibility of partial melt particularlynear the core-mantle boundary (eg Williams and Garnero 1996Lay et al 2004 Shi et al 2013) but this would only give rise to ani-sotropy if melt occurred in parallel thin layers (eg Backus 1962)We will focus here on the development of CPO

Before going into plasticity in the mantle a few words aboutdeformation mechanisms of polycrystalline aggregates are inorder Deformation experiments on minerals have a long historyPfaff (1859) documented mechanical twinning in calcite when astress is applied In the early twentieth century deformation exper-iments at a wide range of temperature and strain conditions wereconducted on metals to explore the deformation behavior (egSchmid 1924) and in this context linear defects called dislocationswere discovered (Polanyi 1934 Taylor 1934) Without disloca-tions it would be very difficult to deform crystals and indeed theyare present in most crystalline materials

Dislocations form in the crystal lattice when a stress is appliedEdge dislocations propagate on a glide plane (hkl) and in a slipdirection [uvw] defined by rational indices relative to crystallo-graphic axes Propagation of dislocations causes crystals to rotaterelative to the applied stress which is conceptually illustrated foran experimentally compressed single crystal in Fig 12 By move-ment of dislocations on glide planes the rectangular crystal attainsa new shape (parallelogram) Since pistons must stay in contactthis results in an effective rotation of b In a polycrystalline aggre-gate neighboring grains play the function of pistons

Based on deformation experiments on metals deformationmechanism maps were established (eg Ashby 1972 Langdonand Mohamed 1978 Frost and Ashby 1982) They define condi-tions such as temperature pressure stress magnitudes strain rateand grain size under which mechanisms such as dislocation glidedislocation climb grain boundary migration and grain boundarysliding are active (Fig 13) Identifying mechanisms is important

Fig 8 Comparison of 6 recent models of lateral variations in the radial anisotropy parameter n = (VshVsv)2 plotted in terms of dlnn referred to isotropy While the modelsdisagree in detail common features are Vsh gt Vsv (blue) in the circum Pacific ring (roughly in agreement with local studies) and pronounced Vsv gt Vsh (orange) in the Fiji-TongaIndonesia region and under southernmost Africa (except SAVANI) Models plotted are (a) SAW642ANb (Panning et al 2010) (b) SAW642AN (Panning andRomanowicz 2006) (c) SAVANI (Auer et al 2014) (d) SGLOBE-rani (Chang et al 2015) (e) S362WANI + M (Moulik and Ekstroumlm 2014) (f) SEMUCB_WM1 (French andRomanowicz 2014)

Fig 9 (a) Experimentally determined PT phase diagram for perovskitebridgmanite (Pv)-post-perovskite (Murakami et al 2004) (b) T-Depth phase diagram plotting the pv-ppv phase boundary and cold and warm geotherms (after Hernlund et al 2005)

B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90 67

because some produce crystal rotations and thus crystallographicpreferred orientation (notably dislocation glide and ndash to someextent ndash dynamic recrystallization) while others generate random

orientations (such as grain boundary sliding in fine-grained mate-rials and dislocation climb) We will return to these issues inSection 48

Fig 10 Crystal structures of (a) periclase (b) bridgmanite and (c) post-perovskite the latter two with octahedrally coordinated silicon

Fig 11 Lower mantle composition for different models (a) pyrolite (b) MORB(from Irifune and Tsuchiya 2015) Pv perovskitebridgmanite Ppv post-perovskiteMw magnesiowuestiteferropericlase Mj majorite Rw ringwoodite SiO2 Ststishovite CC CaCl2 phase AP a-PbO2 phase Al2O Hex CF calcium-ferrite phaseCT calcium-titanate phase

68 B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90

In a polycrystalline aggregate stresses are transmitted acrossgrain boundaries causing heterogeneities even within grains Thisis most realistically approached with finite element methods (egMika and Dawson 1999) but these are still extremely demandingand rarely applied Simpler models have been used in materialsscience for a long time The Taylor (1938) theory developed bythe same Taylor who discovered dislocations (1934) assumeshomogeneous strain All grains undergo the same shape changeirrespective of orientation This leaves grain boundaries intact(Fig 14 left side) The Taylor model is very applicable to cubic met-als with many symmetrically related slip systems Slip on 111h

1 1 0i in fcc metals or cubic periclase has 12 equivalent systemsAnother model (Sachs 1928) assumes stress equilibrium and morefavorably oriented grains deform more than others In the modelthis causes overlaps and gaps at grain boundaries In principle thiswould be more adequate for low symmetry minerals (such asorthorhombic) but of course overlaps and gaps do not exist A com-promise between homogeneous strain and stress equilibrium is aself-consistent model that treats grains as ellipsoidal inclusionsdeforming in an anisotropic viscous medium (Fig 14 centerMolinari et al 1987) It is most widely applied in the Los Alamoscode VPSC (Lebensohn and Tomeacute 1993) and it can be used bothto understand preferred orientation in high pressure experimentsand to predict anisotropy in geodynamic models In the viscoplas-tic self-consistent model grains deform without knowledge of theirneighborhood In a finite element model (Fig 14 right) grains areconstrained by the orientation of neighbors In this sketch it isassumed that each grain has a single orientation In more sophisti-cated FEM models there are strain and orientation gradients devel-oping within grains (eg Mika and Dawson 1999)

When crystals are deformed in a polycrystalline medium theyundergo systematic rotations (Fig 12) and the material attains ananisotropic pattern We need to describe the orientation of a crys-tal relative to the macroscopic sample This is efficiently done byrelating two orthogonal coordinate systems (sample x y z crystal[100] [010] [001]) by three rotations Most frequently the so-called Euler angles are used U is the distance from z to [001]1 is the azimuth of [001] from y (around z) 2 is the azimuthof [100] around [001] (Fig 15) The 3-dimensional crystal orienta-tion distribution (COD) is conventionally described by a continuousorientation distribution function (ODF) The ODF is required to cal-culate anisotropic elastic properties of an aggregate from crystalorientations

For graphical representations of orientation patterns generally2-dimensional spherical projections of the ODF are used Depend-ing on the application one can either use the macroscopic sample xy z as reference and plot crystal directions (pole figures) or use thecrystal as reference and plot sample directions (inverse pole fig-ures) Inverse pole figures are useful if only a single sample direc-tion is of interest eg the compression direction in a compressionexperiment The symmetry of pole figures reflects the symmetry ofthe deformation path In compression experiments pole figures areaxially symmetric The density of poles on the sphere is contouredand then expressed as continuous pole densities usually normal-ized relative to a random distribution and defined as multiples ofa random distribution (mrd) 2ndash5 mrd are moderate CODs20ndash50 mrd very strong CODs The strongest crystal alignmentsin rocks that have been observed are muscovite in slates exceeding100 mrd Fig 16a is a 111 pole figure of rolled copper with roll-

Fig 12 Under stress imposed by pistons a crystal deforms to a new shape by slip of dislocations on a glide plane Since pistons remain in contact with the crystal surfacethere is an effective rotation b In a polycrystal neighboring grains act as effective pistons to transmit the stress

Fig 13 Stress-temperature deformation mechanism map (Langdon and Mohamed1978)

B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90 69

ing R transverse T and normal N sample directions indicatedFig 16b is the corresponding inverse pole figure of the normaldirection Inverse pole figures display the crystal symmetry Bothrepresentations will be used in the following discussion

33 Deformation experiments and rheology

The experiments on plasticity of metals were not applicable tomost minerals because even at elevated temperatures theirdeformation behavior at ambient pressure is generally brittleOne had to wait until high pressure deformation experiments weredeveloped by Griggs (1936) and applied on a wide scale includingolivine (eg Raleigh 1968) Since then sophisticated deformationapparati have been constructed in many laboratories making itpossible to deform rocks at a wide range of pressures and temper-atures They were applied to many minerals and rocks in the crustand upper mantle Studies on olivine (eg Jung and Karato 2001

Hansen et al 2012 Jackson and Faul 2010) documented the com-plex influence of temperature pressure composition (such aswater and iron content) The most sophisticated apparatus wasdeveloped at the Australian National University (Paterson andOlgaard 2000) It allows for deformation experiments on relativelylarge samples (1 cm) in compression tension and torsion Pres-sures are limited to 03 GPa and the limitation in pressure pre-vents these instruments to be used for experiments relevant tothe lower mantle (20ndash150 GPa) and inner core (320ndash360 GPa)

Higher pressure deformation experiments have been reviewedby Weidner and Li (2015) The multi-anvil apparatus called DIAwith three pairs of octahedral pistons (Onodera 1987) has beenmodified to apply stress by preferentially advancing one pistonpair (D-DIA for deformation DIA) The sample can be heated inter-nally Changes in phase structure preferred orientation andmicrostructure can be recorded in situ if the D-DIA apparatus iscombined with a monochromatic synchrotron X-ray beam fordiffraction and imaging (eg Wang et al 2003 2011) The conven-tional D-DIA apparatus has been used to 20 GPa and samples arecylinders 1 mm in diameter (eg Kawazoe et al 2010) A moreadvanced D-DIA (Kawai-type) reaching gt110 GPa with sintereddiamond anvils and smaller samples has been introduced atSPring8 in Japan (Yamazaki et al 2014)

Shear deformation at high pressure can be performed with arotational Drickamer apparatus (RDA) (eg Yamasaki and Karato2001) Shear deformation of a bridgmanite-ferropericlase aggre-gate at 25 GPa and 2100 K has been achieved to large strains(Girard et al 2016) In such torsion experiments the strain variesgreatly as a function of sample radius The experiment documentedthat most of the plastic deformation is accommodated by theweaker ferropericlase

Currently the most accessible method to deform samples atultrahigh pressures (gt500 GPa) is with diamond anvil cells (DAC)where diamonds are used as pistons compressing a small sample(30ndash80 lm in diameter and 50 lm thick) (eg Merkel et al2002 Fig 17) The diamonds are used not only to induce pressurebut also to cause compressive deformation (Fig 17 b c) and theevolution of preferred orientation can be observed in situ if hori-zontal X-rays transmit the sample in radial diffraction geometry(r-DAC) Strong textures have been observed in ferropericlase(eg Merkel et al 2002 Lin et al 2009) perovskitebridgmanite(eg Merkel et al 2003 Wenk et al 2006 Miyagi and Wenk2016 Tsujino et al 2016) and pPv the phase likely to be presentat the core-mantle boundary (eg Merkel et al 2006 2007

Fig 14 2D Sketches of polycrystal plasticity models Gray shades express orien-tation (Left) For the full constraints Taylor model all grains undergo the samedeformation regardless of orientation (Center) The viscoplastic model VPSC treatsgrains as inclusions in an anisotropic viscous medium (Right) In finite elementmodels grains deform differently depending on the orientation of neighbors

Fig 15 Definition of crystal orientation relative to sample coordinates with threerotations (Euler angles) 1 U 2 Projection based on sample coordinate system xy z (pole figure) Crystal coordinate system is defined by axes [100] [010] and[001]

Fig 16 Comparison of (a) 111 pole figure relative to sample coordinates and (b) Ninverse pole figure relative to crystal coordinates for rolled copper Equal areaprojection red colors are high and blue colors are low pole densities N normaldirection R rolling direction and T transverse direction Note the equivalentinformation In the 111 pole figure a maximum in the N direction and in the NDinverse pole figure a maximum in 111

70 B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90

Miyagi et al 2010 2011 Wu et al 2017) Shear deformation canbe induced in rotational DACs (eg Levitas et al 2006) Thismethod has been mainly used to induce phase transformationsand has not yet been applied to study texture evolution at highpressure

In addition to pressure and stress temperature can be inducedin DAC experiments by resistive (eg Liermann et al 2009) andlaser heating (eg Prakapenka et al 2008 Dubrovinsky et al2009) or a combination of the two (Miyagi et al 2013) Tatenoet al (2015) reached temperatures of 6000 K at gt400 GPa on exper-iments on Fe and Fe-Si corresponding to conditions of the Earthrsquos

inner core Obviously there are limitations to DAC experimentssamples are extremely small strain is always compressive andstrain rates are difficult to control

It was surprising to see that silicates and oxides that are brittleat ambient conditions including olivine become ductile at pres-sures of 10GPa even at room temperature and deform by dislo-cation glide (eg Wenk et al 2004) The diffraction image ofMgSiO3 post-perovskite at 150 GPa (Fig 18a) is lsquolsquounrolledrdquo andthe compression direction is indicated by arrows (large 2h smalld Q=1d) (Fig 18b) The elastic lattice distortion (wave-like patternwith azimuth) is related to applied stress and elastic propertiesThe intensity variations with azimuth are indicative of preferredorientation For example there is a strong maximum for 004(fourth order diffraction on the lattice plane 001) in the compres-sion direction This image illustrates why radial diffraction geome-try has to be used to display CPO as function of angle to thecompression direction In axial geometry (X-rays parallel to thediamond axis) Debye-rings have uniform intensity since alldiffracting lattice planes have the same angle to the compressiondirection

A qualitative interpretation of a diffraction image is illustratedin Fig 19 for an experiment with MgGeO3 post-perovskite(Miyagi et al 2011) and used to construct an inverse pole figureof the compression direction (arrow) MgGeO3 is an analog ofMgSiO3 but transforms to pPv at lower pressure There is a maxi-mum for 002 and a minimum for 020 in the compression directionwhich can be plotted in the inverse pole figure (Fig 19 right side)The quantitative deconvolution of diffraction images is not trivialand most often an iterative Rietveld method is applied (egLutterotti et al 2014 Wenk et al 2014) The high pressure syn-chrotron X-ray diffraction deformation images provide quantita-tive information about phases crystal structures density stresselastic properties and preferred orientation

Fig 20a-c shows experimental inverse pole figures of MgSiO3

pPv documenting increasing texture development with pressure-stressndashstrain with a maximum at (001) From the orientation pat-tern active slip systems can be derived by comparing experimentalinverse pole figures with results from polycrystal plasticity calcu-lations that assume certain combinations of slip systems(Fig 20d) Based on the good agreement it can be concluded thatpPv deformed in the experiment by dominant (001)[100] slip(Miyagi et al 2010)

With similar experiments it was suggested that MgSiO3 bridg-manite deforms dominantly by slip on (001) planes in [100][010] and h1 1 0i directions (eg Miyagi and Wenk 2016) but sim-

Fig 18 (a) Diffraction image of MgSiO3 post-perovskite at 150 GPa (b) Unrolled diffractiochanges in Q are due to elastic distortion of the crystal lattice under compression Botquantitative information such as inverse pole figures

Fig 17 Diamond anvil cell for radial diffraction experiments The X-ray beam ishorizontal (a) illustrates the cell and the insert is an enlargement with diamondsand gasket to contain the sample (b c) illustrate that diamonds not only applypressure but also compressive stress that deforms the sample and produces CPO

B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90 71

ple shear experiments in a D-DIA apparatus indicate (100)[001]slip (Tsujino et al 2016) Ferropericlase likely deforms by 110h110i slip (eg Stretton et al 2001 Merkel et al 2002 Linet al 2009) at high pressure conditions For Ca-perovskite domi-nant 110h110i slip was proposed (Miyagi et al 2006 2009)

So far most DAC high-pressure deformation experimentsextracted COD information from intensity variations along Debyerings (eg Fig 18) A new method called multigrain is still underdevelopment It obtains orientation information from individualgrain diffractions (eg Barton and Bernier 2012 Rosa et al2015 Langrand et al 2017) and is especially applicable to coarseraggregates Nisr et al (2012) used information about dislocationsfrom distortion of single crystal diffraction patterns of the post-perovskite analog MgGeO3 and suggested dominant slip on 110and (001) planes

It should be mentioned that information from such high pres-sure experiments is by no means unambiguous Obviously defor-mation conditions in experiments and simulations differconsiderably from those in the deep Earth just to mention temper-ature grain size strain rate interaction of dislocations and interac-tion between grains Furthermore not all CPO patterns that areobserved are due to deformation but could be inherited from orien-tation patterns of precursor phases such as for pPv from perovskite(Dobson et al 2013) or enstatite (Merkel et al 2006 2007 Miyagiet al 2011) Also slip systems may not be the same for pPv phasesof different compositions such as MgGeO3 CaIrO3 NaMgF3 orMn2O3

A different approach has become very important computationof Peierlrsquos stresses and lattice friction for dislocation systems basedon bonding characteristics It was originally developed for metals(eg Kubin et al 1992 Devincre and Kubin 1997) and has morerecently been applied to minerals in the mantle where it allowsto predict slip system activities for a wide range of temperaturendashpressurendashstrain rate conditions (eg Carrez et al 2007Mainprice et al 2008 Cordier et al 2012) Amodeo et al (20122014 2016) propose a switch from 110h010i slip to 100h0 1 1i slip in periclase with pressure Kraych et al (2016) suggest(010)[100] slip in bridgmanite at high pressure According tothese calculations the strength of bridgmanite increases greatlywith pressure and at 60 GPa bridgmanite appears 20 times stron-ger than periclase The critical resolved shear stress decreasesabout 20 from strain rates of 105 s1 (which corresponds to

n image as function of Q (Q = 1d) Intensity variations with azimuth illustrate CPOtom experimental data above fit of the data with the Rietveld method to extract

Fig 19 Explanation of the relationship between DAC diffraction image and inverse pole figure Left Unrolled diffraction image of MgGeO3 post-perovskite Some diffractionlines are labeled The sinusoidal variations are due to imposed stress High stress (high Q low d) is indicated by arrows On the right side is a conceptual construction of theinverse pole figure of the compression axis based on relative diffraction intensities (Miyagi et al 2011)

Fig 20 Inverse pole figures for MgSiO3 post-perovskite (AndashC) experiments (D) Plasticity model with dominant (001) slip equal area projection (Miyagi et al 2010)

72 B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90

experimental values) to 1014 s1 corresponding to likely values atdeep mantle conditions (Fig 21a) The opposite is the case for pPvwhich appears much weaker than periclase at high pressure hightemperature and slow strain rates (Fig 21b Goryaeva et al 20152016) Also the predicted weakest calculated slip system for post-perovskite at deep mantle conditions is (010)[100] correspondingto the layered crystal structure (Fig 21c) but different from thatobserved in DAC experiments (Miyagi et al 2010 Wu et al 2017)

It should be mentioned that a single slip system is not sufficientto deform a polycrystal In the case of the Taylor model at least 5systems have to be active to produce an arbitrary strain (Mises1928) This is relaxed for the self-consistent model but also hereseveral slip systems are active The choice of activity depends onthe crystal orientation relative to the applied stress (Schmid fac-tor) TEM investigations confirm this though some slip systemsusually dominate and the literature refers to the lsquolsquodominantrdquo slipsystem Some dominant slip systems for deep Earth minerals aresummarized in Table 2

34 Elastic properties

Elastic properties of crystals at conditions pertaining to thelower mantle are critical to link microstructural properties of therock with seismic observations The most straightforward experi-mental method that has been applied to many lower mantle min-erals is Brillouin scattering (see review by Speziale et al 2014) andenergy-dispersive X-ray diffraction (eg for calcium silicate per-ovskite Shieh et al 2004) A different approach is with first prin-ciples calculations at high pressure and temperature (for someapplications to bridgmanite CaSiO3 perovskite and pPv see egZhang et al 2013 Wentzcovitch et al 2005 Kawai and

Tsuchiya 2015) First principles results look fairly consistent forminerals at lower mantle conditions but as we will see in Sec-tion 62 predictions for iron at inner core conditions are stillambiguous Furthermore the actual composition of the mineralsparticularly the iron content can be significant (eg Koci et al2007) Values of stiffness coefficients and P-wave anisotropy (An = 200(Pmax Pmin)(Pmax + Pmin) for some low mantle mineralsat lowermost mantle conditions are listed in Table 3 Fig 22 givescorresponding S velocities of single crystals with black lines corre-sponding to the orientation of the fast S-wave polarization As canbe seen in Table 1 periclase and pPv have the highest P-wave ani-sotropy and Ca-perovskite is least anisotropic The S-wave aniso-tropy is considerably higher for pPv and periclase than forbridgmanite and particularly CaSiO3 perovskite

To obtain elastic properties of aggregates one has to averageover all orientations and corresponding elastic tensors takingphase fractions into account Simple averages are upper bound(Voigt 1887) and lower bound (Reuss 1929) Generally an inter-mediate arithmetic mean (Hill 1952) or a geometric mean(Matthies and Humbert 1995) are preferred All these models donot take grain shape into account which is not very significantfor crystalline phases but becomes important for systems withplaty minerals such as graphite or sheet-silicate containing rocksand aggregates with flat oriented pores For such cases a self-consistent (Matthies 2012 Vasin et al 2013) or differential effec-tive medium approach (eg Hornby et al 1994) should be consid-ered It is probably not important for the lower mantle

Note that S-waves passing through anisotropic media have arbi-trary polarization directions in the plane perpendicular to thedirection of propagation as is best displayed for the fast directionof single crystals in Fig 22 but applies also to aggregations of ori-

Fig 21 Critical resolved shear stress CRSS for dislocation glide activities as functionof temperature of (a) bridgmanite at 60 GPa (from Kraych et al 2016) and MgO(from Amodeo et al 2016) at strain rates 105 s1 and 1014 s1 (b) post-perovskiteat 120 GPa at strain rate 1016 s1 (from Goryaeva et al 2016) compared with MgO(from Amodeo et al 2012) Courtesy of P Cordier

B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90 73

ented crystals Seismologists generally consider the projection ofthat polarization direction onto horizontal and vertical axes Thisis convenient because differences in arrival times and waveformsin this representation can be expressed in terms of apparent verti-cal transverse isotropy (VTI) which because of limited azimuthalsampling is often the only anisotropic constraint that can beobtained

4 Linking seismology and mineral physics through predictionsof anisotropy in geodynamic models

41 Isotropic geodynamic models for upper mantle convection

Ever since the concept of plate tectonics became accepted in the1960s convective movements in the Earthrsquos mantle have been pro-posed such as upwelling along oceanic ridges (eg Hess 1964Cann 1968 Fig 1b) The first quantitative models based on hydro-dynamics emerged in the eighties (eg Hager and OrsquoConnell 1981)

Table 2Proposed dominant slip systems in deep Earth minerals

Ferropericlase Lower P 110110High PT also 100011

Bridgmanite Low P (001)[100] [010] 110High P (100)[001](010)[100]

pPv (001)[100](010)[100]

Ca-perovskite 110110e-iron (0001)1120 subordinate 1010

Geodynamic models have been mainly applied to the upper mantleand we will not discuss them here in detail (see eg review by Longand Becker 2010)

Many convection models have been developed to understandthe evolution of the deep Earth Calculations generally assume aviscous fluid and use non-dimensional equations for the conserva-tion of mass momentum and energy applying the Boussineqapproximation Critical parameters are Rayleigh number viscosityboundary temperatures In order to evaluate the strain evolutionduring the convection process tracers are introduced that recordthe velocity gradient tensor at each time step along the path ofthe tracer If the deformation mechanisms are known (eg disloca-tion glide) polycrystal plasticity calculations can be used to calcu-late the evolution of crystal preferred orientation based on thestrain recorded by tracers

Most geodynamic models assume a viscous isotropic mediumwith a smoothly varying viscosity structure and the microstruc-tural processes leading to preferred orientation are introducedpost-mortem Considering an anisotropic medium that constantlychanges its properties greatly increases the complexity of geody-namic calculations However there are models in metallurgy suchas extrusion of an aggregate that illustrate the importance of ananisotropic material behavior (eg Beyerlein et al 2003)

42 Review of upper mantle anisotropic models

We will start the discussion of anisotropic convection byreturning to a simple 2D model (Dawson and Wenk 2000) thatwas originally issued as an educational video by AGU (1999) andcan now be downloaded in digital form (httpepsberkeleyedu~wenkTexturePageMantle-Videohtm) At high Rayleigh number(low viscosity) heat transfer occurs by convection rather than con-duction corresponding to conditions in the Earthrsquos mantle Convec-tion is driven by temperature gradients As aggregates move alongstreamlines the orientation of grains is constantly updated and thelocal texture affects the next deformation step which introducesconsiderable heterogeneities It was surprising to find locallyheterogeneous CPO patterns in the 2D convection cell representingthe upper mantle shown as [100] pole figures of olivine after100 my (Fig 23) Some regions have strong and others very weakpatterns that can be attributed to heterogeneous deformation dueto CPO development and result in lsquolsquoanisotropicrdquo viscosity

Some complexities of different plasticity models for a simplecase of upwelling have been investigated by Blackman et al(1996 2002) and Castelnau et al (2009) If a lower bound behavioris assumed (Sachs 1928) there is very strong CPO developmentFor self-consistent models (Lebensohn and Tomeacute 1993) rotationsare reduced If dislocation glide is combined with dynamic recrys-tallization both grain growth and grain growth combined withnucleation resulting orientation patterns can be very differentRecrystallization is likely in the deep Earth with high temperatureand large strains where grain boundary migration is likely tooccur We will return to the issue of recrystallization in Section 48

Merkel et al (2002) and Lin et al (2009)Amodeo et al (2016)Miyagi and Wenk 2016Tsujino et al (2016)Kraych et al (2016)Miyagi et al (2010) and Wu et al (2017)Goryaeva et al (2016)Miyagi et al (2009) and Ferreacute et al (2009)

Merkel et al (2004) and Miyagi et al (2008)

Table 1Summary of local studies of anisotropy in D00

Authors Region Type ofseismicwaves

VSH gt VSV

A Wookey and Kendall (2007)and Refs therein

Caribbean

Kendall and Silver (1996) Caribbean SSdiffDing and Helmberger

(1997)Caribbean ScS

Rokosky et al (2004) Caribbean ScSB Wookey and Kendall (2007)

and Refs thereinAlaska

Lay and Young (1991) Alaska SScSMatzel et al (1996) Alaska SScSSdiffGarnero and Lay (1997) Alaska SScSSdiffWysession et al (1998) Alaska SdiffFouch et al (2001) Alaska SSdiff

E Ritsema (2000) Indian Ocean SF Thomas and Kendall (2002) Siberia SScSSdiffI Usui et al (2008) Antarctic Ocean S1 Kendall and Silver (1998) NW Pacific SScSSdiff3 Vinnik et al (1995 1998b) north central Pacific Sdiff6 Wookey et al (2005b) N Pacific ScS8 Long (2009) East Pacific SKS-SKKS9 Niu and Perez (2004) N America Asia SKSSKKS11 Vanacore and Niu (2011) Caribbean SKS-SKKS12 He and Long (2011) NW Pacific PcSScS SKS

SKKS13 Wookey and Kendall (2008) Caribbean ScS18 Thomas et al (2007) W Pacific ScS20 Fouch et al (2001) North central Pacific SSdiffSV lt SH4 Pulliam and Sen (1998) Central Pacific SC Ritsema et al (1998) Central Pacific SSdiff22 Kawai and Geller (2010) Central Pacific SScSSKSTiltedazimuthallaterally varying5 Russell et al (1998 1999) North Central Pacific ScS7 Ford et al (2006) South Pacific SSdiffA Garnero et al (2004a) Caribbean SScSSdiffA Maupin et al (2005) Caribbean SScSSdiffA Rokosky et al (2004 2006) Caribbean ScSG Wookey et al (2005a) North West Pacific ScS23 Restivo and Helffrich

(2006)North America SKS SKKS

21 Wang and Wen (2007) EastSouth Africa SKSSKKS10 Nowacki et al (2010) Caribbeanwest US ScS14 Lynner and Long (2012) Central Africa SKS-SKKS15 Cottaar and Romanowicz

(2013)South edge of AfricanLLSVP

Sdiff

16 Lynner and Long (2014) EastSouth Africa SKS-SKKS19 Long and Lynner (2015) Near Perm Anomaly SKS-SKKS17 Ford et al (2015) East Africa SKS-SKKSIsotropic or weak anisotropy2 Kendall and Silver (1996) South Pacific SScSSdiffH Garnero et al (2004b) Atlantic SSdiff9 Niu and Perez (2004) South Africa Antarctica

Southeast PacificSKSSKKS

21 Wang and Wen (2007) Eastern Atlantic SKSSKKS

62 B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90

upper mantle anisotropy sampled along the path of deep mantleseismic waves For example Vinnik et al (1998a) proposed a refer-ence event method to correct Sdiff waveforms for unknown uppermantle anisotropy using SKS and SKKS waveforms In the pasttwo decades characterization of upper mantle anisotropy fromSKS splitting data has progressed significantly (see review byLong and Silver 2009) making it possible to apply relatively robustcorrections in 00known00 upper mantle models both on the sourceand receiver sides and thus augment the number of D00 locationsthat can be sampled

Another approach to minimize effects of upper mantle aniso-tropy has been the use of differential measurements on pairs ofphases One such suitable pair is S and ScS which have similarpaths in the upper mantle on the source and station side but at

appropriate distances only ScS samples D00 (Fig 2) while S samplesa portion of the lower mantle which is assumed to be isotropic (egWookey et al 2005a Nowacki et al 2010) Similarly while SKSand SKKS splitting is most strongly acquired during propagationin the upper mantle the paths of SKS and SKKS waves diverge sig-nificantly in the lowermost mantle so that differential splitting ofthese two phases can sometimes be attributed to anisotropy in thedeep mantle (eg Hall et al 2004 Niu and Perez 2004 Restivo andHelffrich 2006 Wang and Wen 2007) Such an approach has beenapplied to several regions of the world (eg Long 2009 He andLong 2011 Vanacore and Niu 2011 Lynner and Long 20122014 Long and Lynner 2015 Ford et al 2015) Results consis-tently show strong and complex anisotropy on the borders of theLLSVPrsquos and interestingly also in the vicinity of the Perm Anomaly(Long and Lynner 2015) a low velocity anomaly seen at the base ofthe mantle in all tomographic models in the vicinity of the town ofPerm (Russia) and of smaller lateral extent ( 900 km) but corre-sponds to a similar reduction in shear velocity as found in theLLSVPs (eg Lekic et al 2012 Fig 3)

23 Results from array studies

Earlier observations and forward modeling studies of D00 aniso-tropy mostly relied on data from isolated stations which made itdifficult to constrain the geometry of anisotropy for lack of sam-pling of the target regions by waves propagating in different direc-tions (eg Maupin 1994) Thus most studies only reported thedifferences in SH and SV propagation times leading to models ofapparent VTI Yet evidence for azimuthal anisotropy has been sug-gested either from waveform complexity (eg Garnero et al2004a Maupin et al 2005) or when the geometry permitted frommeasurements of splitting on paths sampling the target region inat least two directions (eg Wookey and Kendall 2008) With theadvent of denser broadband arrays more detailed studies haveemerged in recent years aiming at the very least to distinguishVTI from radial anisotropy with tilted axis of symmetry (TTI) withimplications for the interpretation of observations in terms ofintrinsic or extrinsic anisotropy (eg Long et al 2006)

Regions of the world where this has been possible so far arecentral America exploiting ScS S data from the dense USArray(Nowacki et al 2010) and the northwest Pacific (He and Long2011) using ScS data from F-net in Japan Studies of Sdiff at thesouthern border of the African LLSVP based on data from the Kaap-val array show lateral variations in anisotropy (To et al 2005Cottaar and Romanowicz 2013) with strong anisotropy in the fastvelocity region outside the LLSVP increasing towards its borderand apparently disappearing inside it Although caution must betaken when interpreting apparent splitting in Sdiff due to isotropicheterogeneity potentially affecting SVdiff in a significant way(Komatitsch et al 2010) the strong elliptical shape of the particlemotion outside of the African LLSVP (Fig 4 and To et al 2005)where isotropic velocities are relatively fast contrasting with thelinear particle motion for paths travelling inside the LLSVP cannotbe accounted for by isotropic heterogeneity This was demon-strated in the follow-up study of Cottaar and Romanowicz(2013) in which the waveforms of Fig 4 and others were modelledusing the spectral element method a numerical method for 3Dseismic wavefield computations which can take effects of 3D iso-tropic heterogeneity into account accurately Differential splittingin S and ScS has also been exploited in the north Pacific (Wookeyet al 2005a) and in east Africa (Ford et al 2015) where remark-ably several azimuths can be sampled

The recent studies have confirmed earlier results with in gen-eral Vshgt Vsv in the ring of faster than average velocities sur-rounding the two LLSVPs and absence of significant splitting orVshltVsv found primarily within the LLSVPs (Fig 3 Table 1)

Fig 4 Example of change of character of particle motion for paths sampling theborder of the African LLSVP (a) Map showing the paths sampled plotted on top of abackground shear wave tomographic model (SAW24B16 Meacutegnin and Romanowicz2000) The portion of path sampling the D00 region is highlighted in yellow (b) and(c) shows particle motions of Sdiff at distances of 120o and at two azimuths In (b)the path in D00 is outside of the LLSVP and in (c) the path in D00 is inside the LLSVP(from To et al 2005) The color indicates the time with respect to predicted Sdiffarrival from PREM Black 35 to 5 s Blue 5 to 20 s Green 20 to 45 s Red 45 to70 s The elliptical particle motion in (B) contrasts with the linear particle motion in(c) This cannot simply be explained by lateral heterogeneity in isotropic velocity asone would expect larger amplitudes in SV for waves propagating inside the lowvelocity LLSVP This interpretation was later confirmed by 3D numerical waveformmodelling (Cottaar and Romanowicz 2013) (For interpretation of the references tocolor in this figure legend the reader is referred to the web version of this article)

B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90 63

The recent results indicate variability of anisotropy at relativelyshort scales with evidence for azimuthal anisotropy with differentorientations of fast velocity axes at least in regions of faster thanaverage isotropic shear velocity Interestingly the studies ofCottaar and Romanowicz (2013) Lynner and Long (2014) andFord et al (2015) consistently show changes in anisotropy acrossthe border of the African LLSVP with stronger anisotropy outsideof it practically disappearing inside it (eg Fig 5) Interestinglythe same trend although less sharply defined because of the chal-lenging geometry is likely present at the northern edge of the Paci-fic LLSVP (Fig 6) Indeed all studies of the latter region considerpaths from Fiji-Tonga sources to stations in north America Differ-ent results are found for different distance ranges with VsvgtVshfor the shorter distances sampling inside the LLSVP (as well asabove D00) and VshgtVsv at longer distances (Sdiff) which samplea significant portion of the fast Vs region outside of the LLSVPVinnik et al (1995 1998b) used Sdiff data and found VSHgtVSV theportion of the corresponding paths inside the LLSVP was smalland Vinnik et al (1998b) showed that splitting only occurred fordistances larger than 102o when paths sampled more of the fastregion outside of the LLSVP Likewise Fouch et al (2001) andRitsema et al (1998) used S Sdiff and found VshgtVsv for larger dis-tance paths while VsvgtVsh for shorter distance paths that samplewithin the LLSVP and above D00 as did Kawai and Geller (2010)Pulliam and Sen (1998) and Russell et al (1998) used S and ScSrespectively at shorter distances sampling inside the LLSVP andfound VsvgtVsh

All these results point in the same direction evidence for signif-icant anisotropy with generally VshgtVsv within the ring of fastvelocities surrounding the Pacific and African LLSVP possiblyincreasing and tilting at their borders but vanishing or changingsign (VsvgtVsh) inside the LLSVPrsquos

24 Results from global anisotropic tomography

Gaining improved understanding of the distribution and natureof seismic anisotropy at the base of the mantle requires better glo-bal sampling with accurate corrections for upper mantle aniso-tropy One possible approach is to construct global whole mantletomographic models of anisotropy Such an approach is attractivebecause a variety of seismic waveforms can be included in partic-ular fundamental and overtone surface waves which provide con-straints on the strong anisotropy in the uppermost mantle (egDebayle and Ricard 2013) Combining surface wave data with var-ious body waveforms that illuminate the entire mantle should ulti-mately allow improved resolution and characterization of deepmantle anisotropy So far this has proven very challenging forthe deep mantle

Indeed most successful has been the tomographic characteriza-tion of shear wave azimuthal anisotropy in the uppermost 200 kmof the mantle at the global scale using Rayleigh wave dispersiondata (eg Tanimoto and Anderson 1984 Montagner andTanimoto 1990 1991 Fig 1) More recent models developed bydifferent groups show broadly consistent trends (eg Trampertand Woodhouse 2003 Ekstroumlm 2011 Debayle and Ricard 2013Yuan and Beghein 2013) On the other hand the robustness of glo-bal scale transition zone azimuthal anisotropy models that utilizesurface wave overtone information (eg Trampert and van Heijst2002 Yuan and Beghein 2013) is still debated This is becausethe anisotropic signal in overtone surface waves is weak the azi-muthal sampling far from ideal and the number of parametersneeded to invert for azimuthal anisotropy at the global scale evenwhen considering only the dominant terms in 2-w (where w is theazimuth) is very large likely resulting in trade-offs with isotropicstructure It is not possible at present to extend this type of studyto the deep mantle as the sensitivity of available long period over-tone data becomes too weak and azimuthal coverage for bodywaves provided by the current geometry of sources and stationsis not sufficient

Thus tomographic imaging of anisotropy in the whole mantlecan at present only hope to resolve the simplest form of aniso-tropy that does not have as strong requirements on azimuthal cov-erage which is VTI (or apparent VTI) Such studies are based onrelatively long period waveforms mostly sensitive to shear veloc-ity combining fundamental mode surface waves surface waveovertones and shear body waves and aim at solving for the distri-bution of only two anisotropic parameters Vsh and Vsv or alter-natively isotropic velocity Vsiso and the anisotropic parameter n =(VshVsv)2 (Panning and Romanowicz 2004 2006 Panning et al2010 Kustowski et al 2008 French and Romanowicz 2014Moulik and Ekstroumlm 2014 Auer et al 2014 Chang et al 20142015) The other three anisotropic parameters that are necessaryto fully describe a VTI medium are scaled to Vsiso and n using scal-ing relations that are appropriate for the upper mantle (egMontagner and Anderson 1989) but may be questionable for thelower mantle However this may not be a significant issue giventhe dominant sensitivity of the waveforms considered to shearvelocities While the resulting models show qualitative agreementat long wavelengths details vary frommodel to model significantlyenough not to be trustworthy for quantitative interpretations

These models do agree on the following observations on aver-age radial anisotropy is strongest in the uppermost mantle andmost of the lower mantle exhibits little radial anisotropy (Fig 7)

Fig 5 a and b Whole mantle depth cross sections through the isotropic Vs part of model SEMUCB_WM1 (French and Romanowicz 2014) at the southern (a) and eastern (b)edge of the African LLSVP where rapid variations in the direction and strength of anisotropy have been reported decreasing from outside (blue) to inside (pink) the LLSVP inc) the map view is from Lynner and Long (2014) with background shear velocity model GyPSuM of Simmons et al (2012) The cross-section location is indicated on the mapby a straight line c and d corresponding cartoons proposed by the authors respectively (c) Cottaar and Romanowicz (2013) (d) Ford and Long (2015)

64 B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90

Inmostmodels there is an indication of an increase in anisotropy inD00 with Vshgt Vsv (n slightly larger than 1) although there is vari-ability among models due to a combination of parametrizationtypes of seismic waves considered and theoretical assumptions

Common 3D features of these models in D00 are a predominanceof Vsh gt Vsv outside of the LLSVPs with patches of Vsh lt Vsv con-fined within the LLSVPs in agreement with local studies (Fig 8)However the current models do not show consistency in theamplitude of the lateral variations in n nor the wavelengths ofthese variations This is partly due to the parametrization chosenFor example Panning and Romanowicz (2004 2006) and Aueret al (2014) allowed relatively short wavelength lateral variationsin n while Moulik and Ekstroumlm (2014) and French andRomanowicz (2014) chose to assign shorter wavelength lateralvariations to isotropic Vs while constraining the anisotropic partof the model to be smooth Theoretical assumptions on wave prop-agation are also important ray theory is not valid for modelling ofSdiff nor is it valid to use the surface wave approximation for mod-elling this phase as shown by Li and Romanowicz (1995) So faronly the Berkeley models are constructed taking into account finitefrequency effects rather than ray theory for body waves (Panningand Romanowicz 2004 2006 French and Romanowicz 2014)

One fundamental issue is that Sdiff and ScSn data (with ngt1) arenecessary to obtain good coverage of D00 at the global scale As dis-cussed previously SVdiff decays rapidly with distance in modelssuch as the reference model PREM (Dziewonski and Anderson1981) where the velocity in D00 is relatively fast The global datasetsare thus necessarily biased although to various degrees depending

on the particular dataset by the predominance of SHdiff introduc-ing trade-offs between isotropic and anisotropic structure (egKustowski et al 2008 Chang et al 2015) and making it only pos-sible to resolve the very longest wavelengths of VTI in D00 withpoor constraints on their amplitude

In summary robustly mapping even the simplest component ofseismic anisotropy apparent VTI at the base of the mantle at highresolution using a tomographic approach is still a challenging openquestion let alone constraining azimuthal anisotropy at the globalscale Still available global models agree with local studies aboutthe prevalence of VshgtVsv in regions of faster than average velocityin D00

As for P wave anisotropy in the deep mantle only few studieshave tried to constrain it so far Several studies have attemptedto retrieve the global average variation with depth of the radiallyanisotropic parameter g = (VphVpv)2 using normal mode data(Montagner and Kennett 1996 Beghein et al 2006) finding someindication that the anisotropy in gmay be anticorrelated with thatof n in the D00 region with however strong trade-offs with density(to which normal mode data are also sensitive) Note that the anti-correlation of isotropic P and S velocities at long wavelengths inthe deep mantle is in contrast better established (eg Su andDziewonski 1997 Kennett and Widyantoro 1998 Masters et al2000 Ishii and Tromp 1999 Romanowicz and Breacuteger 2000) Thepossibility of P wave anisotropy in the deep mantle using P wavedata (mantle and core phases) has been investigated by Boschiand Dziewonski (2000) concluding that anisotropy may be smallwith significant trade-offs with core-mantle boundary topography

Fig 6 Zoom on the northern edge of the Pacific LLSVP The background tomographic model is the isotropic Vs part of model SEMUCB_WM1 (French and Romanowicz 2014)(A) Map view with locations of studies of D00 shear wave splitting suggesting a change of character of anisotropy across the boundary of the LLSVP Green dots indicate thelocation of major hotspots Black line with white and purple dots is the great circle path corresponding to the depth cross section shown in (B) displaying the Hawaian plumeand transition from low to fast velocities in D00 Kawai and Geller (2010) Pulliam and Sen (1998) and Russell et al (1998) find VSV gt VSH while Ritsema et al (1998) Fouch et al(2001) and Vinnik et al (1998) find that Vsh gt Vsv increasingly so for paths sampling the fast region outside of the LLSVP Note that the color saturation of the tomographicmodel is different in (A) and (B)

B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90 65

and outer core structure The possible anticorrelation of P and Sradial anisotropy in the D00 must therefore be considered with cau-tion at the present time when used as a constraint in modeling

Given these difficulties a currently explored possible avenue isto try and combine constraints not only from seismology but alsofrom mineral physics and geodynamics Each of these approachestaken individually involves many assumptions and uncertaintiesbut by combining them the hope is that the space of acceptablemodels for anisotropy and its causes can be further reduced Theidea is to start with the strain field inferred from a mantle circula-tion model compute the corresponding texture development andpredicted seismic anisotropy using available information on crystalplasticity and elasticity for different lower mantle minerals andcompare these predictions with seismic observations This shouldprovide constraints on the mineral physics assumptions as wellas the deep mantle dynamics or at least allow us to rule out someclasses of models Note that in this approach the fundamentalassumption is that anisotropy is due to CPO development resultingfrom large-scale mantle flow

Before describing these efforts in more detail we will reviewcurrent knowledge and capabilities in mineral physics and describehow seismology and mineral physics can be linked through geody-namics modeling

3 Mineral physics perspective on the deep mantle

31 Dominant mineral phases in the lower mantle

Ringwood (1962) speculated about the composition of thelower mantle suggesting that olivine Mg2SiO4 would first breakdown to spinel Mg2SiO4 and then to MgSiO3 with a lsquolsquocorundum-

likerdquo structure and periclase (MgO) Liu (1974) synthesized thisstructure at high temperature and pressure and identified it asMgSiO3 perovskite (which has recently been named bridgmaniteTschauner et al 2014) At high pressure bridgmanite transformsto post-perovskite pPv (eg Murakami et al 2004 Oganov andOno 2004 Tateno et al 2009 Fig 9a) and this may be the mostimportant phase near the core-mantle boundary particularly alonga cold geotherm within subducting slabs (Fig 9b) Thus it appearsthat cubic periclase (Fig 10a) orthorhombic bridgmanite (Fig 10b)and orthorhombic post-perovskite (Fig 10c) are the dominantminerals in the lower mantle Periclase has the same highly sym-metric structure as halite (NaCl) with close-packed MgOVI octahe-dral coordination polyhedra Bridgmanite (spacegroup Pbnm) is adistorted cubic perovskite structure with SiOVI coordination octa-hedra linked over corners and Mg2+ in large interstices Post-perovskite (spacegroup Cmcm) has layers of SiOVI octahedra alter-nating with layers of Mg The layers are parallel to (010) It isisostructural with CaIrO3 (eg Hunt et al 2009) While the pseu-docubic perovskite structure is elastically fairly isotropic the lay-ered post-perovskite structure is highly anisotropic As we willsee post-perovskite is of critical importance for anisotropy in thelower mantle In the following discussion we will use mostly theabbreviation pPv

Most lower mantle minerals (gt660 km) cannot be studied atsurface conditions Even if lower mantle material has reached thesurface by upwelling minerals have undergone phase transitionsThus information about phase diagrams is based on in situ observa-tions in high pressure experiments and ab initio calculations

Irifune and Tsuchiya (2015) have reviewed the mineralogicalcomposition of the lower mantle Different bulk compositions ofthe lower mantle have been proposed Ringwood (1962 1975) sug-gested a peridotitic-lsquolsquopyroliticrdquo composition (Fig 11a) Subducting

Fig 7 Comparison of depth profiles throughout the mantle of global average radialanisotropy parameter n = (VshVsv)2 in 6 recent global shear velocity models n = 1corresponds to isotropy Model S362ANI (Kustowski et al 2008) is isotropic in thelower mantle While there are differences between models all of them agree thatradial anisotropy is strongest in the first 200 km of the mantle and very weak inmost of the lower mantle In D00 on average Vsh is equal of slightly faster than Vsv

66 B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90

slabs may correspond to more siliceous aluminous and Ca-richmid-ocean ridge basalts (MORB eg Irifune and Ringwood 1993Fig 11b) In both cases MgSiO3-perovskite (bridgmanite) domi-nates in large volumes of the lower mantle but for MORB compo-sitions high pressure silica and alumina phases are alsosignificant and there may be no ferropericlase Calcium perovskite(CaSiO3) is cubic (spacegroup Pm3 m) at lower mantle conditions(eg Wang et al 1996 Kawai and Tscuchiya 2015) and is animportant component at depths beyond 750 km It distorts to atetragonal structure at low temperature and high pressure (egShim et al 2002)

As more details about the lower mantle are revealed composi-tional heterogeneities become apparent (eg Badro et al 2003 LiY et al 2014) Higher concentrations of Si Al and Fe add consider-able complexity The diverse composition is in part the result ofsubduction of slabs composed of crust and upper mantle Silica(SiO2) may exist as stishovite with a rutile structure and 6-foldcoordination or at higher pressure as a cubic phase with CaCl2structure and 8-fold coordination (eg Kingma et al 1995) andat even higher pressure as an orthorhombic (Pbcn) a-PbO2 struc-ture (seifertite) (eg Dubrovinsky et al 2004 Grocholski et al2013 Zhang et al 2016) According to first principles calculationsat extreme pressure SiO2 may transform to a pyrite structure(Kuwayama et al 2005) Al2O3 in the form of trigonal corundumor orthorhombic Rh2O3(II) may be present and Fe may exist asnative iron (eg Frost et al 2004 Shi et al 2013)

Of considerable importance is the oxidation state as well as thespin state of iron that have received a lot of attention (egMcCammon 1997 Badro et al 2003 Li et al 2004 Tsuchiya

et al 2006 Fei et al 2007 Lin et al 2008 Catalli et al 2010Saha et al 2011 2012 Vilella et al 2015) With increasing pres-sure there is a transition from a high spin to a low spin configura-tion It may be responsible for the anomalous viscosity structure inthe central part of the lower mantle (900ndash1200 km eg Rudolphet al 2015) although the spin transition is generally thought tooccur deeper (1500 km)

In addition hydrogen may play a significant role (eg Ohtamiand Sakai 2008) A hydrous aluminosilicate is stable at lower man-tle conditions (eg Tsuchiya and Tsuchiya 2008 2011 Pamatoet al 2014) and dehydration may cause melting at the top of thelower mantle (Schmandt et al 2014)

As far as elastic properties and anisotropy are concerned oneshould keep in mind that the major phases over large volumes ofthe lower mantle are bridgmanite ferropericlase pPv and CaSiO3

perovskite These contribute largely to the bulk elastic propertiesbut there may be local deviations

32 Some comments on plasticity models and representation ofanisotropy

What are the sources of seismic anisotropy in the Earth Veryimportant is the alignment of anisotropic crystals called crystalpreferred orientation (CPO) or texture (based on DrsquoHalloy 1833)and universally used in materials science The crystal anisotropyis linked to the crystal structure A second aspect is crystal shapethat produces a shape-preferred orientation (SPO) CPO and SPOare sometimes linked (in mica for example the crystal plane(001) is parallel to the platelet) Often it is not (eg in quartz orin periclase) Also significant is the orientation of flat fracturesand fractures filled with kerogen This is a very important contribu-tion to anisotropy in shales (eg Hornby et al 1994 Sayers 1994Vasin et al 2013) but insignificant in the lower mantle In thelower mantle there is the possibility of partial melt particularlynear the core-mantle boundary (eg Williams and Garnero 1996Lay et al 2004 Shi et al 2013) but this would only give rise to ani-sotropy if melt occurred in parallel thin layers (eg Backus 1962)We will focus here on the development of CPO

Before going into plasticity in the mantle a few words aboutdeformation mechanisms of polycrystalline aggregates are inorder Deformation experiments on minerals have a long historyPfaff (1859) documented mechanical twinning in calcite when astress is applied In the early twentieth century deformation exper-iments at a wide range of temperature and strain conditions wereconducted on metals to explore the deformation behavior (egSchmid 1924) and in this context linear defects called dislocationswere discovered (Polanyi 1934 Taylor 1934) Without disloca-tions it would be very difficult to deform crystals and indeed theyare present in most crystalline materials

Dislocations form in the crystal lattice when a stress is appliedEdge dislocations propagate on a glide plane (hkl) and in a slipdirection [uvw] defined by rational indices relative to crystallo-graphic axes Propagation of dislocations causes crystals to rotaterelative to the applied stress which is conceptually illustrated foran experimentally compressed single crystal in Fig 12 By move-ment of dislocations on glide planes the rectangular crystal attainsa new shape (parallelogram) Since pistons must stay in contactthis results in an effective rotation of b In a polycrystalline aggre-gate neighboring grains play the function of pistons

Based on deformation experiments on metals deformationmechanism maps were established (eg Ashby 1972 Langdonand Mohamed 1978 Frost and Ashby 1982) They define condi-tions such as temperature pressure stress magnitudes strain rateand grain size under which mechanisms such as dislocation glidedislocation climb grain boundary migration and grain boundarysliding are active (Fig 13) Identifying mechanisms is important

Fig 8 Comparison of 6 recent models of lateral variations in the radial anisotropy parameter n = (VshVsv)2 plotted in terms of dlnn referred to isotropy While the modelsdisagree in detail common features are Vsh gt Vsv (blue) in the circum Pacific ring (roughly in agreement with local studies) and pronounced Vsv gt Vsh (orange) in the Fiji-TongaIndonesia region and under southernmost Africa (except SAVANI) Models plotted are (a) SAW642ANb (Panning et al 2010) (b) SAW642AN (Panning andRomanowicz 2006) (c) SAVANI (Auer et al 2014) (d) SGLOBE-rani (Chang et al 2015) (e) S362WANI + M (Moulik and Ekstroumlm 2014) (f) SEMUCB_WM1 (French andRomanowicz 2014)

Fig 9 (a) Experimentally determined PT phase diagram for perovskitebridgmanite (Pv)-post-perovskite (Murakami et al 2004) (b) T-Depth phase diagram plotting the pv-ppv phase boundary and cold and warm geotherms (after Hernlund et al 2005)

B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90 67

because some produce crystal rotations and thus crystallographicpreferred orientation (notably dislocation glide and ndash to someextent ndash dynamic recrystallization) while others generate random

orientations (such as grain boundary sliding in fine-grained mate-rials and dislocation climb) We will return to these issues inSection 48

Fig 10 Crystal structures of (a) periclase (b) bridgmanite and (c) post-perovskite the latter two with octahedrally coordinated silicon

Fig 11 Lower mantle composition for different models (a) pyrolite (b) MORB(from Irifune and Tsuchiya 2015) Pv perovskitebridgmanite Ppv post-perovskiteMw magnesiowuestiteferropericlase Mj majorite Rw ringwoodite SiO2 Ststishovite CC CaCl2 phase AP a-PbO2 phase Al2O Hex CF calcium-ferrite phaseCT calcium-titanate phase

68 B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90

In a polycrystalline aggregate stresses are transmitted acrossgrain boundaries causing heterogeneities even within grains Thisis most realistically approached with finite element methods (egMika and Dawson 1999) but these are still extremely demandingand rarely applied Simpler models have been used in materialsscience for a long time The Taylor (1938) theory developed bythe same Taylor who discovered dislocations (1934) assumeshomogeneous strain All grains undergo the same shape changeirrespective of orientation This leaves grain boundaries intact(Fig 14 left side) The Taylor model is very applicable to cubic met-als with many symmetrically related slip systems Slip on 111h

1 1 0i in fcc metals or cubic periclase has 12 equivalent systemsAnother model (Sachs 1928) assumes stress equilibrium and morefavorably oriented grains deform more than others In the modelthis causes overlaps and gaps at grain boundaries In principle thiswould be more adequate for low symmetry minerals (such asorthorhombic) but of course overlaps and gaps do not exist A com-promise between homogeneous strain and stress equilibrium is aself-consistent model that treats grains as ellipsoidal inclusionsdeforming in an anisotropic viscous medium (Fig 14 centerMolinari et al 1987) It is most widely applied in the Los Alamoscode VPSC (Lebensohn and Tomeacute 1993) and it can be used bothto understand preferred orientation in high pressure experimentsand to predict anisotropy in geodynamic models In the viscoplas-tic self-consistent model grains deform without knowledge of theirneighborhood In a finite element model (Fig 14 right) grains areconstrained by the orientation of neighbors In this sketch it isassumed that each grain has a single orientation In more sophisti-cated FEM models there are strain and orientation gradients devel-oping within grains (eg Mika and Dawson 1999)

When crystals are deformed in a polycrystalline medium theyundergo systematic rotations (Fig 12) and the material attains ananisotropic pattern We need to describe the orientation of a crys-tal relative to the macroscopic sample This is efficiently done byrelating two orthogonal coordinate systems (sample x y z crystal[100] [010] [001]) by three rotations Most frequently the so-called Euler angles are used U is the distance from z to [001]1 is the azimuth of [001] from y (around z) 2 is the azimuthof [100] around [001] (Fig 15) The 3-dimensional crystal orienta-tion distribution (COD) is conventionally described by a continuousorientation distribution function (ODF) The ODF is required to cal-culate anisotropic elastic properties of an aggregate from crystalorientations

For graphical representations of orientation patterns generally2-dimensional spherical projections of the ODF are used Depend-ing on the application one can either use the macroscopic sample xy z as reference and plot crystal directions (pole figures) or use thecrystal as reference and plot sample directions (inverse pole fig-ures) Inverse pole figures are useful if only a single sample direc-tion is of interest eg the compression direction in a compressionexperiment The symmetry of pole figures reflects the symmetry ofthe deformation path In compression experiments pole figures areaxially symmetric The density of poles on the sphere is contouredand then expressed as continuous pole densities usually normal-ized relative to a random distribution and defined as multiples ofa random distribution (mrd) 2ndash5 mrd are moderate CODs20ndash50 mrd very strong CODs The strongest crystal alignmentsin rocks that have been observed are muscovite in slates exceeding100 mrd Fig 16a is a 111 pole figure of rolled copper with roll-

Fig 12 Under stress imposed by pistons a crystal deforms to a new shape by slip of dislocations on a glide plane Since pistons remain in contact with the crystal surfacethere is an effective rotation b In a polycrystal neighboring grains act as effective pistons to transmit the stress

Fig 13 Stress-temperature deformation mechanism map (Langdon and Mohamed1978)

B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90 69

ing R transverse T and normal N sample directions indicatedFig 16b is the corresponding inverse pole figure of the normaldirection Inverse pole figures display the crystal symmetry Bothrepresentations will be used in the following discussion

33 Deformation experiments and rheology

The experiments on plasticity of metals were not applicable tomost minerals because even at elevated temperatures theirdeformation behavior at ambient pressure is generally brittleOne had to wait until high pressure deformation experiments weredeveloped by Griggs (1936) and applied on a wide scale includingolivine (eg Raleigh 1968) Since then sophisticated deformationapparati have been constructed in many laboratories making itpossible to deform rocks at a wide range of pressures and temper-atures They were applied to many minerals and rocks in the crustand upper mantle Studies on olivine (eg Jung and Karato 2001

Hansen et al 2012 Jackson and Faul 2010) documented the com-plex influence of temperature pressure composition (such aswater and iron content) The most sophisticated apparatus wasdeveloped at the Australian National University (Paterson andOlgaard 2000) It allows for deformation experiments on relativelylarge samples (1 cm) in compression tension and torsion Pres-sures are limited to 03 GPa and the limitation in pressure pre-vents these instruments to be used for experiments relevant tothe lower mantle (20ndash150 GPa) and inner core (320ndash360 GPa)

Higher pressure deformation experiments have been reviewedby Weidner and Li (2015) The multi-anvil apparatus called DIAwith three pairs of octahedral pistons (Onodera 1987) has beenmodified to apply stress by preferentially advancing one pistonpair (D-DIA for deformation DIA) The sample can be heated inter-nally Changes in phase structure preferred orientation andmicrostructure can be recorded in situ if the D-DIA apparatus iscombined with a monochromatic synchrotron X-ray beam fordiffraction and imaging (eg Wang et al 2003 2011) The conven-tional D-DIA apparatus has been used to 20 GPa and samples arecylinders 1 mm in diameter (eg Kawazoe et al 2010) A moreadvanced D-DIA (Kawai-type) reaching gt110 GPa with sintereddiamond anvils and smaller samples has been introduced atSPring8 in Japan (Yamazaki et al 2014)

Shear deformation at high pressure can be performed with arotational Drickamer apparatus (RDA) (eg Yamasaki and Karato2001) Shear deformation of a bridgmanite-ferropericlase aggre-gate at 25 GPa and 2100 K has been achieved to large strains(Girard et al 2016) In such torsion experiments the strain variesgreatly as a function of sample radius The experiment documentedthat most of the plastic deformation is accommodated by theweaker ferropericlase

Currently the most accessible method to deform samples atultrahigh pressures (gt500 GPa) is with diamond anvil cells (DAC)where diamonds are used as pistons compressing a small sample(30ndash80 lm in diameter and 50 lm thick) (eg Merkel et al2002 Fig 17) The diamonds are used not only to induce pressurebut also to cause compressive deformation (Fig 17 b c) and theevolution of preferred orientation can be observed in situ if hori-zontal X-rays transmit the sample in radial diffraction geometry(r-DAC) Strong textures have been observed in ferropericlase(eg Merkel et al 2002 Lin et al 2009) perovskitebridgmanite(eg Merkel et al 2003 Wenk et al 2006 Miyagi and Wenk2016 Tsujino et al 2016) and pPv the phase likely to be presentat the core-mantle boundary (eg Merkel et al 2006 2007

Fig 14 2D Sketches of polycrystal plasticity models Gray shades express orien-tation (Left) For the full constraints Taylor model all grains undergo the samedeformation regardless of orientation (Center) The viscoplastic model VPSC treatsgrains as inclusions in an anisotropic viscous medium (Right) In finite elementmodels grains deform differently depending on the orientation of neighbors

Fig 15 Definition of crystal orientation relative to sample coordinates with threerotations (Euler angles) 1 U 2 Projection based on sample coordinate system xy z (pole figure) Crystal coordinate system is defined by axes [100] [010] and[001]

Fig 16 Comparison of (a) 111 pole figure relative to sample coordinates and (b) Ninverse pole figure relative to crystal coordinates for rolled copper Equal areaprojection red colors are high and blue colors are low pole densities N normaldirection R rolling direction and T transverse direction Note the equivalentinformation In the 111 pole figure a maximum in the N direction and in the NDinverse pole figure a maximum in 111

70 B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90

Miyagi et al 2010 2011 Wu et al 2017) Shear deformation canbe induced in rotational DACs (eg Levitas et al 2006) Thismethod has been mainly used to induce phase transformationsand has not yet been applied to study texture evolution at highpressure

In addition to pressure and stress temperature can be inducedin DAC experiments by resistive (eg Liermann et al 2009) andlaser heating (eg Prakapenka et al 2008 Dubrovinsky et al2009) or a combination of the two (Miyagi et al 2013) Tatenoet al (2015) reached temperatures of 6000 K at gt400 GPa on exper-iments on Fe and Fe-Si corresponding to conditions of the Earthrsquos

inner core Obviously there are limitations to DAC experimentssamples are extremely small strain is always compressive andstrain rates are difficult to control

It was surprising to see that silicates and oxides that are brittleat ambient conditions including olivine become ductile at pres-sures of 10GPa even at room temperature and deform by dislo-cation glide (eg Wenk et al 2004) The diffraction image ofMgSiO3 post-perovskite at 150 GPa (Fig 18a) is lsquolsquounrolledrdquo andthe compression direction is indicated by arrows (large 2h smalld Q=1d) (Fig 18b) The elastic lattice distortion (wave-like patternwith azimuth) is related to applied stress and elastic propertiesThe intensity variations with azimuth are indicative of preferredorientation For example there is a strong maximum for 004(fourth order diffraction on the lattice plane 001) in the compres-sion direction This image illustrates why radial diffraction geome-try has to be used to display CPO as function of angle to thecompression direction In axial geometry (X-rays parallel to thediamond axis) Debye-rings have uniform intensity since alldiffracting lattice planes have the same angle to the compressiondirection

A qualitative interpretation of a diffraction image is illustratedin Fig 19 for an experiment with MgGeO3 post-perovskite(Miyagi et al 2011) and used to construct an inverse pole figureof the compression direction (arrow) MgGeO3 is an analog ofMgSiO3 but transforms to pPv at lower pressure There is a maxi-mum for 002 and a minimum for 020 in the compression directionwhich can be plotted in the inverse pole figure (Fig 19 right side)The quantitative deconvolution of diffraction images is not trivialand most often an iterative Rietveld method is applied (egLutterotti et al 2014 Wenk et al 2014) The high pressure syn-chrotron X-ray diffraction deformation images provide quantita-tive information about phases crystal structures density stresselastic properties and preferred orientation

Fig 20a-c shows experimental inverse pole figures of MgSiO3

pPv documenting increasing texture development with pressure-stressndashstrain with a maximum at (001) From the orientation pat-tern active slip systems can be derived by comparing experimentalinverse pole figures with results from polycrystal plasticity calcu-lations that assume certain combinations of slip systems(Fig 20d) Based on the good agreement it can be concluded thatpPv deformed in the experiment by dominant (001)[100] slip(Miyagi et al 2010)

With similar experiments it was suggested that MgSiO3 bridg-manite deforms dominantly by slip on (001) planes in [100][010] and h1 1 0i directions (eg Miyagi and Wenk 2016) but sim-

Fig 18 (a) Diffraction image of MgSiO3 post-perovskite at 150 GPa (b) Unrolled diffractiochanges in Q are due to elastic distortion of the crystal lattice under compression Botquantitative information such as inverse pole figures

Fig 17 Diamond anvil cell for radial diffraction experiments The X-ray beam ishorizontal (a) illustrates the cell and the insert is an enlargement with diamondsand gasket to contain the sample (b c) illustrate that diamonds not only applypressure but also compressive stress that deforms the sample and produces CPO

B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90 71

ple shear experiments in a D-DIA apparatus indicate (100)[001]slip (Tsujino et al 2016) Ferropericlase likely deforms by 110h110i slip (eg Stretton et al 2001 Merkel et al 2002 Linet al 2009) at high pressure conditions For Ca-perovskite domi-nant 110h110i slip was proposed (Miyagi et al 2006 2009)

So far most DAC high-pressure deformation experimentsextracted COD information from intensity variations along Debyerings (eg Fig 18) A new method called multigrain is still underdevelopment It obtains orientation information from individualgrain diffractions (eg Barton and Bernier 2012 Rosa et al2015 Langrand et al 2017) and is especially applicable to coarseraggregates Nisr et al (2012) used information about dislocationsfrom distortion of single crystal diffraction patterns of the post-perovskite analog MgGeO3 and suggested dominant slip on 110and (001) planes

It should be mentioned that information from such high pres-sure experiments is by no means unambiguous Obviously defor-mation conditions in experiments and simulations differconsiderably from those in the deep Earth just to mention temper-ature grain size strain rate interaction of dislocations and interac-tion between grains Furthermore not all CPO patterns that areobserved are due to deformation but could be inherited from orien-tation patterns of precursor phases such as for pPv from perovskite(Dobson et al 2013) or enstatite (Merkel et al 2006 2007 Miyagiet al 2011) Also slip systems may not be the same for pPv phasesof different compositions such as MgGeO3 CaIrO3 NaMgF3 orMn2O3

A different approach has become very important computationof Peierlrsquos stresses and lattice friction for dislocation systems basedon bonding characteristics It was originally developed for metals(eg Kubin et al 1992 Devincre and Kubin 1997) and has morerecently been applied to minerals in the mantle where it allowsto predict slip system activities for a wide range of temperaturendashpressurendashstrain rate conditions (eg Carrez et al 2007Mainprice et al 2008 Cordier et al 2012) Amodeo et al (20122014 2016) propose a switch from 110h010i slip to 100h0 1 1i slip in periclase with pressure Kraych et al (2016) suggest(010)[100] slip in bridgmanite at high pressure According tothese calculations the strength of bridgmanite increases greatlywith pressure and at 60 GPa bridgmanite appears 20 times stron-ger than periclase The critical resolved shear stress decreasesabout 20 from strain rates of 105 s1 (which corresponds to

n image as function of Q (Q = 1d) Intensity variations with azimuth illustrate CPOtom experimental data above fit of the data with the Rietveld method to extract

Fig 19 Explanation of the relationship between DAC diffraction image and inverse pole figure Left Unrolled diffraction image of MgGeO3 post-perovskite Some diffractionlines are labeled The sinusoidal variations are due to imposed stress High stress (high Q low d) is indicated by arrows On the right side is a conceptual construction of theinverse pole figure of the compression axis based on relative diffraction intensities (Miyagi et al 2011)

Fig 20 Inverse pole figures for MgSiO3 post-perovskite (AndashC) experiments (D) Plasticity model with dominant (001) slip equal area projection (Miyagi et al 2010)

72 B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90

experimental values) to 1014 s1 corresponding to likely values atdeep mantle conditions (Fig 21a) The opposite is the case for pPvwhich appears much weaker than periclase at high pressure hightemperature and slow strain rates (Fig 21b Goryaeva et al 20152016) Also the predicted weakest calculated slip system for post-perovskite at deep mantle conditions is (010)[100] correspondingto the layered crystal structure (Fig 21c) but different from thatobserved in DAC experiments (Miyagi et al 2010 Wu et al 2017)

It should be mentioned that a single slip system is not sufficientto deform a polycrystal In the case of the Taylor model at least 5systems have to be active to produce an arbitrary strain (Mises1928) This is relaxed for the self-consistent model but also hereseveral slip systems are active The choice of activity depends onthe crystal orientation relative to the applied stress (Schmid fac-tor) TEM investigations confirm this though some slip systemsusually dominate and the literature refers to the lsquolsquodominantrdquo slipsystem Some dominant slip systems for deep Earth minerals aresummarized in Table 2

34 Elastic properties

Elastic properties of crystals at conditions pertaining to thelower mantle are critical to link microstructural properties of therock with seismic observations The most straightforward experi-mental method that has been applied to many lower mantle min-erals is Brillouin scattering (see review by Speziale et al 2014) andenergy-dispersive X-ray diffraction (eg for calcium silicate per-ovskite Shieh et al 2004) A different approach is with first prin-ciples calculations at high pressure and temperature (for someapplications to bridgmanite CaSiO3 perovskite and pPv see egZhang et al 2013 Wentzcovitch et al 2005 Kawai and

Tsuchiya 2015) First principles results look fairly consistent forminerals at lower mantle conditions but as we will see in Sec-tion 62 predictions for iron at inner core conditions are stillambiguous Furthermore the actual composition of the mineralsparticularly the iron content can be significant (eg Koci et al2007) Values of stiffness coefficients and P-wave anisotropy (An = 200(Pmax Pmin)(Pmax + Pmin) for some low mantle mineralsat lowermost mantle conditions are listed in Table 3 Fig 22 givescorresponding S velocities of single crystals with black lines corre-sponding to the orientation of the fast S-wave polarization As canbe seen in Table 1 periclase and pPv have the highest P-wave ani-sotropy and Ca-perovskite is least anisotropic The S-wave aniso-tropy is considerably higher for pPv and periclase than forbridgmanite and particularly CaSiO3 perovskite

To obtain elastic properties of aggregates one has to averageover all orientations and corresponding elastic tensors takingphase fractions into account Simple averages are upper bound(Voigt 1887) and lower bound (Reuss 1929) Generally an inter-mediate arithmetic mean (Hill 1952) or a geometric mean(Matthies and Humbert 1995) are preferred All these models donot take grain shape into account which is not very significantfor crystalline phases but becomes important for systems withplaty minerals such as graphite or sheet-silicate containing rocksand aggregates with flat oriented pores For such cases a self-consistent (Matthies 2012 Vasin et al 2013) or differential effec-tive medium approach (eg Hornby et al 1994) should be consid-ered It is probably not important for the lower mantle

Note that S-waves passing through anisotropic media have arbi-trary polarization directions in the plane perpendicular to thedirection of propagation as is best displayed for the fast directionof single crystals in Fig 22 but applies also to aggregations of ori-

Fig 21 Critical resolved shear stress CRSS for dislocation glide activities as functionof temperature of (a) bridgmanite at 60 GPa (from Kraych et al 2016) and MgO(from Amodeo et al 2016) at strain rates 105 s1 and 1014 s1 (b) post-perovskiteat 120 GPa at strain rate 1016 s1 (from Goryaeva et al 2016) compared with MgO(from Amodeo et al 2012) Courtesy of P Cordier

B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90 73

ented crystals Seismologists generally consider the projection ofthat polarization direction onto horizontal and vertical axes Thisis convenient because differences in arrival times and waveformsin this representation can be expressed in terms of apparent verti-cal transverse isotropy (VTI) which because of limited azimuthalsampling is often the only anisotropic constraint that can beobtained

4 Linking seismology and mineral physics through predictionsof anisotropy in geodynamic models

41 Isotropic geodynamic models for upper mantle convection

Ever since the concept of plate tectonics became accepted in the1960s convective movements in the Earthrsquos mantle have been pro-posed such as upwelling along oceanic ridges (eg Hess 1964Cann 1968 Fig 1b) The first quantitative models based on hydro-dynamics emerged in the eighties (eg Hager and OrsquoConnell 1981)

Table 2Proposed dominant slip systems in deep Earth minerals

Ferropericlase Lower P 110110High PT also 100011

Bridgmanite Low P (001)[100] [010] 110High P (100)[001](010)[100]

pPv (001)[100](010)[100]

Ca-perovskite 110110e-iron (0001)1120 subordinate 1010

Geodynamic models have been mainly applied to the upper mantleand we will not discuss them here in detail (see eg review by Longand Becker 2010)

Many convection models have been developed to understandthe evolution of the deep Earth Calculations generally assume aviscous fluid and use non-dimensional equations for the conserva-tion of mass momentum and energy applying the Boussineqapproximation Critical parameters are Rayleigh number viscosityboundary temperatures In order to evaluate the strain evolutionduring the convection process tracers are introduced that recordthe velocity gradient tensor at each time step along the path ofthe tracer If the deformation mechanisms are known (eg disloca-tion glide) polycrystal plasticity calculations can be used to calcu-late the evolution of crystal preferred orientation based on thestrain recorded by tracers

Most geodynamic models assume a viscous isotropic mediumwith a smoothly varying viscosity structure and the microstruc-tural processes leading to preferred orientation are introducedpost-mortem Considering an anisotropic medium that constantlychanges its properties greatly increases the complexity of geody-namic calculations However there are models in metallurgy suchas extrusion of an aggregate that illustrate the importance of ananisotropic material behavior (eg Beyerlein et al 2003)

42 Review of upper mantle anisotropic models

We will start the discussion of anisotropic convection byreturning to a simple 2D model (Dawson and Wenk 2000) thatwas originally issued as an educational video by AGU (1999) andcan now be downloaded in digital form (httpepsberkeleyedu~wenkTexturePageMantle-Videohtm) At high Rayleigh number(low viscosity) heat transfer occurs by convection rather than con-duction corresponding to conditions in the Earthrsquos mantle Convec-tion is driven by temperature gradients As aggregates move alongstreamlines the orientation of grains is constantly updated and thelocal texture affects the next deformation step which introducesconsiderable heterogeneities It was surprising to find locallyheterogeneous CPO patterns in the 2D convection cell representingthe upper mantle shown as [100] pole figures of olivine after100 my (Fig 23) Some regions have strong and others very weakpatterns that can be attributed to heterogeneous deformation dueto CPO development and result in lsquolsquoanisotropicrdquo viscosity

Some complexities of different plasticity models for a simplecase of upwelling have been investigated by Blackman et al(1996 2002) and Castelnau et al (2009) If a lower bound behavioris assumed (Sachs 1928) there is very strong CPO developmentFor self-consistent models (Lebensohn and Tomeacute 1993) rotationsare reduced If dislocation glide is combined with dynamic recrys-tallization both grain growth and grain growth combined withnucleation resulting orientation patterns can be very differentRecrystallization is likely in the deep Earth with high temperatureand large strains where grain boundary migration is likely tooccur We will return to the issue of recrystallization in Section 48

Merkel et al (2002) and Lin et al (2009)Amodeo et al (2016)Miyagi and Wenk 2016Tsujino et al (2016)Kraych et al (2016)Miyagi et al (2010) and Wu et al (2017)Goryaeva et al (2016)Miyagi et al (2009) and Ferreacute et al (2009)

Merkel et al (2004) and Miyagi et al (2008)

Fig 4 Example of change of character of particle motion for paths sampling theborder of the African LLSVP (a) Map showing the paths sampled plotted on top of abackground shear wave tomographic model (SAW24B16 Meacutegnin and Romanowicz2000) The portion of path sampling the D00 region is highlighted in yellow (b) and(c) shows particle motions of Sdiff at distances of 120o and at two azimuths In (b)the path in D00 is outside of the LLSVP and in (c) the path in D00 is inside the LLSVP(from To et al 2005) The color indicates the time with respect to predicted Sdiffarrival from PREM Black 35 to 5 s Blue 5 to 20 s Green 20 to 45 s Red 45 to70 s The elliptical particle motion in (B) contrasts with the linear particle motion in(c) This cannot simply be explained by lateral heterogeneity in isotropic velocity asone would expect larger amplitudes in SV for waves propagating inside the lowvelocity LLSVP This interpretation was later confirmed by 3D numerical waveformmodelling (Cottaar and Romanowicz 2013) (For interpretation of the references tocolor in this figure legend the reader is referred to the web version of this article)

B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90 63

The recent results indicate variability of anisotropy at relativelyshort scales with evidence for azimuthal anisotropy with differentorientations of fast velocity axes at least in regions of faster thanaverage isotropic shear velocity Interestingly the studies ofCottaar and Romanowicz (2013) Lynner and Long (2014) andFord et al (2015) consistently show changes in anisotropy acrossthe border of the African LLSVP with stronger anisotropy outsideof it practically disappearing inside it (eg Fig 5) Interestinglythe same trend although less sharply defined because of the chal-lenging geometry is likely present at the northern edge of the Paci-fic LLSVP (Fig 6) Indeed all studies of the latter region considerpaths from Fiji-Tonga sources to stations in north America Differ-ent results are found for different distance ranges with VsvgtVshfor the shorter distances sampling inside the LLSVP (as well asabove D00) and VshgtVsv at longer distances (Sdiff) which samplea significant portion of the fast Vs region outside of the LLSVPVinnik et al (1995 1998b) used Sdiff data and found VSHgtVSV theportion of the corresponding paths inside the LLSVP was smalland Vinnik et al (1998b) showed that splitting only occurred fordistances larger than 102o when paths sampled more of the fastregion outside of the LLSVP Likewise Fouch et al (2001) andRitsema et al (1998) used S Sdiff and found VshgtVsv for larger dis-tance paths while VsvgtVsh for shorter distance paths that samplewithin the LLSVP and above D00 as did Kawai and Geller (2010)Pulliam and Sen (1998) and Russell et al (1998) used S and ScSrespectively at shorter distances sampling inside the LLSVP andfound VsvgtVsh

All these results point in the same direction evidence for signif-icant anisotropy with generally VshgtVsv within the ring of fastvelocities surrounding the Pacific and African LLSVP possiblyincreasing and tilting at their borders but vanishing or changingsign (VsvgtVsh) inside the LLSVPrsquos

24 Results from global anisotropic tomography

Gaining improved understanding of the distribution and natureof seismic anisotropy at the base of the mantle requires better glo-bal sampling with accurate corrections for upper mantle aniso-tropy One possible approach is to construct global whole mantletomographic models of anisotropy Such an approach is attractivebecause a variety of seismic waveforms can be included in partic-ular fundamental and overtone surface waves which provide con-straints on the strong anisotropy in the uppermost mantle (egDebayle and Ricard 2013) Combining surface wave data with var-ious body waveforms that illuminate the entire mantle should ulti-mately allow improved resolution and characterization of deepmantle anisotropy So far this has proven very challenging forthe deep mantle

Indeed most successful has been the tomographic characteriza-tion of shear wave azimuthal anisotropy in the uppermost 200 kmof the mantle at the global scale using Rayleigh wave dispersiondata (eg Tanimoto and Anderson 1984 Montagner andTanimoto 1990 1991 Fig 1) More recent models developed bydifferent groups show broadly consistent trends (eg Trampertand Woodhouse 2003 Ekstroumlm 2011 Debayle and Ricard 2013Yuan and Beghein 2013) On the other hand the robustness of glo-bal scale transition zone azimuthal anisotropy models that utilizesurface wave overtone information (eg Trampert and van Heijst2002 Yuan and Beghein 2013) is still debated This is becausethe anisotropic signal in overtone surface waves is weak the azi-muthal sampling far from ideal and the number of parametersneeded to invert for azimuthal anisotropy at the global scale evenwhen considering only the dominant terms in 2-w (where w is theazimuth) is very large likely resulting in trade-offs with isotropicstructure It is not possible at present to extend this type of studyto the deep mantle as the sensitivity of available long period over-tone data becomes too weak and azimuthal coverage for bodywaves provided by the current geometry of sources and stationsis not sufficient

Thus tomographic imaging of anisotropy in the whole mantlecan at present only hope to resolve the simplest form of aniso-tropy that does not have as strong requirements on azimuthal cov-erage which is VTI (or apparent VTI) Such studies are based onrelatively long period waveforms mostly sensitive to shear veloc-ity combining fundamental mode surface waves surface waveovertones and shear body waves and aim at solving for the distri-bution of only two anisotropic parameters Vsh and Vsv or alter-natively isotropic velocity Vsiso and the anisotropic parameter n =(VshVsv)2 (Panning and Romanowicz 2004 2006 Panning et al2010 Kustowski et al 2008 French and Romanowicz 2014Moulik and Ekstroumlm 2014 Auer et al 2014 Chang et al 20142015) The other three anisotropic parameters that are necessaryto fully describe a VTI medium are scaled to Vsiso and n using scal-ing relations that are appropriate for the upper mantle (egMontagner and Anderson 1989) but may be questionable for thelower mantle However this may not be a significant issue giventhe dominant sensitivity of the waveforms considered to shearvelocities While the resulting models show qualitative agreementat long wavelengths details vary frommodel to model significantlyenough not to be trustworthy for quantitative interpretations

These models do agree on the following observations on aver-age radial anisotropy is strongest in the uppermost mantle andmost of the lower mantle exhibits little radial anisotropy (Fig 7)

Fig 5 a and b Whole mantle depth cross sections through the isotropic Vs part of model SEMUCB_WM1 (French and Romanowicz 2014) at the southern (a) and eastern (b)edge of the African LLSVP where rapid variations in the direction and strength of anisotropy have been reported decreasing from outside (blue) to inside (pink) the LLSVP inc) the map view is from Lynner and Long (2014) with background shear velocity model GyPSuM of Simmons et al (2012) The cross-section location is indicated on the mapby a straight line c and d corresponding cartoons proposed by the authors respectively (c) Cottaar and Romanowicz (2013) (d) Ford and Long (2015)

64 B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90

Inmostmodels there is an indication of an increase in anisotropy inD00 with Vshgt Vsv (n slightly larger than 1) although there is vari-ability among models due to a combination of parametrizationtypes of seismic waves considered and theoretical assumptions

Common 3D features of these models in D00 are a predominanceof Vsh gt Vsv outside of the LLSVPs with patches of Vsh lt Vsv con-fined within the LLSVPs in agreement with local studies (Fig 8)However the current models do not show consistency in theamplitude of the lateral variations in n nor the wavelengths ofthese variations This is partly due to the parametrization chosenFor example Panning and Romanowicz (2004 2006) and Aueret al (2014) allowed relatively short wavelength lateral variationsin n while Moulik and Ekstroumlm (2014) and French andRomanowicz (2014) chose to assign shorter wavelength lateralvariations to isotropic Vs while constraining the anisotropic partof the model to be smooth Theoretical assumptions on wave prop-agation are also important ray theory is not valid for modelling ofSdiff nor is it valid to use the surface wave approximation for mod-elling this phase as shown by Li and Romanowicz (1995) So faronly the Berkeley models are constructed taking into account finitefrequency effects rather than ray theory for body waves (Panningand Romanowicz 2004 2006 French and Romanowicz 2014)

One fundamental issue is that Sdiff and ScSn data (with ngt1) arenecessary to obtain good coverage of D00 at the global scale As dis-cussed previously SVdiff decays rapidly with distance in modelssuch as the reference model PREM (Dziewonski and Anderson1981) where the velocity in D00 is relatively fast The global datasetsare thus necessarily biased although to various degrees depending

on the particular dataset by the predominance of SHdiff introduc-ing trade-offs between isotropic and anisotropic structure (egKustowski et al 2008 Chang et al 2015) and making it only pos-sible to resolve the very longest wavelengths of VTI in D00 withpoor constraints on their amplitude

In summary robustly mapping even the simplest component ofseismic anisotropy apparent VTI at the base of the mantle at highresolution using a tomographic approach is still a challenging openquestion let alone constraining azimuthal anisotropy at the globalscale Still available global models agree with local studies aboutthe prevalence of VshgtVsv in regions of faster than average velocityin D00

As for P wave anisotropy in the deep mantle only few studieshave tried to constrain it so far Several studies have attemptedto retrieve the global average variation with depth of the radiallyanisotropic parameter g = (VphVpv)2 using normal mode data(Montagner and Kennett 1996 Beghein et al 2006) finding someindication that the anisotropy in gmay be anticorrelated with thatof n in the D00 region with however strong trade-offs with density(to which normal mode data are also sensitive) Note that the anti-correlation of isotropic P and S velocities at long wavelengths inthe deep mantle is in contrast better established (eg Su andDziewonski 1997 Kennett and Widyantoro 1998 Masters et al2000 Ishii and Tromp 1999 Romanowicz and Breacuteger 2000) Thepossibility of P wave anisotropy in the deep mantle using P wavedata (mantle and core phases) has been investigated by Boschiand Dziewonski (2000) concluding that anisotropy may be smallwith significant trade-offs with core-mantle boundary topography

Fig 6 Zoom on the northern edge of the Pacific LLSVP The background tomographic model is the isotropic Vs part of model SEMUCB_WM1 (French and Romanowicz 2014)(A) Map view with locations of studies of D00 shear wave splitting suggesting a change of character of anisotropy across the boundary of the LLSVP Green dots indicate thelocation of major hotspots Black line with white and purple dots is the great circle path corresponding to the depth cross section shown in (B) displaying the Hawaian plumeand transition from low to fast velocities in D00 Kawai and Geller (2010) Pulliam and Sen (1998) and Russell et al (1998) find VSV gt VSH while Ritsema et al (1998) Fouch et al(2001) and Vinnik et al (1998) find that Vsh gt Vsv increasingly so for paths sampling the fast region outside of the LLSVP Note that the color saturation of the tomographicmodel is different in (A) and (B)

B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90 65

and outer core structure The possible anticorrelation of P and Sradial anisotropy in the D00 must therefore be considered with cau-tion at the present time when used as a constraint in modeling

Given these difficulties a currently explored possible avenue isto try and combine constraints not only from seismology but alsofrom mineral physics and geodynamics Each of these approachestaken individually involves many assumptions and uncertaintiesbut by combining them the hope is that the space of acceptablemodels for anisotropy and its causes can be further reduced Theidea is to start with the strain field inferred from a mantle circula-tion model compute the corresponding texture development andpredicted seismic anisotropy using available information on crystalplasticity and elasticity for different lower mantle minerals andcompare these predictions with seismic observations This shouldprovide constraints on the mineral physics assumptions as wellas the deep mantle dynamics or at least allow us to rule out someclasses of models Note that in this approach the fundamentalassumption is that anisotropy is due to CPO development resultingfrom large-scale mantle flow

Before describing these efforts in more detail we will reviewcurrent knowledge and capabilities in mineral physics and describehow seismology and mineral physics can be linked through geody-namics modeling

3 Mineral physics perspective on the deep mantle

31 Dominant mineral phases in the lower mantle

Ringwood (1962) speculated about the composition of thelower mantle suggesting that olivine Mg2SiO4 would first breakdown to spinel Mg2SiO4 and then to MgSiO3 with a lsquolsquocorundum-

likerdquo structure and periclase (MgO) Liu (1974) synthesized thisstructure at high temperature and pressure and identified it asMgSiO3 perovskite (which has recently been named bridgmaniteTschauner et al 2014) At high pressure bridgmanite transformsto post-perovskite pPv (eg Murakami et al 2004 Oganov andOno 2004 Tateno et al 2009 Fig 9a) and this may be the mostimportant phase near the core-mantle boundary particularly alonga cold geotherm within subducting slabs (Fig 9b) Thus it appearsthat cubic periclase (Fig 10a) orthorhombic bridgmanite (Fig 10b)and orthorhombic post-perovskite (Fig 10c) are the dominantminerals in the lower mantle Periclase has the same highly sym-metric structure as halite (NaCl) with close-packed MgOVI octahe-dral coordination polyhedra Bridgmanite (spacegroup Pbnm) is adistorted cubic perovskite structure with SiOVI coordination octa-hedra linked over corners and Mg2+ in large interstices Post-perovskite (spacegroup Cmcm) has layers of SiOVI octahedra alter-nating with layers of Mg The layers are parallel to (010) It isisostructural with CaIrO3 (eg Hunt et al 2009) While the pseu-docubic perovskite structure is elastically fairly isotropic the lay-ered post-perovskite structure is highly anisotropic As we willsee post-perovskite is of critical importance for anisotropy in thelower mantle In the following discussion we will use mostly theabbreviation pPv

Most lower mantle minerals (gt660 km) cannot be studied atsurface conditions Even if lower mantle material has reached thesurface by upwelling minerals have undergone phase transitionsThus information about phase diagrams is based on in situ observa-tions in high pressure experiments and ab initio calculations

Irifune and Tsuchiya (2015) have reviewed the mineralogicalcomposition of the lower mantle Different bulk compositions ofthe lower mantle have been proposed Ringwood (1962 1975) sug-gested a peridotitic-lsquolsquopyroliticrdquo composition (Fig 11a) Subducting

Fig 7 Comparison of depth profiles throughout the mantle of global average radialanisotropy parameter n = (VshVsv)2 in 6 recent global shear velocity models n = 1corresponds to isotropy Model S362ANI (Kustowski et al 2008) is isotropic in thelower mantle While there are differences between models all of them agree thatradial anisotropy is strongest in the first 200 km of the mantle and very weak inmost of the lower mantle In D00 on average Vsh is equal of slightly faster than Vsv

66 B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90

slabs may correspond to more siliceous aluminous and Ca-richmid-ocean ridge basalts (MORB eg Irifune and Ringwood 1993Fig 11b) In both cases MgSiO3-perovskite (bridgmanite) domi-nates in large volumes of the lower mantle but for MORB compo-sitions high pressure silica and alumina phases are alsosignificant and there may be no ferropericlase Calcium perovskite(CaSiO3) is cubic (spacegroup Pm3 m) at lower mantle conditions(eg Wang et al 1996 Kawai and Tscuchiya 2015) and is animportant component at depths beyond 750 km It distorts to atetragonal structure at low temperature and high pressure (egShim et al 2002)

As more details about the lower mantle are revealed composi-tional heterogeneities become apparent (eg Badro et al 2003 LiY et al 2014) Higher concentrations of Si Al and Fe add consider-able complexity The diverse composition is in part the result ofsubduction of slabs composed of crust and upper mantle Silica(SiO2) may exist as stishovite with a rutile structure and 6-foldcoordination or at higher pressure as a cubic phase with CaCl2structure and 8-fold coordination (eg Kingma et al 1995) andat even higher pressure as an orthorhombic (Pbcn) a-PbO2 struc-ture (seifertite) (eg Dubrovinsky et al 2004 Grocholski et al2013 Zhang et al 2016) According to first principles calculationsat extreme pressure SiO2 may transform to a pyrite structure(Kuwayama et al 2005) Al2O3 in the form of trigonal corundumor orthorhombic Rh2O3(II) may be present and Fe may exist asnative iron (eg Frost et al 2004 Shi et al 2013)

Of considerable importance is the oxidation state as well as thespin state of iron that have received a lot of attention (egMcCammon 1997 Badro et al 2003 Li et al 2004 Tsuchiya

et al 2006 Fei et al 2007 Lin et al 2008 Catalli et al 2010Saha et al 2011 2012 Vilella et al 2015) With increasing pres-sure there is a transition from a high spin to a low spin configura-tion It may be responsible for the anomalous viscosity structure inthe central part of the lower mantle (900ndash1200 km eg Rudolphet al 2015) although the spin transition is generally thought tooccur deeper (1500 km)

In addition hydrogen may play a significant role (eg Ohtamiand Sakai 2008) A hydrous aluminosilicate is stable at lower man-tle conditions (eg Tsuchiya and Tsuchiya 2008 2011 Pamatoet al 2014) and dehydration may cause melting at the top of thelower mantle (Schmandt et al 2014)

As far as elastic properties and anisotropy are concerned oneshould keep in mind that the major phases over large volumes ofthe lower mantle are bridgmanite ferropericlase pPv and CaSiO3

perovskite These contribute largely to the bulk elastic propertiesbut there may be local deviations

32 Some comments on plasticity models and representation ofanisotropy

What are the sources of seismic anisotropy in the Earth Veryimportant is the alignment of anisotropic crystals called crystalpreferred orientation (CPO) or texture (based on DrsquoHalloy 1833)and universally used in materials science The crystal anisotropyis linked to the crystal structure A second aspect is crystal shapethat produces a shape-preferred orientation (SPO) CPO and SPOare sometimes linked (in mica for example the crystal plane(001) is parallel to the platelet) Often it is not (eg in quartz orin periclase) Also significant is the orientation of flat fracturesand fractures filled with kerogen This is a very important contribu-tion to anisotropy in shales (eg Hornby et al 1994 Sayers 1994Vasin et al 2013) but insignificant in the lower mantle In thelower mantle there is the possibility of partial melt particularlynear the core-mantle boundary (eg Williams and Garnero 1996Lay et al 2004 Shi et al 2013) but this would only give rise to ani-sotropy if melt occurred in parallel thin layers (eg Backus 1962)We will focus here on the development of CPO

Before going into plasticity in the mantle a few words aboutdeformation mechanisms of polycrystalline aggregates are inorder Deformation experiments on minerals have a long historyPfaff (1859) documented mechanical twinning in calcite when astress is applied In the early twentieth century deformation exper-iments at a wide range of temperature and strain conditions wereconducted on metals to explore the deformation behavior (egSchmid 1924) and in this context linear defects called dislocationswere discovered (Polanyi 1934 Taylor 1934) Without disloca-tions it would be very difficult to deform crystals and indeed theyare present in most crystalline materials

Dislocations form in the crystal lattice when a stress is appliedEdge dislocations propagate on a glide plane (hkl) and in a slipdirection [uvw] defined by rational indices relative to crystallo-graphic axes Propagation of dislocations causes crystals to rotaterelative to the applied stress which is conceptually illustrated foran experimentally compressed single crystal in Fig 12 By move-ment of dislocations on glide planes the rectangular crystal attainsa new shape (parallelogram) Since pistons must stay in contactthis results in an effective rotation of b In a polycrystalline aggre-gate neighboring grains play the function of pistons

Based on deformation experiments on metals deformationmechanism maps were established (eg Ashby 1972 Langdonand Mohamed 1978 Frost and Ashby 1982) They define condi-tions such as temperature pressure stress magnitudes strain rateand grain size under which mechanisms such as dislocation glidedislocation climb grain boundary migration and grain boundarysliding are active (Fig 13) Identifying mechanisms is important

Fig 8 Comparison of 6 recent models of lateral variations in the radial anisotropy parameter n = (VshVsv)2 plotted in terms of dlnn referred to isotropy While the modelsdisagree in detail common features are Vsh gt Vsv (blue) in the circum Pacific ring (roughly in agreement with local studies) and pronounced Vsv gt Vsh (orange) in the Fiji-TongaIndonesia region and under southernmost Africa (except SAVANI) Models plotted are (a) SAW642ANb (Panning et al 2010) (b) SAW642AN (Panning andRomanowicz 2006) (c) SAVANI (Auer et al 2014) (d) SGLOBE-rani (Chang et al 2015) (e) S362WANI + M (Moulik and Ekstroumlm 2014) (f) SEMUCB_WM1 (French andRomanowicz 2014)

Fig 9 (a) Experimentally determined PT phase diagram for perovskitebridgmanite (Pv)-post-perovskite (Murakami et al 2004) (b) T-Depth phase diagram plotting the pv-ppv phase boundary and cold and warm geotherms (after Hernlund et al 2005)

B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90 67

because some produce crystal rotations and thus crystallographicpreferred orientation (notably dislocation glide and ndash to someextent ndash dynamic recrystallization) while others generate random

orientations (such as grain boundary sliding in fine-grained mate-rials and dislocation climb) We will return to these issues inSection 48

Fig 10 Crystal structures of (a) periclase (b) bridgmanite and (c) post-perovskite the latter two with octahedrally coordinated silicon

Fig 11 Lower mantle composition for different models (a) pyrolite (b) MORB(from Irifune and Tsuchiya 2015) Pv perovskitebridgmanite Ppv post-perovskiteMw magnesiowuestiteferropericlase Mj majorite Rw ringwoodite SiO2 Ststishovite CC CaCl2 phase AP a-PbO2 phase Al2O Hex CF calcium-ferrite phaseCT calcium-titanate phase

68 B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90

In a polycrystalline aggregate stresses are transmitted acrossgrain boundaries causing heterogeneities even within grains Thisis most realistically approached with finite element methods (egMika and Dawson 1999) but these are still extremely demandingand rarely applied Simpler models have been used in materialsscience for a long time The Taylor (1938) theory developed bythe same Taylor who discovered dislocations (1934) assumeshomogeneous strain All grains undergo the same shape changeirrespective of orientation This leaves grain boundaries intact(Fig 14 left side) The Taylor model is very applicable to cubic met-als with many symmetrically related slip systems Slip on 111h

1 1 0i in fcc metals or cubic periclase has 12 equivalent systemsAnother model (Sachs 1928) assumes stress equilibrium and morefavorably oriented grains deform more than others In the modelthis causes overlaps and gaps at grain boundaries In principle thiswould be more adequate for low symmetry minerals (such asorthorhombic) but of course overlaps and gaps do not exist A com-promise between homogeneous strain and stress equilibrium is aself-consistent model that treats grains as ellipsoidal inclusionsdeforming in an anisotropic viscous medium (Fig 14 centerMolinari et al 1987) It is most widely applied in the Los Alamoscode VPSC (Lebensohn and Tomeacute 1993) and it can be used bothto understand preferred orientation in high pressure experimentsand to predict anisotropy in geodynamic models In the viscoplas-tic self-consistent model grains deform without knowledge of theirneighborhood In a finite element model (Fig 14 right) grains areconstrained by the orientation of neighbors In this sketch it isassumed that each grain has a single orientation In more sophisti-cated FEM models there are strain and orientation gradients devel-oping within grains (eg Mika and Dawson 1999)

When crystals are deformed in a polycrystalline medium theyundergo systematic rotations (Fig 12) and the material attains ananisotropic pattern We need to describe the orientation of a crys-tal relative to the macroscopic sample This is efficiently done byrelating two orthogonal coordinate systems (sample x y z crystal[100] [010] [001]) by three rotations Most frequently the so-called Euler angles are used U is the distance from z to [001]1 is the azimuth of [001] from y (around z) 2 is the azimuthof [100] around [001] (Fig 15) The 3-dimensional crystal orienta-tion distribution (COD) is conventionally described by a continuousorientation distribution function (ODF) The ODF is required to cal-culate anisotropic elastic properties of an aggregate from crystalorientations

For graphical representations of orientation patterns generally2-dimensional spherical projections of the ODF are used Depend-ing on the application one can either use the macroscopic sample xy z as reference and plot crystal directions (pole figures) or use thecrystal as reference and plot sample directions (inverse pole fig-ures) Inverse pole figures are useful if only a single sample direc-tion is of interest eg the compression direction in a compressionexperiment The symmetry of pole figures reflects the symmetry ofthe deformation path In compression experiments pole figures areaxially symmetric The density of poles on the sphere is contouredand then expressed as continuous pole densities usually normal-ized relative to a random distribution and defined as multiples ofa random distribution (mrd) 2ndash5 mrd are moderate CODs20ndash50 mrd very strong CODs The strongest crystal alignmentsin rocks that have been observed are muscovite in slates exceeding100 mrd Fig 16a is a 111 pole figure of rolled copper with roll-

Fig 12 Under stress imposed by pistons a crystal deforms to a new shape by slip of dislocations on a glide plane Since pistons remain in contact with the crystal surfacethere is an effective rotation b In a polycrystal neighboring grains act as effective pistons to transmit the stress

Fig 13 Stress-temperature deformation mechanism map (Langdon and Mohamed1978)

B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90 69

ing R transverse T and normal N sample directions indicatedFig 16b is the corresponding inverse pole figure of the normaldirection Inverse pole figures display the crystal symmetry Bothrepresentations will be used in the following discussion

33 Deformation experiments and rheology

The experiments on plasticity of metals were not applicable tomost minerals because even at elevated temperatures theirdeformation behavior at ambient pressure is generally brittleOne had to wait until high pressure deformation experiments weredeveloped by Griggs (1936) and applied on a wide scale includingolivine (eg Raleigh 1968) Since then sophisticated deformationapparati have been constructed in many laboratories making itpossible to deform rocks at a wide range of pressures and temper-atures They were applied to many minerals and rocks in the crustand upper mantle Studies on olivine (eg Jung and Karato 2001

Hansen et al 2012 Jackson and Faul 2010) documented the com-plex influence of temperature pressure composition (such aswater and iron content) The most sophisticated apparatus wasdeveloped at the Australian National University (Paterson andOlgaard 2000) It allows for deformation experiments on relativelylarge samples (1 cm) in compression tension and torsion Pres-sures are limited to 03 GPa and the limitation in pressure pre-vents these instruments to be used for experiments relevant tothe lower mantle (20ndash150 GPa) and inner core (320ndash360 GPa)

Higher pressure deformation experiments have been reviewedby Weidner and Li (2015) The multi-anvil apparatus called DIAwith three pairs of octahedral pistons (Onodera 1987) has beenmodified to apply stress by preferentially advancing one pistonpair (D-DIA for deformation DIA) The sample can be heated inter-nally Changes in phase structure preferred orientation andmicrostructure can be recorded in situ if the D-DIA apparatus iscombined with a monochromatic synchrotron X-ray beam fordiffraction and imaging (eg Wang et al 2003 2011) The conven-tional D-DIA apparatus has been used to 20 GPa and samples arecylinders 1 mm in diameter (eg Kawazoe et al 2010) A moreadvanced D-DIA (Kawai-type) reaching gt110 GPa with sintereddiamond anvils and smaller samples has been introduced atSPring8 in Japan (Yamazaki et al 2014)

Shear deformation at high pressure can be performed with arotational Drickamer apparatus (RDA) (eg Yamasaki and Karato2001) Shear deformation of a bridgmanite-ferropericlase aggre-gate at 25 GPa and 2100 K has been achieved to large strains(Girard et al 2016) In such torsion experiments the strain variesgreatly as a function of sample radius The experiment documentedthat most of the plastic deformation is accommodated by theweaker ferropericlase

Currently the most accessible method to deform samples atultrahigh pressures (gt500 GPa) is with diamond anvil cells (DAC)where diamonds are used as pistons compressing a small sample(30ndash80 lm in diameter and 50 lm thick) (eg Merkel et al2002 Fig 17) The diamonds are used not only to induce pressurebut also to cause compressive deformation (Fig 17 b c) and theevolution of preferred orientation can be observed in situ if hori-zontal X-rays transmit the sample in radial diffraction geometry(r-DAC) Strong textures have been observed in ferropericlase(eg Merkel et al 2002 Lin et al 2009) perovskitebridgmanite(eg Merkel et al 2003 Wenk et al 2006 Miyagi and Wenk2016 Tsujino et al 2016) and pPv the phase likely to be presentat the core-mantle boundary (eg Merkel et al 2006 2007

Fig 14 2D Sketches of polycrystal plasticity models Gray shades express orien-tation (Left) For the full constraints Taylor model all grains undergo the samedeformation regardless of orientation (Center) The viscoplastic model VPSC treatsgrains as inclusions in an anisotropic viscous medium (Right) In finite elementmodels grains deform differently depending on the orientation of neighbors

Fig 15 Definition of crystal orientation relative to sample coordinates with threerotations (Euler angles) 1 U 2 Projection based on sample coordinate system xy z (pole figure) Crystal coordinate system is defined by axes [100] [010] and[001]

Fig 16 Comparison of (a) 111 pole figure relative to sample coordinates and (b) Ninverse pole figure relative to crystal coordinates for rolled copper Equal areaprojection red colors are high and blue colors are low pole densities N normaldirection R rolling direction and T transverse direction Note the equivalentinformation In the 111 pole figure a maximum in the N direction and in the NDinverse pole figure a maximum in 111

70 B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90

Miyagi et al 2010 2011 Wu et al 2017) Shear deformation canbe induced in rotational DACs (eg Levitas et al 2006) Thismethod has been mainly used to induce phase transformationsand has not yet been applied to study texture evolution at highpressure

In addition to pressure and stress temperature can be inducedin DAC experiments by resistive (eg Liermann et al 2009) andlaser heating (eg Prakapenka et al 2008 Dubrovinsky et al2009) or a combination of the two (Miyagi et al 2013) Tatenoet al (2015) reached temperatures of 6000 K at gt400 GPa on exper-iments on Fe and Fe-Si corresponding to conditions of the Earthrsquos

inner core Obviously there are limitations to DAC experimentssamples are extremely small strain is always compressive andstrain rates are difficult to control

It was surprising to see that silicates and oxides that are brittleat ambient conditions including olivine become ductile at pres-sures of 10GPa even at room temperature and deform by dislo-cation glide (eg Wenk et al 2004) The diffraction image ofMgSiO3 post-perovskite at 150 GPa (Fig 18a) is lsquolsquounrolledrdquo andthe compression direction is indicated by arrows (large 2h smalld Q=1d) (Fig 18b) The elastic lattice distortion (wave-like patternwith azimuth) is related to applied stress and elastic propertiesThe intensity variations with azimuth are indicative of preferredorientation For example there is a strong maximum for 004(fourth order diffraction on the lattice plane 001) in the compres-sion direction This image illustrates why radial diffraction geome-try has to be used to display CPO as function of angle to thecompression direction In axial geometry (X-rays parallel to thediamond axis) Debye-rings have uniform intensity since alldiffracting lattice planes have the same angle to the compressiondirection

A qualitative interpretation of a diffraction image is illustratedin Fig 19 for an experiment with MgGeO3 post-perovskite(Miyagi et al 2011) and used to construct an inverse pole figureof the compression direction (arrow) MgGeO3 is an analog ofMgSiO3 but transforms to pPv at lower pressure There is a maxi-mum for 002 and a minimum for 020 in the compression directionwhich can be plotted in the inverse pole figure (Fig 19 right side)The quantitative deconvolution of diffraction images is not trivialand most often an iterative Rietveld method is applied (egLutterotti et al 2014 Wenk et al 2014) The high pressure syn-chrotron X-ray diffraction deformation images provide quantita-tive information about phases crystal structures density stresselastic properties and preferred orientation

Fig 20a-c shows experimental inverse pole figures of MgSiO3

pPv documenting increasing texture development with pressure-stressndashstrain with a maximum at (001) From the orientation pat-tern active slip systems can be derived by comparing experimentalinverse pole figures with results from polycrystal plasticity calcu-lations that assume certain combinations of slip systems(Fig 20d) Based on the good agreement it can be concluded thatpPv deformed in the experiment by dominant (001)[100] slip(Miyagi et al 2010)

With similar experiments it was suggested that MgSiO3 bridg-manite deforms dominantly by slip on (001) planes in [100][010] and h1 1 0i directions (eg Miyagi and Wenk 2016) but sim-

Fig 18 (a) Diffraction image of MgSiO3 post-perovskite at 150 GPa (b) Unrolled diffractiochanges in Q are due to elastic distortion of the crystal lattice under compression Botquantitative information such as inverse pole figures

Fig 17 Diamond anvil cell for radial diffraction experiments The X-ray beam ishorizontal (a) illustrates the cell and the insert is an enlargement with diamondsand gasket to contain the sample (b c) illustrate that diamonds not only applypressure but also compressive stress that deforms the sample and produces CPO

B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90 71

ple shear experiments in a D-DIA apparatus indicate (100)[001]slip (Tsujino et al 2016) Ferropericlase likely deforms by 110h110i slip (eg Stretton et al 2001 Merkel et al 2002 Linet al 2009) at high pressure conditions For Ca-perovskite domi-nant 110h110i slip was proposed (Miyagi et al 2006 2009)

So far most DAC high-pressure deformation experimentsextracted COD information from intensity variations along Debyerings (eg Fig 18) A new method called multigrain is still underdevelopment It obtains orientation information from individualgrain diffractions (eg Barton and Bernier 2012 Rosa et al2015 Langrand et al 2017) and is especially applicable to coarseraggregates Nisr et al (2012) used information about dislocationsfrom distortion of single crystal diffraction patterns of the post-perovskite analog MgGeO3 and suggested dominant slip on 110and (001) planes

It should be mentioned that information from such high pres-sure experiments is by no means unambiguous Obviously defor-mation conditions in experiments and simulations differconsiderably from those in the deep Earth just to mention temper-ature grain size strain rate interaction of dislocations and interac-tion between grains Furthermore not all CPO patterns that areobserved are due to deformation but could be inherited from orien-tation patterns of precursor phases such as for pPv from perovskite(Dobson et al 2013) or enstatite (Merkel et al 2006 2007 Miyagiet al 2011) Also slip systems may not be the same for pPv phasesof different compositions such as MgGeO3 CaIrO3 NaMgF3 orMn2O3

A different approach has become very important computationof Peierlrsquos stresses and lattice friction for dislocation systems basedon bonding characteristics It was originally developed for metals(eg Kubin et al 1992 Devincre and Kubin 1997) and has morerecently been applied to minerals in the mantle where it allowsto predict slip system activities for a wide range of temperaturendashpressurendashstrain rate conditions (eg Carrez et al 2007Mainprice et al 2008 Cordier et al 2012) Amodeo et al (20122014 2016) propose a switch from 110h010i slip to 100h0 1 1i slip in periclase with pressure Kraych et al (2016) suggest(010)[100] slip in bridgmanite at high pressure According tothese calculations the strength of bridgmanite increases greatlywith pressure and at 60 GPa bridgmanite appears 20 times stron-ger than periclase The critical resolved shear stress decreasesabout 20 from strain rates of 105 s1 (which corresponds to

n image as function of Q (Q = 1d) Intensity variations with azimuth illustrate CPOtom experimental data above fit of the data with the Rietveld method to extract

Fig 19 Explanation of the relationship between DAC diffraction image and inverse pole figure Left Unrolled diffraction image of MgGeO3 post-perovskite Some diffractionlines are labeled The sinusoidal variations are due to imposed stress High stress (high Q low d) is indicated by arrows On the right side is a conceptual construction of theinverse pole figure of the compression axis based on relative diffraction intensities (Miyagi et al 2011)

Fig 20 Inverse pole figures for MgSiO3 post-perovskite (AndashC) experiments (D) Plasticity model with dominant (001) slip equal area projection (Miyagi et al 2010)

72 B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90

experimental values) to 1014 s1 corresponding to likely values atdeep mantle conditions (Fig 21a) The opposite is the case for pPvwhich appears much weaker than periclase at high pressure hightemperature and slow strain rates (Fig 21b Goryaeva et al 20152016) Also the predicted weakest calculated slip system for post-perovskite at deep mantle conditions is (010)[100] correspondingto the layered crystal structure (Fig 21c) but different from thatobserved in DAC experiments (Miyagi et al 2010 Wu et al 2017)

It should be mentioned that a single slip system is not sufficientto deform a polycrystal In the case of the Taylor model at least 5systems have to be active to produce an arbitrary strain (Mises1928) This is relaxed for the self-consistent model but also hereseveral slip systems are active The choice of activity depends onthe crystal orientation relative to the applied stress (Schmid fac-tor) TEM investigations confirm this though some slip systemsusually dominate and the literature refers to the lsquolsquodominantrdquo slipsystem Some dominant slip systems for deep Earth minerals aresummarized in Table 2

34 Elastic properties

Elastic properties of crystals at conditions pertaining to thelower mantle are critical to link microstructural properties of therock with seismic observations The most straightforward experi-mental method that has been applied to many lower mantle min-erals is Brillouin scattering (see review by Speziale et al 2014) andenergy-dispersive X-ray diffraction (eg for calcium silicate per-ovskite Shieh et al 2004) A different approach is with first prin-ciples calculations at high pressure and temperature (for someapplications to bridgmanite CaSiO3 perovskite and pPv see egZhang et al 2013 Wentzcovitch et al 2005 Kawai and

Tsuchiya 2015) First principles results look fairly consistent forminerals at lower mantle conditions but as we will see in Sec-tion 62 predictions for iron at inner core conditions are stillambiguous Furthermore the actual composition of the mineralsparticularly the iron content can be significant (eg Koci et al2007) Values of stiffness coefficients and P-wave anisotropy (An = 200(Pmax Pmin)(Pmax + Pmin) for some low mantle mineralsat lowermost mantle conditions are listed in Table 3 Fig 22 givescorresponding S velocities of single crystals with black lines corre-sponding to the orientation of the fast S-wave polarization As canbe seen in Table 1 periclase and pPv have the highest P-wave ani-sotropy and Ca-perovskite is least anisotropic The S-wave aniso-tropy is considerably higher for pPv and periclase than forbridgmanite and particularly CaSiO3 perovskite

To obtain elastic properties of aggregates one has to averageover all orientations and corresponding elastic tensors takingphase fractions into account Simple averages are upper bound(Voigt 1887) and lower bound (Reuss 1929) Generally an inter-mediate arithmetic mean (Hill 1952) or a geometric mean(Matthies and Humbert 1995) are preferred All these models donot take grain shape into account which is not very significantfor crystalline phases but becomes important for systems withplaty minerals such as graphite or sheet-silicate containing rocksand aggregates with flat oriented pores For such cases a self-consistent (Matthies 2012 Vasin et al 2013) or differential effec-tive medium approach (eg Hornby et al 1994) should be consid-ered It is probably not important for the lower mantle

Note that S-waves passing through anisotropic media have arbi-trary polarization directions in the plane perpendicular to thedirection of propagation as is best displayed for the fast directionof single crystals in Fig 22 but applies also to aggregations of ori-

Fig 21 Critical resolved shear stress CRSS for dislocation glide activities as functionof temperature of (a) bridgmanite at 60 GPa (from Kraych et al 2016) and MgO(from Amodeo et al 2016) at strain rates 105 s1 and 1014 s1 (b) post-perovskiteat 120 GPa at strain rate 1016 s1 (from Goryaeva et al 2016) compared with MgO(from Amodeo et al 2012) Courtesy of P Cordier

B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90 73

ented crystals Seismologists generally consider the projection ofthat polarization direction onto horizontal and vertical axes Thisis convenient because differences in arrival times and waveformsin this representation can be expressed in terms of apparent verti-cal transverse isotropy (VTI) which because of limited azimuthalsampling is often the only anisotropic constraint that can beobtained

4 Linking seismology and mineral physics through predictionsof anisotropy in geodynamic models

41 Isotropic geodynamic models for upper mantle convection

Ever since the concept of plate tectonics became accepted in the1960s convective movements in the Earthrsquos mantle have been pro-posed such as upwelling along oceanic ridges (eg Hess 1964Cann 1968 Fig 1b) The first quantitative models based on hydro-dynamics emerged in the eighties (eg Hager and OrsquoConnell 1981)

Table 2Proposed dominant slip systems in deep Earth minerals

Ferropericlase Lower P 110110High PT also 100011

Bridgmanite Low P (001)[100] [010] 110High P (100)[001](010)[100]

pPv (001)[100](010)[100]

Ca-perovskite 110110e-iron (0001)1120 subordinate 1010

Geodynamic models have been mainly applied to the upper mantleand we will not discuss them here in detail (see eg review by Longand Becker 2010)

Many convection models have been developed to understandthe evolution of the deep Earth Calculations generally assume aviscous fluid and use non-dimensional equations for the conserva-tion of mass momentum and energy applying the Boussineqapproximation Critical parameters are Rayleigh number viscosityboundary temperatures In order to evaluate the strain evolutionduring the convection process tracers are introduced that recordthe velocity gradient tensor at each time step along the path ofthe tracer If the deformation mechanisms are known (eg disloca-tion glide) polycrystal plasticity calculations can be used to calcu-late the evolution of crystal preferred orientation based on thestrain recorded by tracers

Most geodynamic models assume a viscous isotropic mediumwith a smoothly varying viscosity structure and the microstruc-tural processes leading to preferred orientation are introducedpost-mortem Considering an anisotropic medium that constantlychanges its properties greatly increases the complexity of geody-namic calculations However there are models in metallurgy suchas extrusion of an aggregate that illustrate the importance of ananisotropic material behavior (eg Beyerlein et al 2003)

42 Review of upper mantle anisotropic models

We will start the discussion of anisotropic convection byreturning to a simple 2D model (Dawson and Wenk 2000) thatwas originally issued as an educational video by AGU (1999) andcan now be downloaded in digital form (httpepsberkeleyedu~wenkTexturePageMantle-Videohtm) At high Rayleigh number(low viscosity) heat transfer occurs by convection rather than con-duction corresponding to conditions in the Earthrsquos mantle Convec-tion is driven by temperature gradients As aggregates move alongstreamlines the orientation of grains is constantly updated and thelocal texture affects the next deformation step which introducesconsiderable heterogeneities It was surprising to find locallyheterogeneous CPO patterns in the 2D convection cell representingthe upper mantle shown as [100] pole figures of olivine after100 my (Fig 23) Some regions have strong and others very weakpatterns that can be attributed to heterogeneous deformation dueto CPO development and result in lsquolsquoanisotropicrdquo viscosity

Some complexities of different plasticity models for a simplecase of upwelling have been investigated by Blackman et al(1996 2002) and Castelnau et al (2009) If a lower bound behavioris assumed (Sachs 1928) there is very strong CPO developmentFor self-consistent models (Lebensohn and Tomeacute 1993) rotationsare reduced If dislocation glide is combined with dynamic recrys-tallization both grain growth and grain growth combined withnucleation resulting orientation patterns can be very differentRecrystallization is likely in the deep Earth with high temperatureand large strains where grain boundary migration is likely tooccur We will return to the issue of recrystallization in Section 48

Merkel et al (2002) and Lin et al (2009)Amodeo et al (2016)Miyagi and Wenk 2016Tsujino et al (2016)Kraych et al (2016)Miyagi et al (2010) and Wu et al (2017)Goryaeva et al (2016)Miyagi et al (2009) and Ferreacute et al (2009)

Merkel et al (2004) and Miyagi et al (2008)

Fig 5 a and b Whole mantle depth cross sections through the isotropic Vs part of model SEMUCB_WM1 (French and Romanowicz 2014) at the southern (a) and eastern (b)edge of the African LLSVP where rapid variations in the direction and strength of anisotropy have been reported decreasing from outside (blue) to inside (pink) the LLSVP inc) the map view is from Lynner and Long (2014) with background shear velocity model GyPSuM of Simmons et al (2012) The cross-section location is indicated on the mapby a straight line c and d corresponding cartoons proposed by the authors respectively (c) Cottaar and Romanowicz (2013) (d) Ford and Long (2015)

64 B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90

Inmostmodels there is an indication of an increase in anisotropy inD00 with Vshgt Vsv (n slightly larger than 1) although there is vari-ability among models due to a combination of parametrizationtypes of seismic waves considered and theoretical assumptions

Common 3D features of these models in D00 are a predominanceof Vsh gt Vsv outside of the LLSVPs with patches of Vsh lt Vsv con-fined within the LLSVPs in agreement with local studies (Fig 8)However the current models do not show consistency in theamplitude of the lateral variations in n nor the wavelengths ofthese variations This is partly due to the parametrization chosenFor example Panning and Romanowicz (2004 2006) and Aueret al (2014) allowed relatively short wavelength lateral variationsin n while Moulik and Ekstroumlm (2014) and French andRomanowicz (2014) chose to assign shorter wavelength lateralvariations to isotropic Vs while constraining the anisotropic partof the model to be smooth Theoretical assumptions on wave prop-agation are also important ray theory is not valid for modelling ofSdiff nor is it valid to use the surface wave approximation for mod-elling this phase as shown by Li and Romanowicz (1995) So faronly the Berkeley models are constructed taking into account finitefrequency effects rather than ray theory for body waves (Panningand Romanowicz 2004 2006 French and Romanowicz 2014)

One fundamental issue is that Sdiff and ScSn data (with ngt1) arenecessary to obtain good coverage of D00 at the global scale As dis-cussed previously SVdiff decays rapidly with distance in modelssuch as the reference model PREM (Dziewonski and Anderson1981) where the velocity in D00 is relatively fast The global datasetsare thus necessarily biased although to various degrees depending

on the particular dataset by the predominance of SHdiff introduc-ing trade-offs between isotropic and anisotropic structure (egKustowski et al 2008 Chang et al 2015) and making it only pos-sible to resolve the very longest wavelengths of VTI in D00 withpoor constraints on their amplitude

In summary robustly mapping even the simplest component ofseismic anisotropy apparent VTI at the base of the mantle at highresolution using a tomographic approach is still a challenging openquestion let alone constraining azimuthal anisotropy at the globalscale Still available global models agree with local studies aboutthe prevalence of VshgtVsv in regions of faster than average velocityin D00

As for P wave anisotropy in the deep mantle only few studieshave tried to constrain it so far Several studies have attemptedto retrieve the global average variation with depth of the radiallyanisotropic parameter g = (VphVpv)2 using normal mode data(Montagner and Kennett 1996 Beghein et al 2006) finding someindication that the anisotropy in gmay be anticorrelated with thatof n in the D00 region with however strong trade-offs with density(to which normal mode data are also sensitive) Note that the anti-correlation of isotropic P and S velocities at long wavelengths inthe deep mantle is in contrast better established (eg Su andDziewonski 1997 Kennett and Widyantoro 1998 Masters et al2000 Ishii and Tromp 1999 Romanowicz and Breacuteger 2000) Thepossibility of P wave anisotropy in the deep mantle using P wavedata (mantle and core phases) has been investigated by Boschiand Dziewonski (2000) concluding that anisotropy may be smallwith significant trade-offs with core-mantle boundary topography

Fig 6 Zoom on the northern edge of the Pacific LLSVP The background tomographic model is the isotropic Vs part of model SEMUCB_WM1 (French and Romanowicz 2014)(A) Map view with locations of studies of D00 shear wave splitting suggesting a change of character of anisotropy across the boundary of the LLSVP Green dots indicate thelocation of major hotspots Black line with white and purple dots is the great circle path corresponding to the depth cross section shown in (B) displaying the Hawaian plumeand transition from low to fast velocities in D00 Kawai and Geller (2010) Pulliam and Sen (1998) and Russell et al (1998) find VSV gt VSH while Ritsema et al (1998) Fouch et al(2001) and Vinnik et al (1998) find that Vsh gt Vsv increasingly so for paths sampling the fast region outside of the LLSVP Note that the color saturation of the tomographicmodel is different in (A) and (B)

B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90 65

and outer core structure The possible anticorrelation of P and Sradial anisotropy in the D00 must therefore be considered with cau-tion at the present time when used as a constraint in modeling

Given these difficulties a currently explored possible avenue isto try and combine constraints not only from seismology but alsofrom mineral physics and geodynamics Each of these approachestaken individually involves many assumptions and uncertaintiesbut by combining them the hope is that the space of acceptablemodels for anisotropy and its causes can be further reduced Theidea is to start with the strain field inferred from a mantle circula-tion model compute the corresponding texture development andpredicted seismic anisotropy using available information on crystalplasticity and elasticity for different lower mantle minerals andcompare these predictions with seismic observations This shouldprovide constraints on the mineral physics assumptions as wellas the deep mantle dynamics or at least allow us to rule out someclasses of models Note that in this approach the fundamentalassumption is that anisotropy is due to CPO development resultingfrom large-scale mantle flow

Before describing these efforts in more detail we will reviewcurrent knowledge and capabilities in mineral physics and describehow seismology and mineral physics can be linked through geody-namics modeling

3 Mineral physics perspective on the deep mantle

31 Dominant mineral phases in the lower mantle

Ringwood (1962) speculated about the composition of thelower mantle suggesting that olivine Mg2SiO4 would first breakdown to spinel Mg2SiO4 and then to MgSiO3 with a lsquolsquocorundum-

likerdquo structure and periclase (MgO) Liu (1974) synthesized thisstructure at high temperature and pressure and identified it asMgSiO3 perovskite (which has recently been named bridgmaniteTschauner et al 2014) At high pressure bridgmanite transformsto post-perovskite pPv (eg Murakami et al 2004 Oganov andOno 2004 Tateno et al 2009 Fig 9a) and this may be the mostimportant phase near the core-mantle boundary particularly alonga cold geotherm within subducting slabs (Fig 9b) Thus it appearsthat cubic periclase (Fig 10a) orthorhombic bridgmanite (Fig 10b)and orthorhombic post-perovskite (Fig 10c) are the dominantminerals in the lower mantle Periclase has the same highly sym-metric structure as halite (NaCl) with close-packed MgOVI octahe-dral coordination polyhedra Bridgmanite (spacegroup Pbnm) is adistorted cubic perovskite structure with SiOVI coordination octa-hedra linked over corners and Mg2+ in large interstices Post-perovskite (spacegroup Cmcm) has layers of SiOVI octahedra alter-nating with layers of Mg The layers are parallel to (010) It isisostructural with CaIrO3 (eg Hunt et al 2009) While the pseu-docubic perovskite structure is elastically fairly isotropic the lay-ered post-perovskite structure is highly anisotropic As we willsee post-perovskite is of critical importance for anisotropy in thelower mantle In the following discussion we will use mostly theabbreviation pPv

Most lower mantle minerals (gt660 km) cannot be studied atsurface conditions Even if lower mantle material has reached thesurface by upwelling minerals have undergone phase transitionsThus information about phase diagrams is based on in situ observa-tions in high pressure experiments and ab initio calculations

Irifune and Tsuchiya (2015) have reviewed the mineralogicalcomposition of the lower mantle Different bulk compositions ofthe lower mantle have been proposed Ringwood (1962 1975) sug-gested a peridotitic-lsquolsquopyroliticrdquo composition (Fig 11a) Subducting

Fig 7 Comparison of depth profiles throughout the mantle of global average radialanisotropy parameter n = (VshVsv)2 in 6 recent global shear velocity models n = 1corresponds to isotropy Model S362ANI (Kustowski et al 2008) is isotropic in thelower mantle While there are differences between models all of them agree thatradial anisotropy is strongest in the first 200 km of the mantle and very weak inmost of the lower mantle In D00 on average Vsh is equal of slightly faster than Vsv

66 B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90

slabs may correspond to more siliceous aluminous and Ca-richmid-ocean ridge basalts (MORB eg Irifune and Ringwood 1993Fig 11b) In both cases MgSiO3-perovskite (bridgmanite) domi-nates in large volumes of the lower mantle but for MORB compo-sitions high pressure silica and alumina phases are alsosignificant and there may be no ferropericlase Calcium perovskite(CaSiO3) is cubic (spacegroup Pm3 m) at lower mantle conditions(eg Wang et al 1996 Kawai and Tscuchiya 2015) and is animportant component at depths beyond 750 km It distorts to atetragonal structure at low temperature and high pressure (egShim et al 2002)

As more details about the lower mantle are revealed composi-tional heterogeneities become apparent (eg Badro et al 2003 LiY et al 2014) Higher concentrations of Si Al and Fe add consider-able complexity The diverse composition is in part the result ofsubduction of slabs composed of crust and upper mantle Silica(SiO2) may exist as stishovite with a rutile structure and 6-foldcoordination or at higher pressure as a cubic phase with CaCl2structure and 8-fold coordination (eg Kingma et al 1995) andat even higher pressure as an orthorhombic (Pbcn) a-PbO2 struc-ture (seifertite) (eg Dubrovinsky et al 2004 Grocholski et al2013 Zhang et al 2016) According to first principles calculationsat extreme pressure SiO2 may transform to a pyrite structure(Kuwayama et al 2005) Al2O3 in the form of trigonal corundumor orthorhombic Rh2O3(II) may be present and Fe may exist asnative iron (eg Frost et al 2004 Shi et al 2013)

Of considerable importance is the oxidation state as well as thespin state of iron that have received a lot of attention (egMcCammon 1997 Badro et al 2003 Li et al 2004 Tsuchiya

et al 2006 Fei et al 2007 Lin et al 2008 Catalli et al 2010Saha et al 2011 2012 Vilella et al 2015) With increasing pres-sure there is a transition from a high spin to a low spin configura-tion It may be responsible for the anomalous viscosity structure inthe central part of the lower mantle (900ndash1200 km eg Rudolphet al 2015) although the spin transition is generally thought tooccur deeper (1500 km)

In addition hydrogen may play a significant role (eg Ohtamiand Sakai 2008) A hydrous aluminosilicate is stable at lower man-tle conditions (eg Tsuchiya and Tsuchiya 2008 2011 Pamatoet al 2014) and dehydration may cause melting at the top of thelower mantle (Schmandt et al 2014)

As far as elastic properties and anisotropy are concerned oneshould keep in mind that the major phases over large volumes ofthe lower mantle are bridgmanite ferropericlase pPv and CaSiO3

perovskite These contribute largely to the bulk elastic propertiesbut there may be local deviations

32 Some comments on plasticity models and representation ofanisotropy

What are the sources of seismic anisotropy in the Earth Veryimportant is the alignment of anisotropic crystals called crystalpreferred orientation (CPO) or texture (based on DrsquoHalloy 1833)and universally used in materials science The crystal anisotropyis linked to the crystal structure A second aspect is crystal shapethat produces a shape-preferred orientation (SPO) CPO and SPOare sometimes linked (in mica for example the crystal plane(001) is parallel to the platelet) Often it is not (eg in quartz orin periclase) Also significant is the orientation of flat fracturesand fractures filled with kerogen This is a very important contribu-tion to anisotropy in shales (eg Hornby et al 1994 Sayers 1994Vasin et al 2013) but insignificant in the lower mantle In thelower mantle there is the possibility of partial melt particularlynear the core-mantle boundary (eg Williams and Garnero 1996Lay et al 2004 Shi et al 2013) but this would only give rise to ani-sotropy if melt occurred in parallel thin layers (eg Backus 1962)We will focus here on the development of CPO

Before going into plasticity in the mantle a few words aboutdeformation mechanisms of polycrystalline aggregates are inorder Deformation experiments on minerals have a long historyPfaff (1859) documented mechanical twinning in calcite when astress is applied In the early twentieth century deformation exper-iments at a wide range of temperature and strain conditions wereconducted on metals to explore the deformation behavior (egSchmid 1924) and in this context linear defects called dislocationswere discovered (Polanyi 1934 Taylor 1934) Without disloca-tions it would be very difficult to deform crystals and indeed theyare present in most crystalline materials

Dislocations form in the crystal lattice when a stress is appliedEdge dislocations propagate on a glide plane (hkl) and in a slipdirection [uvw] defined by rational indices relative to crystallo-graphic axes Propagation of dislocations causes crystals to rotaterelative to the applied stress which is conceptually illustrated foran experimentally compressed single crystal in Fig 12 By move-ment of dislocations on glide planes the rectangular crystal attainsa new shape (parallelogram) Since pistons must stay in contactthis results in an effective rotation of b In a polycrystalline aggre-gate neighboring grains play the function of pistons

Based on deformation experiments on metals deformationmechanism maps were established (eg Ashby 1972 Langdonand Mohamed 1978 Frost and Ashby 1982) They define condi-tions such as temperature pressure stress magnitudes strain rateand grain size under which mechanisms such as dislocation glidedislocation climb grain boundary migration and grain boundarysliding are active (Fig 13) Identifying mechanisms is important

Fig 8 Comparison of 6 recent models of lateral variations in the radial anisotropy parameter n = (VshVsv)2 plotted in terms of dlnn referred to isotropy While the modelsdisagree in detail common features are Vsh gt Vsv (blue) in the circum Pacific ring (roughly in agreement with local studies) and pronounced Vsv gt Vsh (orange) in the Fiji-TongaIndonesia region and under southernmost Africa (except SAVANI) Models plotted are (a) SAW642ANb (Panning et al 2010) (b) SAW642AN (Panning andRomanowicz 2006) (c) SAVANI (Auer et al 2014) (d) SGLOBE-rani (Chang et al 2015) (e) S362WANI + M (Moulik and Ekstroumlm 2014) (f) SEMUCB_WM1 (French andRomanowicz 2014)

Fig 9 (a) Experimentally determined PT phase diagram for perovskitebridgmanite (Pv)-post-perovskite (Murakami et al 2004) (b) T-Depth phase diagram plotting the pv-ppv phase boundary and cold and warm geotherms (after Hernlund et al 2005)

B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90 67

because some produce crystal rotations and thus crystallographicpreferred orientation (notably dislocation glide and ndash to someextent ndash dynamic recrystallization) while others generate random

orientations (such as grain boundary sliding in fine-grained mate-rials and dislocation climb) We will return to these issues inSection 48

Fig 10 Crystal structures of (a) periclase (b) bridgmanite and (c) post-perovskite the latter two with octahedrally coordinated silicon

Fig 11 Lower mantle composition for different models (a) pyrolite (b) MORB(from Irifune and Tsuchiya 2015) Pv perovskitebridgmanite Ppv post-perovskiteMw magnesiowuestiteferropericlase Mj majorite Rw ringwoodite SiO2 Ststishovite CC CaCl2 phase AP a-PbO2 phase Al2O Hex CF calcium-ferrite phaseCT calcium-titanate phase

68 B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90

In a polycrystalline aggregate stresses are transmitted acrossgrain boundaries causing heterogeneities even within grains Thisis most realistically approached with finite element methods (egMika and Dawson 1999) but these are still extremely demandingand rarely applied Simpler models have been used in materialsscience for a long time The Taylor (1938) theory developed bythe same Taylor who discovered dislocations (1934) assumeshomogeneous strain All grains undergo the same shape changeirrespective of orientation This leaves grain boundaries intact(Fig 14 left side) The Taylor model is very applicable to cubic met-als with many symmetrically related slip systems Slip on 111h

1 1 0i in fcc metals or cubic periclase has 12 equivalent systemsAnother model (Sachs 1928) assumes stress equilibrium and morefavorably oriented grains deform more than others In the modelthis causes overlaps and gaps at grain boundaries In principle thiswould be more adequate for low symmetry minerals (such asorthorhombic) but of course overlaps and gaps do not exist A com-promise between homogeneous strain and stress equilibrium is aself-consistent model that treats grains as ellipsoidal inclusionsdeforming in an anisotropic viscous medium (Fig 14 centerMolinari et al 1987) It is most widely applied in the Los Alamoscode VPSC (Lebensohn and Tomeacute 1993) and it can be used bothto understand preferred orientation in high pressure experimentsand to predict anisotropy in geodynamic models In the viscoplas-tic self-consistent model grains deform without knowledge of theirneighborhood In a finite element model (Fig 14 right) grains areconstrained by the orientation of neighbors In this sketch it isassumed that each grain has a single orientation In more sophisti-cated FEM models there are strain and orientation gradients devel-oping within grains (eg Mika and Dawson 1999)

When crystals are deformed in a polycrystalline medium theyundergo systematic rotations (Fig 12) and the material attains ananisotropic pattern We need to describe the orientation of a crys-tal relative to the macroscopic sample This is efficiently done byrelating two orthogonal coordinate systems (sample x y z crystal[100] [010] [001]) by three rotations Most frequently the so-called Euler angles are used U is the distance from z to [001]1 is the azimuth of [001] from y (around z) 2 is the azimuthof [100] around [001] (Fig 15) The 3-dimensional crystal orienta-tion distribution (COD) is conventionally described by a continuousorientation distribution function (ODF) The ODF is required to cal-culate anisotropic elastic properties of an aggregate from crystalorientations

For graphical representations of orientation patterns generally2-dimensional spherical projections of the ODF are used Depend-ing on the application one can either use the macroscopic sample xy z as reference and plot crystal directions (pole figures) or use thecrystal as reference and plot sample directions (inverse pole fig-ures) Inverse pole figures are useful if only a single sample direc-tion is of interest eg the compression direction in a compressionexperiment The symmetry of pole figures reflects the symmetry ofthe deformation path In compression experiments pole figures areaxially symmetric The density of poles on the sphere is contouredand then expressed as continuous pole densities usually normal-ized relative to a random distribution and defined as multiples ofa random distribution (mrd) 2ndash5 mrd are moderate CODs20ndash50 mrd very strong CODs The strongest crystal alignmentsin rocks that have been observed are muscovite in slates exceeding100 mrd Fig 16a is a 111 pole figure of rolled copper with roll-

Fig 12 Under stress imposed by pistons a crystal deforms to a new shape by slip of dislocations on a glide plane Since pistons remain in contact with the crystal surfacethere is an effective rotation b In a polycrystal neighboring grains act as effective pistons to transmit the stress

Fig 13 Stress-temperature deformation mechanism map (Langdon and Mohamed1978)

B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90 69

ing R transverse T and normal N sample directions indicatedFig 16b is the corresponding inverse pole figure of the normaldirection Inverse pole figures display the crystal symmetry Bothrepresentations will be used in the following discussion

33 Deformation experiments and rheology

The experiments on plasticity of metals were not applicable tomost minerals because even at elevated temperatures theirdeformation behavior at ambient pressure is generally brittleOne had to wait until high pressure deformation experiments weredeveloped by Griggs (1936) and applied on a wide scale includingolivine (eg Raleigh 1968) Since then sophisticated deformationapparati have been constructed in many laboratories making itpossible to deform rocks at a wide range of pressures and temper-atures They were applied to many minerals and rocks in the crustand upper mantle Studies on olivine (eg Jung and Karato 2001

Hansen et al 2012 Jackson and Faul 2010) documented the com-plex influence of temperature pressure composition (such aswater and iron content) The most sophisticated apparatus wasdeveloped at the Australian National University (Paterson andOlgaard 2000) It allows for deformation experiments on relativelylarge samples (1 cm) in compression tension and torsion Pres-sures are limited to 03 GPa and the limitation in pressure pre-vents these instruments to be used for experiments relevant tothe lower mantle (20ndash150 GPa) and inner core (320ndash360 GPa)

Higher pressure deformation experiments have been reviewedby Weidner and Li (2015) The multi-anvil apparatus called DIAwith three pairs of octahedral pistons (Onodera 1987) has beenmodified to apply stress by preferentially advancing one pistonpair (D-DIA for deformation DIA) The sample can be heated inter-nally Changes in phase structure preferred orientation andmicrostructure can be recorded in situ if the D-DIA apparatus iscombined with a monochromatic synchrotron X-ray beam fordiffraction and imaging (eg Wang et al 2003 2011) The conven-tional D-DIA apparatus has been used to 20 GPa and samples arecylinders 1 mm in diameter (eg Kawazoe et al 2010) A moreadvanced D-DIA (Kawai-type) reaching gt110 GPa with sintereddiamond anvils and smaller samples has been introduced atSPring8 in Japan (Yamazaki et al 2014)

Shear deformation at high pressure can be performed with arotational Drickamer apparatus (RDA) (eg Yamasaki and Karato2001) Shear deformation of a bridgmanite-ferropericlase aggre-gate at 25 GPa and 2100 K has been achieved to large strains(Girard et al 2016) In such torsion experiments the strain variesgreatly as a function of sample radius The experiment documentedthat most of the plastic deformation is accommodated by theweaker ferropericlase

Currently the most accessible method to deform samples atultrahigh pressures (gt500 GPa) is with diamond anvil cells (DAC)where diamonds are used as pistons compressing a small sample(30ndash80 lm in diameter and 50 lm thick) (eg Merkel et al2002 Fig 17) The diamonds are used not only to induce pressurebut also to cause compressive deformation (Fig 17 b c) and theevolution of preferred orientation can be observed in situ if hori-zontal X-rays transmit the sample in radial diffraction geometry(r-DAC) Strong textures have been observed in ferropericlase(eg Merkel et al 2002 Lin et al 2009) perovskitebridgmanite(eg Merkel et al 2003 Wenk et al 2006 Miyagi and Wenk2016 Tsujino et al 2016) and pPv the phase likely to be presentat the core-mantle boundary (eg Merkel et al 2006 2007

Fig 14 2D Sketches of polycrystal plasticity models Gray shades express orien-tation (Left) For the full constraints Taylor model all grains undergo the samedeformation regardless of orientation (Center) The viscoplastic model VPSC treatsgrains as inclusions in an anisotropic viscous medium (Right) In finite elementmodels grains deform differently depending on the orientation of neighbors

Fig 15 Definition of crystal orientation relative to sample coordinates with threerotations (Euler angles) 1 U 2 Projection based on sample coordinate system xy z (pole figure) Crystal coordinate system is defined by axes [100] [010] and[001]

Fig 16 Comparison of (a) 111 pole figure relative to sample coordinates and (b) Ninverse pole figure relative to crystal coordinates for rolled copper Equal areaprojection red colors are high and blue colors are low pole densities N normaldirection R rolling direction and T transverse direction Note the equivalentinformation In the 111 pole figure a maximum in the N direction and in the NDinverse pole figure a maximum in 111

70 B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90

Miyagi et al 2010 2011 Wu et al 2017) Shear deformation canbe induced in rotational DACs (eg Levitas et al 2006) Thismethod has been mainly used to induce phase transformationsand has not yet been applied to study texture evolution at highpressure

In addition to pressure and stress temperature can be inducedin DAC experiments by resistive (eg Liermann et al 2009) andlaser heating (eg Prakapenka et al 2008 Dubrovinsky et al2009) or a combination of the two (Miyagi et al 2013) Tatenoet al (2015) reached temperatures of 6000 K at gt400 GPa on exper-iments on Fe and Fe-Si corresponding to conditions of the Earthrsquos

inner core Obviously there are limitations to DAC experimentssamples are extremely small strain is always compressive andstrain rates are difficult to control

It was surprising to see that silicates and oxides that are brittleat ambient conditions including olivine become ductile at pres-sures of 10GPa even at room temperature and deform by dislo-cation glide (eg Wenk et al 2004) The diffraction image ofMgSiO3 post-perovskite at 150 GPa (Fig 18a) is lsquolsquounrolledrdquo andthe compression direction is indicated by arrows (large 2h smalld Q=1d) (Fig 18b) The elastic lattice distortion (wave-like patternwith azimuth) is related to applied stress and elastic propertiesThe intensity variations with azimuth are indicative of preferredorientation For example there is a strong maximum for 004(fourth order diffraction on the lattice plane 001) in the compres-sion direction This image illustrates why radial diffraction geome-try has to be used to display CPO as function of angle to thecompression direction In axial geometry (X-rays parallel to thediamond axis) Debye-rings have uniform intensity since alldiffracting lattice planes have the same angle to the compressiondirection

A qualitative interpretation of a diffraction image is illustratedin Fig 19 for an experiment with MgGeO3 post-perovskite(Miyagi et al 2011) and used to construct an inverse pole figureof the compression direction (arrow) MgGeO3 is an analog ofMgSiO3 but transforms to pPv at lower pressure There is a maxi-mum for 002 and a minimum for 020 in the compression directionwhich can be plotted in the inverse pole figure (Fig 19 right side)The quantitative deconvolution of diffraction images is not trivialand most often an iterative Rietveld method is applied (egLutterotti et al 2014 Wenk et al 2014) The high pressure syn-chrotron X-ray diffraction deformation images provide quantita-tive information about phases crystal structures density stresselastic properties and preferred orientation

Fig 20a-c shows experimental inverse pole figures of MgSiO3

pPv documenting increasing texture development with pressure-stressndashstrain with a maximum at (001) From the orientation pat-tern active slip systems can be derived by comparing experimentalinverse pole figures with results from polycrystal plasticity calcu-lations that assume certain combinations of slip systems(Fig 20d) Based on the good agreement it can be concluded thatpPv deformed in the experiment by dominant (001)[100] slip(Miyagi et al 2010)

With similar experiments it was suggested that MgSiO3 bridg-manite deforms dominantly by slip on (001) planes in [100][010] and h1 1 0i directions (eg Miyagi and Wenk 2016) but sim-

Fig 18 (a) Diffraction image of MgSiO3 post-perovskite at 150 GPa (b) Unrolled diffractiochanges in Q are due to elastic distortion of the crystal lattice under compression Botquantitative information such as inverse pole figures

Fig 17 Diamond anvil cell for radial diffraction experiments The X-ray beam ishorizontal (a) illustrates the cell and the insert is an enlargement with diamondsand gasket to contain the sample (b c) illustrate that diamonds not only applypressure but also compressive stress that deforms the sample and produces CPO

B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90 71

ple shear experiments in a D-DIA apparatus indicate (100)[001]slip (Tsujino et al 2016) Ferropericlase likely deforms by 110h110i slip (eg Stretton et al 2001 Merkel et al 2002 Linet al 2009) at high pressure conditions For Ca-perovskite domi-nant 110h110i slip was proposed (Miyagi et al 2006 2009)

So far most DAC high-pressure deformation experimentsextracted COD information from intensity variations along Debyerings (eg Fig 18) A new method called multigrain is still underdevelopment It obtains orientation information from individualgrain diffractions (eg Barton and Bernier 2012 Rosa et al2015 Langrand et al 2017) and is especially applicable to coarseraggregates Nisr et al (2012) used information about dislocationsfrom distortion of single crystal diffraction patterns of the post-perovskite analog MgGeO3 and suggested dominant slip on 110and (001) planes

It should be mentioned that information from such high pres-sure experiments is by no means unambiguous Obviously defor-mation conditions in experiments and simulations differconsiderably from those in the deep Earth just to mention temper-ature grain size strain rate interaction of dislocations and interac-tion between grains Furthermore not all CPO patterns that areobserved are due to deformation but could be inherited from orien-tation patterns of precursor phases such as for pPv from perovskite(Dobson et al 2013) or enstatite (Merkel et al 2006 2007 Miyagiet al 2011) Also slip systems may not be the same for pPv phasesof different compositions such as MgGeO3 CaIrO3 NaMgF3 orMn2O3

A different approach has become very important computationof Peierlrsquos stresses and lattice friction for dislocation systems basedon bonding characteristics It was originally developed for metals(eg Kubin et al 1992 Devincre and Kubin 1997) and has morerecently been applied to minerals in the mantle where it allowsto predict slip system activities for a wide range of temperaturendashpressurendashstrain rate conditions (eg Carrez et al 2007Mainprice et al 2008 Cordier et al 2012) Amodeo et al (20122014 2016) propose a switch from 110h010i slip to 100h0 1 1i slip in periclase with pressure Kraych et al (2016) suggest(010)[100] slip in bridgmanite at high pressure According tothese calculations the strength of bridgmanite increases greatlywith pressure and at 60 GPa bridgmanite appears 20 times stron-ger than periclase The critical resolved shear stress decreasesabout 20 from strain rates of 105 s1 (which corresponds to

n image as function of Q (Q = 1d) Intensity variations with azimuth illustrate CPOtom experimental data above fit of the data with the Rietveld method to extract

Fig 19 Explanation of the relationship between DAC diffraction image and inverse pole figure Left Unrolled diffraction image of MgGeO3 post-perovskite Some diffractionlines are labeled The sinusoidal variations are due to imposed stress High stress (high Q low d) is indicated by arrows On the right side is a conceptual construction of theinverse pole figure of the compression axis based on relative diffraction intensities (Miyagi et al 2011)

Fig 20 Inverse pole figures for MgSiO3 post-perovskite (AndashC) experiments (D) Plasticity model with dominant (001) slip equal area projection (Miyagi et al 2010)

72 B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90

experimental values) to 1014 s1 corresponding to likely values atdeep mantle conditions (Fig 21a) The opposite is the case for pPvwhich appears much weaker than periclase at high pressure hightemperature and slow strain rates (Fig 21b Goryaeva et al 20152016) Also the predicted weakest calculated slip system for post-perovskite at deep mantle conditions is (010)[100] correspondingto the layered crystal structure (Fig 21c) but different from thatobserved in DAC experiments (Miyagi et al 2010 Wu et al 2017)

It should be mentioned that a single slip system is not sufficientto deform a polycrystal In the case of the Taylor model at least 5systems have to be active to produce an arbitrary strain (Mises1928) This is relaxed for the self-consistent model but also hereseveral slip systems are active The choice of activity depends onthe crystal orientation relative to the applied stress (Schmid fac-tor) TEM investigations confirm this though some slip systemsusually dominate and the literature refers to the lsquolsquodominantrdquo slipsystem Some dominant slip systems for deep Earth minerals aresummarized in Table 2

34 Elastic properties

Elastic properties of crystals at conditions pertaining to thelower mantle are critical to link microstructural properties of therock with seismic observations The most straightforward experi-mental method that has been applied to many lower mantle min-erals is Brillouin scattering (see review by Speziale et al 2014) andenergy-dispersive X-ray diffraction (eg for calcium silicate per-ovskite Shieh et al 2004) A different approach is with first prin-ciples calculations at high pressure and temperature (for someapplications to bridgmanite CaSiO3 perovskite and pPv see egZhang et al 2013 Wentzcovitch et al 2005 Kawai and

Tsuchiya 2015) First principles results look fairly consistent forminerals at lower mantle conditions but as we will see in Sec-tion 62 predictions for iron at inner core conditions are stillambiguous Furthermore the actual composition of the mineralsparticularly the iron content can be significant (eg Koci et al2007) Values of stiffness coefficients and P-wave anisotropy (An = 200(Pmax Pmin)(Pmax + Pmin) for some low mantle mineralsat lowermost mantle conditions are listed in Table 3 Fig 22 givescorresponding S velocities of single crystals with black lines corre-sponding to the orientation of the fast S-wave polarization As canbe seen in Table 1 periclase and pPv have the highest P-wave ani-sotropy and Ca-perovskite is least anisotropic The S-wave aniso-tropy is considerably higher for pPv and periclase than forbridgmanite and particularly CaSiO3 perovskite

To obtain elastic properties of aggregates one has to averageover all orientations and corresponding elastic tensors takingphase fractions into account Simple averages are upper bound(Voigt 1887) and lower bound (Reuss 1929) Generally an inter-mediate arithmetic mean (Hill 1952) or a geometric mean(Matthies and Humbert 1995) are preferred All these models donot take grain shape into account which is not very significantfor crystalline phases but becomes important for systems withplaty minerals such as graphite or sheet-silicate containing rocksand aggregates with flat oriented pores For such cases a self-consistent (Matthies 2012 Vasin et al 2013) or differential effec-tive medium approach (eg Hornby et al 1994) should be consid-ered It is probably not important for the lower mantle

Note that S-waves passing through anisotropic media have arbi-trary polarization directions in the plane perpendicular to thedirection of propagation as is best displayed for the fast directionof single crystals in Fig 22 but applies also to aggregations of ori-

Fig 21 Critical resolved shear stress CRSS for dislocation glide activities as functionof temperature of (a) bridgmanite at 60 GPa (from Kraych et al 2016) and MgO(from Amodeo et al 2016) at strain rates 105 s1 and 1014 s1 (b) post-perovskiteat 120 GPa at strain rate 1016 s1 (from Goryaeva et al 2016) compared with MgO(from Amodeo et al 2012) Courtesy of P Cordier

B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90 73

ented crystals Seismologists generally consider the projection ofthat polarization direction onto horizontal and vertical axes Thisis convenient because differences in arrival times and waveformsin this representation can be expressed in terms of apparent verti-cal transverse isotropy (VTI) which because of limited azimuthalsampling is often the only anisotropic constraint that can beobtained

4 Linking seismology and mineral physics through predictionsof anisotropy in geodynamic models

41 Isotropic geodynamic models for upper mantle convection

Ever since the concept of plate tectonics became accepted in the1960s convective movements in the Earthrsquos mantle have been pro-posed such as upwelling along oceanic ridges (eg Hess 1964Cann 1968 Fig 1b) The first quantitative models based on hydro-dynamics emerged in the eighties (eg Hager and OrsquoConnell 1981)

Table 2Proposed dominant slip systems in deep Earth minerals

Ferropericlase Lower P 110110High PT also 100011

Bridgmanite Low P (001)[100] [010] 110High P (100)[001](010)[100]

pPv (001)[100](010)[100]

Ca-perovskite 110110e-iron (0001)1120 subordinate 1010

Geodynamic models have been mainly applied to the upper mantleand we will not discuss them here in detail (see eg review by Longand Becker 2010)

Many convection models have been developed to understandthe evolution of the deep Earth Calculations generally assume aviscous fluid and use non-dimensional equations for the conserva-tion of mass momentum and energy applying the Boussineqapproximation Critical parameters are Rayleigh number viscosityboundary temperatures In order to evaluate the strain evolutionduring the convection process tracers are introduced that recordthe velocity gradient tensor at each time step along the path ofthe tracer If the deformation mechanisms are known (eg disloca-tion glide) polycrystal plasticity calculations can be used to calcu-late the evolution of crystal preferred orientation based on thestrain recorded by tracers

Most geodynamic models assume a viscous isotropic mediumwith a smoothly varying viscosity structure and the microstruc-tural processes leading to preferred orientation are introducedpost-mortem Considering an anisotropic medium that constantlychanges its properties greatly increases the complexity of geody-namic calculations However there are models in metallurgy suchas extrusion of an aggregate that illustrate the importance of ananisotropic material behavior (eg Beyerlein et al 2003)

42 Review of upper mantle anisotropic models

We will start the discussion of anisotropic convection byreturning to a simple 2D model (Dawson and Wenk 2000) thatwas originally issued as an educational video by AGU (1999) andcan now be downloaded in digital form (httpepsberkeleyedu~wenkTexturePageMantle-Videohtm) At high Rayleigh number(low viscosity) heat transfer occurs by convection rather than con-duction corresponding to conditions in the Earthrsquos mantle Convec-tion is driven by temperature gradients As aggregates move alongstreamlines the orientation of grains is constantly updated and thelocal texture affects the next deformation step which introducesconsiderable heterogeneities It was surprising to find locallyheterogeneous CPO patterns in the 2D convection cell representingthe upper mantle shown as [100] pole figures of olivine after100 my (Fig 23) Some regions have strong and others very weakpatterns that can be attributed to heterogeneous deformation dueto CPO development and result in lsquolsquoanisotropicrdquo viscosity

Some complexities of different plasticity models for a simplecase of upwelling have been investigated by Blackman et al(1996 2002) and Castelnau et al (2009) If a lower bound behavioris assumed (Sachs 1928) there is very strong CPO developmentFor self-consistent models (Lebensohn and Tomeacute 1993) rotationsare reduced If dislocation glide is combined with dynamic recrys-tallization both grain growth and grain growth combined withnucleation resulting orientation patterns can be very differentRecrystallization is likely in the deep Earth with high temperatureand large strains where grain boundary migration is likely tooccur We will return to the issue of recrystallization in Section 48

Merkel et al (2002) and Lin et al (2009)Amodeo et al (2016)Miyagi and Wenk 2016Tsujino et al (2016)Kraych et al (2016)Miyagi et al (2010) and Wu et al (2017)Goryaeva et al (2016)Miyagi et al (2009) and Ferreacute et al (2009)

Merkel et al (2004) and Miyagi et al (2008)

Fig 6 Zoom on the northern edge of the Pacific LLSVP The background tomographic model is the isotropic Vs part of model SEMUCB_WM1 (French and Romanowicz 2014)(A) Map view with locations of studies of D00 shear wave splitting suggesting a change of character of anisotropy across the boundary of the LLSVP Green dots indicate thelocation of major hotspots Black line with white and purple dots is the great circle path corresponding to the depth cross section shown in (B) displaying the Hawaian plumeand transition from low to fast velocities in D00 Kawai and Geller (2010) Pulliam and Sen (1998) and Russell et al (1998) find VSV gt VSH while Ritsema et al (1998) Fouch et al(2001) and Vinnik et al (1998) find that Vsh gt Vsv increasingly so for paths sampling the fast region outside of the LLSVP Note that the color saturation of the tomographicmodel is different in (A) and (B)

B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90 65

and outer core structure The possible anticorrelation of P and Sradial anisotropy in the D00 must therefore be considered with cau-tion at the present time when used as a constraint in modeling

Given these difficulties a currently explored possible avenue isto try and combine constraints not only from seismology but alsofrom mineral physics and geodynamics Each of these approachestaken individually involves many assumptions and uncertaintiesbut by combining them the hope is that the space of acceptablemodels for anisotropy and its causes can be further reduced Theidea is to start with the strain field inferred from a mantle circula-tion model compute the corresponding texture development andpredicted seismic anisotropy using available information on crystalplasticity and elasticity for different lower mantle minerals andcompare these predictions with seismic observations This shouldprovide constraints on the mineral physics assumptions as wellas the deep mantle dynamics or at least allow us to rule out someclasses of models Note that in this approach the fundamentalassumption is that anisotropy is due to CPO development resultingfrom large-scale mantle flow

Before describing these efforts in more detail we will reviewcurrent knowledge and capabilities in mineral physics and describehow seismology and mineral physics can be linked through geody-namics modeling

3 Mineral physics perspective on the deep mantle

31 Dominant mineral phases in the lower mantle

Ringwood (1962) speculated about the composition of thelower mantle suggesting that olivine Mg2SiO4 would first breakdown to spinel Mg2SiO4 and then to MgSiO3 with a lsquolsquocorundum-

likerdquo structure and periclase (MgO) Liu (1974) synthesized thisstructure at high temperature and pressure and identified it asMgSiO3 perovskite (which has recently been named bridgmaniteTschauner et al 2014) At high pressure bridgmanite transformsto post-perovskite pPv (eg Murakami et al 2004 Oganov andOno 2004 Tateno et al 2009 Fig 9a) and this may be the mostimportant phase near the core-mantle boundary particularly alonga cold geotherm within subducting slabs (Fig 9b) Thus it appearsthat cubic periclase (Fig 10a) orthorhombic bridgmanite (Fig 10b)and orthorhombic post-perovskite (Fig 10c) are the dominantminerals in the lower mantle Periclase has the same highly sym-metric structure as halite (NaCl) with close-packed MgOVI octahe-dral coordination polyhedra Bridgmanite (spacegroup Pbnm) is adistorted cubic perovskite structure with SiOVI coordination octa-hedra linked over corners and Mg2+ in large interstices Post-perovskite (spacegroup Cmcm) has layers of SiOVI octahedra alter-nating with layers of Mg The layers are parallel to (010) It isisostructural with CaIrO3 (eg Hunt et al 2009) While the pseu-docubic perovskite structure is elastically fairly isotropic the lay-ered post-perovskite structure is highly anisotropic As we willsee post-perovskite is of critical importance for anisotropy in thelower mantle In the following discussion we will use mostly theabbreviation pPv

Most lower mantle minerals (gt660 km) cannot be studied atsurface conditions Even if lower mantle material has reached thesurface by upwelling minerals have undergone phase transitionsThus information about phase diagrams is based on in situ observa-tions in high pressure experiments and ab initio calculations

Irifune and Tsuchiya (2015) have reviewed the mineralogicalcomposition of the lower mantle Different bulk compositions ofthe lower mantle have been proposed Ringwood (1962 1975) sug-gested a peridotitic-lsquolsquopyroliticrdquo composition (Fig 11a) Subducting

Fig 7 Comparison of depth profiles throughout the mantle of global average radialanisotropy parameter n = (VshVsv)2 in 6 recent global shear velocity models n = 1corresponds to isotropy Model S362ANI (Kustowski et al 2008) is isotropic in thelower mantle While there are differences between models all of them agree thatradial anisotropy is strongest in the first 200 km of the mantle and very weak inmost of the lower mantle In D00 on average Vsh is equal of slightly faster than Vsv

66 B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90

slabs may correspond to more siliceous aluminous and Ca-richmid-ocean ridge basalts (MORB eg Irifune and Ringwood 1993Fig 11b) In both cases MgSiO3-perovskite (bridgmanite) domi-nates in large volumes of the lower mantle but for MORB compo-sitions high pressure silica and alumina phases are alsosignificant and there may be no ferropericlase Calcium perovskite(CaSiO3) is cubic (spacegroup Pm3 m) at lower mantle conditions(eg Wang et al 1996 Kawai and Tscuchiya 2015) and is animportant component at depths beyond 750 km It distorts to atetragonal structure at low temperature and high pressure (egShim et al 2002)

As more details about the lower mantle are revealed composi-tional heterogeneities become apparent (eg Badro et al 2003 LiY et al 2014) Higher concentrations of Si Al and Fe add consider-able complexity The diverse composition is in part the result ofsubduction of slabs composed of crust and upper mantle Silica(SiO2) may exist as stishovite with a rutile structure and 6-foldcoordination or at higher pressure as a cubic phase with CaCl2structure and 8-fold coordination (eg Kingma et al 1995) andat even higher pressure as an orthorhombic (Pbcn) a-PbO2 struc-ture (seifertite) (eg Dubrovinsky et al 2004 Grocholski et al2013 Zhang et al 2016) According to first principles calculationsat extreme pressure SiO2 may transform to a pyrite structure(Kuwayama et al 2005) Al2O3 in the form of trigonal corundumor orthorhombic Rh2O3(II) may be present and Fe may exist asnative iron (eg Frost et al 2004 Shi et al 2013)

Of considerable importance is the oxidation state as well as thespin state of iron that have received a lot of attention (egMcCammon 1997 Badro et al 2003 Li et al 2004 Tsuchiya

et al 2006 Fei et al 2007 Lin et al 2008 Catalli et al 2010Saha et al 2011 2012 Vilella et al 2015) With increasing pres-sure there is a transition from a high spin to a low spin configura-tion It may be responsible for the anomalous viscosity structure inthe central part of the lower mantle (900ndash1200 km eg Rudolphet al 2015) although the spin transition is generally thought tooccur deeper (1500 km)

In addition hydrogen may play a significant role (eg Ohtamiand Sakai 2008) A hydrous aluminosilicate is stable at lower man-tle conditions (eg Tsuchiya and Tsuchiya 2008 2011 Pamatoet al 2014) and dehydration may cause melting at the top of thelower mantle (Schmandt et al 2014)

As far as elastic properties and anisotropy are concerned oneshould keep in mind that the major phases over large volumes ofthe lower mantle are bridgmanite ferropericlase pPv and CaSiO3

perovskite These contribute largely to the bulk elastic propertiesbut there may be local deviations

32 Some comments on plasticity models and representation ofanisotropy

What are the sources of seismic anisotropy in the Earth Veryimportant is the alignment of anisotropic crystals called crystalpreferred orientation (CPO) or texture (based on DrsquoHalloy 1833)and universally used in materials science The crystal anisotropyis linked to the crystal structure A second aspect is crystal shapethat produces a shape-preferred orientation (SPO) CPO and SPOare sometimes linked (in mica for example the crystal plane(001) is parallel to the platelet) Often it is not (eg in quartz orin periclase) Also significant is the orientation of flat fracturesand fractures filled with kerogen This is a very important contribu-tion to anisotropy in shales (eg Hornby et al 1994 Sayers 1994Vasin et al 2013) but insignificant in the lower mantle In thelower mantle there is the possibility of partial melt particularlynear the core-mantle boundary (eg Williams and Garnero 1996Lay et al 2004 Shi et al 2013) but this would only give rise to ani-sotropy if melt occurred in parallel thin layers (eg Backus 1962)We will focus here on the development of CPO

Before going into plasticity in the mantle a few words aboutdeformation mechanisms of polycrystalline aggregates are inorder Deformation experiments on minerals have a long historyPfaff (1859) documented mechanical twinning in calcite when astress is applied In the early twentieth century deformation exper-iments at a wide range of temperature and strain conditions wereconducted on metals to explore the deformation behavior (egSchmid 1924) and in this context linear defects called dislocationswere discovered (Polanyi 1934 Taylor 1934) Without disloca-tions it would be very difficult to deform crystals and indeed theyare present in most crystalline materials

Dislocations form in the crystal lattice when a stress is appliedEdge dislocations propagate on a glide plane (hkl) and in a slipdirection [uvw] defined by rational indices relative to crystallo-graphic axes Propagation of dislocations causes crystals to rotaterelative to the applied stress which is conceptually illustrated foran experimentally compressed single crystal in Fig 12 By move-ment of dislocations on glide planes the rectangular crystal attainsa new shape (parallelogram) Since pistons must stay in contactthis results in an effective rotation of b In a polycrystalline aggre-gate neighboring grains play the function of pistons

Based on deformation experiments on metals deformationmechanism maps were established (eg Ashby 1972 Langdonand Mohamed 1978 Frost and Ashby 1982) They define condi-tions such as temperature pressure stress magnitudes strain rateand grain size under which mechanisms such as dislocation glidedislocation climb grain boundary migration and grain boundarysliding are active (Fig 13) Identifying mechanisms is important

Fig 8 Comparison of 6 recent models of lateral variations in the radial anisotropy parameter n = (VshVsv)2 plotted in terms of dlnn referred to isotropy While the modelsdisagree in detail common features are Vsh gt Vsv (blue) in the circum Pacific ring (roughly in agreement with local studies) and pronounced Vsv gt Vsh (orange) in the Fiji-TongaIndonesia region and under southernmost Africa (except SAVANI) Models plotted are (a) SAW642ANb (Panning et al 2010) (b) SAW642AN (Panning andRomanowicz 2006) (c) SAVANI (Auer et al 2014) (d) SGLOBE-rani (Chang et al 2015) (e) S362WANI + M (Moulik and Ekstroumlm 2014) (f) SEMUCB_WM1 (French andRomanowicz 2014)

Fig 9 (a) Experimentally determined PT phase diagram for perovskitebridgmanite (Pv)-post-perovskite (Murakami et al 2004) (b) T-Depth phase diagram plotting the pv-ppv phase boundary and cold and warm geotherms (after Hernlund et al 2005)

B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90 67

because some produce crystal rotations and thus crystallographicpreferred orientation (notably dislocation glide and ndash to someextent ndash dynamic recrystallization) while others generate random

orientations (such as grain boundary sliding in fine-grained mate-rials and dislocation climb) We will return to these issues inSection 48

Fig 10 Crystal structures of (a) periclase (b) bridgmanite and (c) post-perovskite the latter two with octahedrally coordinated silicon

Fig 11 Lower mantle composition for different models (a) pyrolite (b) MORB(from Irifune and Tsuchiya 2015) Pv perovskitebridgmanite Ppv post-perovskiteMw magnesiowuestiteferropericlase Mj majorite Rw ringwoodite SiO2 Ststishovite CC CaCl2 phase AP a-PbO2 phase Al2O Hex CF calcium-ferrite phaseCT calcium-titanate phase

68 B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90

In a polycrystalline aggregate stresses are transmitted acrossgrain boundaries causing heterogeneities even within grains Thisis most realistically approached with finite element methods (egMika and Dawson 1999) but these are still extremely demandingand rarely applied Simpler models have been used in materialsscience for a long time The Taylor (1938) theory developed bythe same Taylor who discovered dislocations (1934) assumeshomogeneous strain All grains undergo the same shape changeirrespective of orientation This leaves grain boundaries intact(Fig 14 left side) The Taylor model is very applicable to cubic met-als with many symmetrically related slip systems Slip on 111h

1 1 0i in fcc metals or cubic periclase has 12 equivalent systemsAnother model (Sachs 1928) assumes stress equilibrium and morefavorably oriented grains deform more than others In the modelthis causes overlaps and gaps at grain boundaries In principle thiswould be more adequate for low symmetry minerals (such asorthorhombic) but of course overlaps and gaps do not exist A com-promise between homogeneous strain and stress equilibrium is aself-consistent model that treats grains as ellipsoidal inclusionsdeforming in an anisotropic viscous medium (Fig 14 centerMolinari et al 1987) It is most widely applied in the Los Alamoscode VPSC (Lebensohn and Tomeacute 1993) and it can be used bothto understand preferred orientation in high pressure experimentsand to predict anisotropy in geodynamic models In the viscoplas-tic self-consistent model grains deform without knowledge of theirneighborhood In a finite element model (Fig 14 right) grains areconstrained by the orientation of neighbors In this sketch it isassumed that each grain has a single orientation In more sophisti-cated FEM models there are strain and orientation gradients devel-oping within grains (eg Mika and Dawson 1999)

When crystals are deformed in a polycrystalline medium theyundergo systematic rotations (Fig 12) and the material attains ananisotropic pattern We need to describe the orientation of a crys-tal relative to the macroscopic sample This is efficiently done byrelating two orthogonal coordinate systems (sample x y z crystal[100] [010] [001]) by three rotations Most frequently the so-called Euler angles are used U is the distance from z to [001]1 is the azimuth of [001] from y (around z) 2 is the azimuthof [100] around [001] (Fig 15) The 3-dimensional crystal orienta-tion distribution (COD) is conventionally described by a continuousorientation distribution function (ODF) The ODF is required to cal-culate anisotropic elastic properties of an aggregate from crystalorientations

For graphical representations of orientation patterns generally2-dimensional spherical projections of the ODF are used Depend-ing on the application one can either use the macroscopic sample xy z as reference and plot crystal directions (pole figures) or use thecrystal as reference and plot sample directions (inverse pole fig-ures) Inverse pole figures are useful if only a single sample direc-tion is of interest eg the compression direction in a compressionexperiment The symmetry of pole figures reflects the symmetry ofthe deformation path In compression experiments pole figures areaxially symmetric The density of poles on the sphere is contouredand then expressed as continuous pole densities usually normal-ized relative to a random distribution and defined as multiples ofa random distribution (mrd) 2ndash5 mrd are moderate CODs20ndash50 mrd very strong CODs The strongest crystal alignmentsin rocks that have been observed are muscovite in slates exceeding100 mrd Fig 16a is a 111 pole figure of rolled copper with roll-

Fig 12 Under stress imposed by pistons a crystal deforms to a new shape by slip of dislocations on a glide plane Since pistons remain in contact with the crystal surfacethere is an effective rotation b In a polycrystal neighboring grains act as effective pistons to transmit the stress

Fig 13 Stress-temperature deformation mechanism map (Langdon and Mohamed1978)

B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90 69

ing R transverse T and normal N sample directions indicatedFig 16b is the corresponding inverse pole figure of the normaldirection Inverse pole figures display the crystal symmetry Bothrepresentations will be used in the following discussion

33 Deformation experiments and rheology

The experiments on plasticity of metals were not applicable tomost minerals because even at elevated temperatures theirdeformation behavior at ambient pressure is generally brittleOne had to wait until high pressure deformation experiments weredeveloped by Griggs (1936) and applied on a wide scale includingolivine (eg Raleigh 1968) Since then sophisticated deformationapparati have been constructed in many laboratories making itpossible to deform rocks at a wide range of pressures and temper-atures They were applied to many minerals and rocks in the crustand upper mantle Studies on olivine (eg Jung and Karato 2001

Hansen et al 2012 Jackson and Faul 2010) documented the com-plex influence of temperature pressure composition (such aswater and iron content) The most sophisticated apparatus wasdeveloped at the Australian National University (Paterson andOlgaard 2000) It allows for deformation experiments on relativelylarge samples (1 cm) in compression tension and torsion Pres-sures are limited to 03 GPa and the limitation in pressure pre-vents these instruments to be used for experiments relevant tothe lower mantle (20ndash150 GPa) and inner core (320ndash360 GPa)

Higher pressure deformation experiments have been reviewedby Weidner and Li (2015) The multi-anvil apparatus called DIAwith three pairs of octahedral pistons (Onodera 1987) has beenmodified to apply stress by preferentially advancing one pistonpair (D-DIA for deformation DIA) The sample can be heated inter-nally Changes in phase structure preferred orientation andmicrostructure can be recorded in situ if the D-DIA apparatus iscombined with a monochromatic synchrotron X-ray beam fordiffraction and imaging (eg Wang et al 2003 2011) The conven-tional D-DIA apparatus has been used to 20 GPa and samples arecylinders 1 mm in diameter (eg Kawazoe et al 2010) A moreadvanced D-DIA (Kawai-type) reaching gt110 GPa with sintereddiamond anvils and smaller samples has been introduced atSPring8 in Japan (Yamazaki et al 2014)

Shear deformation at high pressure can be performed with arotational Drickamer apparatus (RDA) (eg Yamasaki and Karato2001) Shear deformation of a bridgmanite-ferropericlase aggre-gate at 25 GPa and 2100 K has been achieved to large strains(Girard et al 2016) In such torsion experiments the strain variesgreatly as a function of sample radius The experiment documentedthat most of the plastic deformation is accommodated by theweaker ferropericlase

Currently the most accessible method to deform samples atultrahigh pressures (gt500 GPa) is with diamond anvil cells (DAC)where diamonds are used as pistons compressing a small sample(30ndash80 lm in diameter and 50 lm thick) (eg Merkel et al2002 Fig 17) The diamonds are used not only to induce pressurebut also to cause compressive deformation (Fig 17 b c) and theevolution of preferred orientation can be observed in situ if hori-zontal X-rays transmit the sample in radial diffraction geometry(r-DAC) Strong textures have been observed in ferropericlase(eg Merkel et al 2002 Lin et al 2009) perovskitebridgmanite(eg Merkel et al 2003 Wenk et al 2006 Miyagi and Wenk2016 Tsujino et al 2016) and pPv the phase likely to be presentat the core-mantle boundary (eg Merkel et al 2006 2007

Fig 14 2D Sketches of polycrystal plasticity models Gray shades express orien-tation (Left) For the full constraints Taylor model all grains undergo the samedeformation regardless of orientation (Center) The viscoplastic model VPSC treatsgrains as inclusions in an anisotropic viscous medium (Right) In finite elementmodels grains deform differently depending on the orientation of neighbors

Fig 15 Definition of crystal orientation relative to sample coordinates with threerotations (Euler angles) 1 U 2 Projection based on sample coordinate system xy z (pole figure) Crystal coordinate system is defined by axes [100] [010] and[001]

Fig 16 Comparison of (a) 111 pole figure relative to sample coordinates and (b) Ninverse pole figure relative to crystal coordinates for rolled copper Equal areaprojection red colors are high and blue colors are low pole densities N normaldirection R rolling direction and T transverse direction Note the equivalentinformation In the 111 pole figure a maximum in the N direction and in the NDinverse pole figure a maximum in 111

70 B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90

Miyagi et al 2010 2011 Wu et al 2017) Shear deformation canbe induced in rotational DACs (eg Levitas et al 2006) Thismethod has been mainly used to induce phase transformationsand has not yet been applied to study texture evolution at highpressure

In addition to pressure and stress temperature can be inducedin DAC experiments by resistive (eg Liermann et al 2009) andlaser heating (eg Prakapenka et al 2008 Dubrovinsky et al2009) or a combination of the two (Miyagi et al 2013) Tatenoet al (2015) reached temperatures of 6000 K at gt400 GPa on exper-iments on Fe and Fe-Si corresponding to conditions of the Earthrsquos

inner core Obviously there are limitations to DAC experimentssamples are extremely small strain is always compressive andstrain rates are difficult to control

It was surprising to see that silicates and oxides that are brittleat ambient conditions including olivine become ductile at pres-sures of 10GPa even at room temperature and deform by dislo-cation glide (eg Wenk et al 2004) The diffraction image ofMgSiO3 post-perovskite at 150 GPa (Fig 18a) is lsquolsquounrolledrdquo andthe compression direction is indicated by arrows (large 2h smalld Q=1d) (Fig 18b) The elastic lattice distortion (wave-like patternwith azimuth) is related to applied stress and elastic propertiesThe intensity variations with azimuth are indicative of preferredorientation For example there is a strong maximum for 004(fourth order diffraction on the lattice plane 001) in the compres-sion direction This image illustrates why radial diffraction geome-try has to be used to display CPO as function of angle to thecompression direction In axial geometry (X-rays parallel to thediamond axis) Debye-rings have uniform intensity since alldiffracting lattice planes have the same angle to the compressiondirection

A qualitative interpretation of a diffraction image is illustratedin Fig 19 for an experiment with MgGeO3 post-perovskite(Miyagi et al 2011) and used to construct an inverse pole figureof the compression direction (arrow) MgGeO3 is an analog ofMgSiO3 but transforms to pPv at lower pressure There is a maxi-mum for 002 and a minimum for 020 in the compression directionwhich can be plotted in the inverse pole figure (Fig 19 right side)The quantitative deconvolution of diffraction images is not trivialand most often an iterative Rietveld method is applied (egLutterotti et al 2014 Wenk et al 2014) The high pressure syn-chrotron X-ray diffraction deformation images provide quantita-tive information about phases crystal structures density stresselastic properties and preferred orientation

Fig 20a-c shows experimental inverse pole figures of MgSiO3

pPv documenting increasing texture development with pressure-stressndashstrain with a maximum at (001) From the orientation pat-tern active slip systems can be derived by comparing experimentalinverse pole figures with results from polycrystal plasticity calcu-lations that assume certain combinations of slip systems(Fig 20d) Based on the good agreement it can be concluded thatpPv deformed in the experiment by dominant (001)[100] slip(Miyagi et al 2010)

With similar experiments it was suggested that MgSiO3 bridg-manite deforms dominantly by slip on (001) planes in [100][010] and h1 1 0i directions (eg Miyagi and Wenk 2016) but sim-

Fig 18 (a) Diffraction image of MgSiO3 post-perovskite at 150 GPa (b) Unrolled diffractiochanges in Q are due to elastic distortion of the crystal lattice under compression Botquantitative information such as inverse pole figures

Fig 17 Diamond anvil cell for radial diffraction experiments The X-ray beam ishorizontal (a) illustrates the cell and the insert is an enlargement with diamondsand gasket to contain the sample (b c) illustrate that diamonds not only applypressure but also compressive stress that deforms the sample and produces CPO

B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90 71

ple shear experiments in a D-DIA apparatus indicate (100)[001]slip (Tsujino et al 2016) Ferropericlase likely deforms by 110h110i slip (eg Stretton et al 2001 Merkel et al 2002 Linet al 2009) at high pressure conditions For Ca-perovskite domi-nant 110h110i slip was proposed (Miyagi et al 2006 2009)

So far most DAC high-pressure deformation experimentsextracted COD information from intensity variations along Debyerings (eg Fig 18) A new method called multigrain is still underdevelopment It obtains orientation information from individualgrain diffractions (eg Barton and Bernier 2012 Rosa et al2015 Langrand et al 2017) and is especially applicable to coarseraggregates Nisr et al (2012) used information about dislocationsfrom distortion of single crystal diffraction patterns of the post-perovskite analog MgGeO3 and suggested dominant slip on 110and (001) planes

It should be mentioned that information from such high pres-sure experiments is by no means unambiguous Obviously defor-mation conditions in experiments and simulations differconsiderably from those in the deep Earth just to mention temper-ature grain size strain rate interaction of dislocations and interac-tion between grains Furthermore not all CPO patterns that areobserved are due to deformation but could be inherited from orien-tation patterns of precursor phases such as for pPv from perovskite(Dobson et al 2013) or enstatite (Merkel et al 2006 2007 Miyagiet al 2011) Also slip systems may not be the same for pPv phasesof different compositions such as MgGeO3 CaIrO3 NaMgF3 orMn2O3

A different approach has become very important computationof Peierlrsquos stresses and lattice friction for dislocation systems basedon bonding characteristics It was originally developed for metals(eg Kubin et al 1992 Devincre and Kubin 1997) and has morerecently been applied to minerals in the mantle where it allowsto predict slip system activities for a wide range of temperaturendashpressurendashstrain rate conditions (eg Carrez et al 2007Mainprice et al 2008 Cordier et al 2012) Amodeo et al (20122014 2016) propose a switch from 110h010i slip to 100h0 1 1i slip in periclase with pressure Kraych et al (2016) suggest(010)[100] slip in bridgmanite at high pressure According tothese calculations the strength of bridgmanite increases greatlywith pressure and at 60 GPa bridgmanite appears 20 times stron-ger than periclase The critical resolved shear stress decreasesabout 20 from strain rates of 105 s1 (which corresponds to

n image as function of Q (Q = 1d) Intensity variations with azimuth illustrate CPOtom experimental data above fit of the data with the Rietveld method to extract

Fig 19 Explanation of the relationship between DAC diffraction image and inverse pole figure Left Unrolled diffraction image of MgGeO3 post-perovskite Some diffractionlines are labeled The sinusoidal variations are due to imposed stress High stress (high Q low d) is indicated by arrows On the right side is a conceptual construction of theinverse pole figure of the compression axis based on relative diffraction intensities (Miyagi et al 2011)

Fig 20 Inverse pole figures for MgSiO3 post-perovskite (AndashC) experiments (D) Plasticity model with dominant (001) slip equal area projection (Miyagi et al 2010)

72 B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90

experimental values) to 1014 s1 corresponding to likely values atdeep mantle conditions (Fig 21a) The opposite is the case for pPvwhich appears much weaker than periclase at high pressure hightemperature and slow strain rates (Fig 21b Goryaeva et al 20152016) Also the predicted weakest calculated slip system for post-perovskite at deep mantle conditions is (010)[100] correspondingto the layered crystal structure (Fig 21c) but different from thatobserved in DAC experiments (Miyagi et al 2010 Wu et al 2017)

It should be mentioned that a single slip system is not sufficientto deform a polycrystal In the case of the Taylor model at least 5systems have to be active to produce an arbitrary strain (Mises1928) This is relaxed for the self-consistent model but also hereseveral slip systems are active The choice of activity depends onthe crystal orientation relative to the applied stress (Schmid fac-tor) TEM investigations confirm this though some slip systemsusually dominate and the literature refers to the lsquolsquodominantrdquo slipsystem Some dominant slip systems for deep Earth minerals aresummarized in Table 2

34 Elastic properties

Elastic properties of crystals at conditions pertaining to thelower mantle are critical to link microstructural properties of therock with seismic observations The most straightforward experi-mental method that has been applied to many lower mantle min-erals is Brillouin scattering (see review by Speziale et al 2014) andenergy-dispersive X-ray diffraction (eg for calcium silicate per-ovskite Shieh et al 2004) A different approach is with first prin-ciples calculations at high pressure and temperature (for someapplications to bridgmanite CaSiO3 perovskite and pPv see egZhang et al 2013 Wentzcovitch et al 2005 Kawai and

Tsuchiya 2015) First principles results look fairly consistent forminerals at lower mantle conditions but as we will see in Sec-tion 62 predictions for iron at inner core conditions are stillambiguous Furthermore the actual composition of the mineralsparticularly the iron content can be significant (eg Koci et al2007) Values of stiffness coefficients and P-wave anisotropy (An = 200(Pmax Pmin)(Pmax + Pmin) for some low mantle mineralsat lowermost mantle conditions are listed in Table 3 Fig 22 givescorresponding S velocities of single crystals with black lines corre-sponding to the orientation of the fast S-wave polarization As canbe seen in Table 1 periclase and pPv have the highest P-wave ani-sotropy and Ca-perovskite is least anisotropic The S-wave aniso-tropy is considerably higher for pPv and periclase than forbridgmanite and particularly CaSiO3 perovskite

To obtain elastic properties of aggregates one has to averageover all orientations and corresponding elastic tensors takingphase fractions into account Simple averages are upper bound(Voigt 1887) and lower bound (Reuss 1929) Generally an inter-mediate arithmetic mean (Hill 1952) or a geometric mean(Matthies and Humbert 1995) are preferred All these models donot take grain shape into account which is not very significantfor crystalline phases but becomes important for systems withplaty minerals such as graphite or sheet-silicate containing rocksand aggregates with flat oriented pores For such cases a self-consistent (Matthies 2012 Vasin et al 2013) or differential effec-tive medium approach (eg Hornby et al 1994) should be consid-ered It is probably not important for the lower mantle

Note that S-waves passing through anisotropic media have arbi-trary polarization directions in the plane perpendicular to thedirection of propagation as is best displayed for the fast directionof single crystals in Fig 22 but applies also to aggregations of ori-

Fig 21 Critical resolved shear stress CRSS for dislocation glide activities as functionof temperature of (a) bridgmanite at 60 GPa (from Kraych et al 2016) and MgO(from Amodeo et al 2016) at strain rates 105 s1 and 1014 s1 (b) post-perovskiteat 120 GPa at strain rate 1016 s1 (from Goryaeva et al 2016) compared with MgO(from Amodeo et al 2012) Courtesy of P Cordier

B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90 73

ented crystals Seismologists generally consider the projection ofthat polarization direction onto horizontal and vertical axes Thisis convenient because differences in arrival times and waveformsin this representation can be expressed in terms of apparent verti-cal transverse isotropy (VTI) which because of limited azimuthalsampling is often the only anisotropic constraint that can beobtained

4 Linking seismology and mineral physics through predictionsof anisotropy in geodynamic models

41 Isotropic geodynamic models for upper mantle convection

Ever since the concept of plate tectonics became accepted in the1960s convective movements in the Earthrsquos mantle have been pro-posed such as upwelling along oceanic ridges (eg Hess 1964Cann 1968 Fig 1b) The first quantitative models based on hydro-dynamics emerged in the eighties (eg Hager and OrsquoConnell 1981)

Table 2Proposed dominant slip systems in deep Earth minerals

Ferropericlase Lower P 110110High PT also 100011

Bridgmanite Low P (001)[100] [010] 110High P (100)[001](010)[100]

pPv (001)[100](010)[100]

Ca-perovskite 110110e-iron (0001)1120 subordinate 1010

Geodynamic models have been mainly applied to the upper mantleand we will not discuss them here in detail (see eg review by Longand Becker 2010)

Many convection models have been developed to understandthe evolution of the deep Earth Calculations generally assume aviscous fluid and use non-dimensional equations for the conserva-tion of mass momentum and energy applying the Boussineqapproximation Critical parameters are Rayleigh number viscosityboundary temperatures In order to evaluate the strain evolutionduring the convection process tracers are introduced that recordthe velocity gradient tensor at each time step along the path ofthe tracer If the deformation mechanisms are known (eg disloca-tion glide) polycrystal plasticity calculations can be used to calcu-late the evolution of crystal preferred orientation based on thestrain recorded by tracers

Most geodynamic models assume a viscous isotropic mediumwith a smoothly varying viscosity structure and the microstruc-tural processes leading to preferred orientation are introducedpost-mortem Considering an anisotropic medium that constantlychanges its properties greatly increases the complexity of geody-namic calculations However there are models in metallurgy suchas extrusion of an aggregate that illustrate the importance of ananisotropic material behavior (eg Beyerlein et al 2003)

42 Review of upper mantle anisotropic models

We will start the discussion of anisotropic convection byreturning to a simple 2D model (Dawson and Wenk 2000) thatwas originally issued as an educational video by AGU (1999) andcan now be downloaded in digital form (httpepsberkeleyedu~wenkTexturePageMantle-Videohtm) At high Rayleigh number(low viscosity) heat transfer occurs by convection rather than con-duction corresponding to conditions in the Earthrsquos mantle Convec-tion is driven by temperature gradients As aggregates move alongstreamlines the orientation of grains is constantly updated and thelocal texture affects the next deformation step which introducesconsiderable heterogeneities It was surprising to find locallyheterogeneous CPO patterns in the 2D convection cell representingthe upper mantle shown as [100] pole figures of olivine after100 my (Fig 23) Some regions have strong and others very weakpatterns that can be attributed to heterogeneous deformation dueto CPO development and result in lsquolsquoanisotropicrdquo viscosity

Some complexities of different plasticity models for a simplecase of upwelling have been investigated by Blackman et al(1996 2002) and Castelnau et al (2009) If a lower bound behavioris assumed (Sachs 1928) there is very strong CPO developmentFor self-consistent models (Lebensohn and Tomeacute 1993) rotationsare reduced If dislocation glide is combined with dynamic recrys-tallization both grain growth and grain growth combined withnucleation resulting orientation patterns can be very differentRecrystallization is likely in the deep Earth with high temperatureand large strains where grain boundary migration is likely tooccur We will return to the issue of recrystallization in Section 48

Merkel et al (2002) and Lin et al (2009)Amodeo et al (2016)Miyagi and Wenk 2016Tsujino et al (2016)Kraych et al (2016)Miyagi et al (2010) and Wu et al (2017)Goryaeva et al (2016)Miyagi et al (2009) and Ferreacute et al (2009)

Merkel et al (2004) and Miyagi et al (2008)

Fig 7 Comparison of depth profiles throughout the mantle of global average radialanisotropy parameter n = (VshVsv)2 in 6 recent global shear velocity models n = 1corresponds to isotropy Model S362ANI (Kustowski et al 2008) is isotropic in thelower mantle While there are differences between models all of them agree thatradial anisotropy is strongest in the first 200 km of the mantle and very weak inmost of the lower mantle In D00 on average Vsh is equal of slightly faster than Vsv

66 B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90

slabs may correspond to more siliceous aluminous and Ca-richmid-ocean ridge basalts (MORB eg Irifune and Ringwood 1993Fig 11b) In both cases MgSiO3-perovskite (bridgmanite) domi-nates in large volumes of the lower mantle but for MORB compo-sitions high pressure silica and alumina phases are alsosignificant and there may be no ferropericlase Calcium perovskite(CaSiO3) is cubic (spacegroup Pm3 m) at lower mantle conditions(eg Wang et al 1996 Kawai and Tscuchiya 2015) and is animportant component at depths beyond 750 km It distorts to atetragonal structure at low temperature and high pressure (egShim et al 2002)

As more details about the lower mantle are revealed composi-tional heterogeneities become apparent (eg Badro et al 2003 LiY et al 2014) Higher concentrations of Si Al and Fe add consider-able complexity The diverse composition is in part the result ofsubduction of slabs composed of crust and upper mantle Silica(SiO2) may exist as stishovite with a rutile structure and 6-foldcoordination or at higher pressure as a cubic phase with CaCl2structure and 8-fold coordination (eg Kingma et al 1995) andat even higher pressure as an orthorhombic (Pbcn) a-PbO2 struc-ture (seifertite) (eg Dubrovinsky et al 2004 Grocholski et al2013 Zhang et al 2016) According to first principles calculationsat extreme pressure SiO2 may transform to a pyrite structure(Kuwayama et al 2005) Al2O3 in the form of trigonal corundumor orthorhombic Rh2O3(II) may be present and Fe may exist asnative iron (eg Frost et al 2004 Shi et al 2013)

Of considerable importance is the oxidation state as well as thespin state of iron that have received a lot of attention (egMcCammon 1997 Badro et al 2003 Li et al 2004 Tsuchiya

et al 2006 Fei et al 2007 Lin et al 2008 Catalli et al 2010Saha et al 2011 2012 Vilella et al 2015) With increasing pres-sure there is a transition from a high spin to a low spin configura-tion It may be responsible for the anomalous viscosity structure inthe central part of the lower mantle (900ndash1200 km eg Rudolphet al 2015) although the spin transition is generally thought tooccur deeper (1500 km)

In addition hydrogen may play a significant role (eg Ohtamiand Sakai 2008) A hydrous aluminosilicate is stable at lower man-tle conditions (eg Tsuchiya and Tsuchiya 2008 2011 Pamatoet al 2014) and dehydration may cause melting at the top of thelower mantle (Schmandt et al 2014)

As far as elastic properties and anisotropy are concerned oneshould keep in mind that the major phases over large volumes ofthe lower mantle are bridgmanite ferropericlase pPv and CaSiO3

perovskite These contribute largely to the bulk elastic propertiesbut there may be local deviations

32 Some comments on plasticity models and representation ofanisotropy

What are the sources of seismic anisotropy in the Earth Veryimportant is the alignment of anisotropic crystals called crystalpreferred orientation (CPO) or texture (based on DrsquoHalloy 1833)and universally used in materials science The crystal anisotropyis linked to the crystal structure A second aspect is crystal shapethat produces a shape-preferred orientation (SPO) CPO and SPOare sometimes linked (in mica for example the crystal plane(001) is parallel to the platelet) Often it is not (eg in quartz orin periclase) Also significant is the orientation of flat fracturesand fractures filled with kerogen This is a very important contribu-tion to anisotropy in shales (eg Hornby et al 1994 Sayers 1994Vasin et al 2013) but insignificant in the lower mantle In thelower mantle there is the possibility of partial melt particularlynear the core-mantle boundary (eg Williams and Garnero 1996Lay et al 2004 Shi et al 2013) but this would only give rise to ani-sotropy if melt occurred in parallel thin layers (eg Backus 1962)We will focus here on the development of CPO

Before going into plasticity in the mantle a few words aboutdeformation mechanisms of polycrystalline aggregates are inorder Deformation experiments on minerals have a long historyPfaff (1859) documented mechanical twinning in calcite when astress is applied In the early twentieth century deformation exper-iments at a wide range of temperature and strain conditions wereconducted on metals to explore the deformation behavior (egSchmid 1924) and in this context linear defects called dislocationswere discovered (Polanyi 1934 Taylor 1934) Without disloca-tions it would be very difficult to deform crystals and indeed theyare present in most crystalline materials

Dislocations form in the crystal lattice when a stress is appliedEdge dislocations propagate on a glide plane (hkl) and in a slipdirection [uvw] defined by rational indices relative to crystallo-graphic axes Propagation of dislocations causes crystals to rotaterelative to the applied stress which is conceptually illustrated foran experimentally compressed single crystal in Fig 12 By move-ment of dislocations on glide planes the rectangular crystal attainsa new shape (parallelogram) Since pistons must stay in contactthis results in an effective rotation of b In a polycrystalline aggre-gate neighboring grains play the function of pistons

Based on deformation experiments on metals deformationmechanism maps were established (eg Ashby 1972 Langdonand Mohamed 1978 Frost and Ashby 1982) They define condi-tions such as temperature pressure stress magnitudes strain rateand grain size under which mechanisms such as dislocation glidedislocation climb grain boundary migration and grain boundarysliding are active (Fig 13) Identifying mechanisms is important

Fig 8 Comparison of 6 recent models of lateral variations in the radial anisotropy parameter n = (VshVsv)2 plotted in terms of dlnn referred to isotropy While the modelsdisagree in detail common features are Vsh gt Vsv (blue) in the circum Pacific ring (roughly in agreement with local studies) and pronounced Vsv gt Vsh (orange) in the Fiji-TongaIndonesia region and under southernmost Africa (except SAVANI) Models plotted are (a) SAW642ANb (Panning et al 2010) (b) SAW642AN (Panning andRomanowicz 2006) (c) SAVANI (Auer et al 2014) (d) SGLOBE-rani (Chang et al 2015) (e) S362WANI + M (Moulik and Ekstroumlm 2014) (f) SEMUCB_WM1 (French andRomanowicz 2014)

Fig 9 (a) Experimentally determined PT phase diagram for perovskitebridgmanite (Pv)-post-perovskite (Murakami et al 2004) (b) T-Depth phase diagram plotting the pv-ppv phase boundary and cold and warm geotherms (after Hernlund et al 2005)

B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90 67

because some produce crystal rotations and thus crystallographicpreferred orientation (notably dislocation glide and ndash to someextent ndash dynamic recrystallization) while others generate random

orientations (such as grain boundary sliding in fine-grained mate-rials and dislocation climb) We will return to these issues inSection 48

Fig 10 Crystal structures of (a) periclase (b) bridgmanite and (c) post-perovskite the latter two with octahedrally coordinated silicon

Fig 11 Lower mantle composition for different models (a) pyrolite (b) MORB(from Irifune and Tsuchiya 2015) Pv perovskitebridgmanite Ppv post-perovskiteMw magnesiowuestiteferropericlase Mj majorite Rw ringwoodite SiO2 Ststishovite CC CaCl2 phase AP a-PbO2 phase Al2O Hex CF calcium-ferrite phaseCT calcium-titanate phase

68 B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90

In a polycrystalline aggregate stresses are transmitted acrossgrain boundaries causing heterogeneities even within grains Thisis most realistically approached with finite element methods (egMika and Dawson 1999) but these are still extremely demandingand rarely applied Simpler models have been used in materialsscience for a long time The Taylor (1938) theory developed bythe same Taylor who discovered dislocations (1934) assumeshomogeneous strain All grains undergo the same shape changeirrespective of orientation This leaves grain boundaries intact(Fig 14 left side) The Taylor model is very applicable to cubic met-als with many symmetrically related slip systems Slip on 111h

1 1 0i in fcc metals or cubic periclase has 12 equivalent systemsAnother model (Sachs 1928) assumes stress equilibrium and morefavorably oriented grains deform more than others In the modelthis causes overlaps and gaps at grain boundaries In principle thiswould be more adequate for low symmetry minerals (such asorthorhombic) but of course overlaps and gaps do not exist A com-promise between homogeneous strain and stress equilibrium is aself-consistent model that treats grains as ellipsoidal inclusionsdeforming in an anisotropic viscous medium (Fig 14 centerMolinari et al 1987) It is most widely applied in the Los Alamoscode VPSC (Lebensohn and Tomeacute 1993) and it can be used bothto understand preferred orientation in high pressure experimentsand to predict anisotropy in geodynamic models In the viscoplas-tic self-consistent model grains deform without knowledge of theirneighborhood In a finite element model (Fig 14 right) grains areconstrained by the orientation of neighbors In this sketch it isassumed that each grain has a single orientation In more sophisti-cated FEM models there are strain and orientation gradients devel-oping within grains (eg Mika and Dawson 1999)

When crystals are deformed in a polycrystalline medium theyundergo systematic rotations (Fig 12) and the material attains ananisotropic pattern We need to describe the orientation of a crys-tal relative to the macroscopic sample This is efficiently done byrelating two orthogonal coordinate systems (sample x y z crystal[100] [010] [001]) by three rotations Most frequently the so-called Euler angles are used U is the distance from z to [001]1 is the azimuth of [001] from y (around z) 2 is the azimuthof [100] around [001] (Fig 15) The 3-dimensional crystal orienta-tion distribution (COD) is conventionally described by a continuousorientation distribution function (ODF) The ODF is required to cal-culate anisotropic elastic properties of an aggregate from crystalorientations

For graphical representations of orientation patterns generally2-dimensional spherical projections of the ODF are used Depend-ing on the application one can either use the macroscopic sample xy z as reference and plot crystal directions (pole figures) or use thecrystal as reference and plot sample directions (inverse pole fig-ures) Inverse pole figures are useful if only a single sample direc-tion is of interest eg the compression direction in a compressionexperiment The symmetry of pole figures reflects the symmetry ofthe deformation path In compression experiments pole figures areaxially symmetric The density of poles on the sphere is contouredand then expressed as continuous pole densities usually normal-ized relative to a random distribution and defined as multiples ofa random distribution (mrd) 2ndash5 mrd are moderate CODs20ndash50 mrd very strong CODs The strongest crystal alignmentsin rocks that have been observed are muscovite in slates exceeding100 mrd Fig 16a is a 111 pole figure of rolled copper with roll-

Fig 12 Under stress imposed by pistons a crystal deforms to a new shape by slip of dislocations on a glide plane Since pistons remain in contact with the crystal surfacethere is an effective rotation b In a polycrystal neighboring grains act as effective pistons to transmit the stress

Fig 13 Stress-temperature deformation mechanism map (Langdon and Mohamed1978)

B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90 69

ing R transverse T and normal N sample directions indicatedFig 16b is the corresponding inverse pole figure of the normaldirection Inverse pole figures display the crystal symmetry Bothrepresentations will be used in the following discussion

33 Deformation experiments and rheology

The experiments on plasticity of metals were not applicable tomost minerals because even at elevated temperatures theirdeformation behavior at ambient pressure is generally brittleOne had to wait until high pressure deformation experiments weredeveloped by Griggs (1936) and applied on a wide scale includingolivine (eg Raleigh 1968) Since then sophisticated deformationapparati have been constructed in many laboratories making itpossible to deform rocks at a wide range of pressures and temper-atures They were applied to many minerals and rocks in the crustand upper mantle Studies on olivine (eg Jung and Karato 2001

Hansen et al 2012 Jackson and Faul 2010) documented the com-plex influence of temperature pressure composition (such aswater and iron content) The most sophisticated apparatus wasdeveloped at the Australian National University (Paterson andOlgaard 2000) It allows for deformation experiments on relativelylarge samples (1 cm) in compression tension and torsion Pres-sures are limited to 03 GPa and the limitation in pressure pre-vents these instruments to be used for experiments relevant tothe lower mantle (20ndash150 GPa) and inner core (320ndash360 GPa)

Higher pressure deformation experiments have been reviewedby Weidner and Li (2015) The multi-anvil apparatus called DIAwith three pairs of octahedral pistons (Onodera 1987) has beenmodified to apply stress by preferentially advancing one pistonpair (D-DIA for deformation DIA) The sample can be heated inter-nally Changes in phase structure preferred orientation andmicrostructure can be recorded in situ if the D-DIA apparatus iscombined with a monochromatic synchrotron X-ray beam fordiffraction and imaging (eg Wang et al 2003 2011) The conven-tional D-DIA apparatus has been used to 20 GPa and samples arecylinders 1 mm in diameter (eg Kawazoe et al 2010) A moreadvanced D-DIA (Kawai-type) reaching gt110 GPa with sintereddiamond anvils and smaller samples has been introduced atSPring8 in Japan (Yamazaki et al 2014)

Shear deformation at high pressure can be performed with arotational Drickamer apparatus (RDA) (eg Yamasaki and Karato2001) Shear deformation of a bridgmanite-ferropericlase aggre-gate at 25 GPa and 2100 K has been achieved to large strains(Girard et al 2016) In such torsion experiments the strain variesgreatly as a function of sample radius The experiment documentedthat most of the plastic deformation is accommodated by theweaker ferropericlase

Currently the most accessible method to deform samples atultrahigh pressures (gt500 GPa) is with diamond anvil cells (DAC)where diamonds are used as pistons compressing a small sample(30ndash80 lm in diameter and 50 lm thick) (eg Merkel et al2002 Fig 17) The diamonds are used not only to induce pressurebut also to cause compressive deformation (Fig 17 b c) and theevolution of preferred orientation can be observed in situ if hori-zontal X-rays transmit the sample in radial diffraction geometry(r-DAC) Strong textures have been observed in ferropericlase(eg Merkel et al 2002 Lin et al 2009) perovskitebridgmanite(eg Merkel et al 2003 Wenk et al 2006 Miyagi and Wenk2016 Tsujino et al 2016) and pPv the phase likely to be presentat the core-mantle boundary (eg Merkel et al 2006 2007

Fig 14 2D Sketches of polycrystal plasticity models Gray shades express orien-tation (Left) For the full constraints Taylor model all grains undergo the samedeformation regardless of orientation (Center) The viscoplastic model VPSC treatsgrains as inclusions in an anisotropic viscous medium (Right) In finite elementmodels grains deform differently depending on the orientation of neighbors

Fig 15 Definition of crystal orientation relative to sample coordinates with threerotations (Euler angles) 1 U 2 Projection based on sample coordinate system xy z (pole figure) Crystal coordinate system is defined by axes [100] [010] and[001]

Fig 16 Comparison of (a) 111 pole figure relative to sample coordinates and (b) Ninverse pole figure relative to crystal coordinates for rolled copper Equal areaprojection red colors are high and blue colors are low pole densities N normaldirection R rolling direction and T transverse direction Note the equivalentinformation In the 111 pole figure a maximum in the N direction and in the NDinverse pole figure a maximum in 111

70 B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90

Miyagi et al 2010 2011 Wu et al 2017) Shear deformation canbe induced in rotational DACs (eg Levitas et al 2006) Thismethod has been mainly used to induce phase transformationsand has not yet been applied to study texture evolution at highpressure

In addition to pressure and stress temperature can be inducedin DAC experiments by resistive (eg Liermann et al 2009) andlaser heating (eg Prakapenka et al 2008 Dubrovinsky et al2009) or a combination of the two (Miyagi et al 2013) Tatenoet al (2015) reached temperatures of 6000 K at gt400 GPa on exper-iments on Fe and Fe-Si corresponding to conditions of the Earthrsquos

inner core Obviously there are limitations to DAC experimentssamples are extremely small strain is always compressive andstrain rates are difficult to control

It was surprising to see that silicates and oxides that are brittleat ambient conditions including olivine become ductile at pres-sures of 10GPa even at room temperature and deform by dislo-cation glide (eg Wenk et al 2004) The diffraction image ofMgSiO3 post-perovskite at 150 GPa (Fig 18a) is lsquolsquounrolledrdquo andthe compression direction is indicated by arrows (large 2h smalld Q=1d) (Fig 18b) The elastic lattice distortion (wave-like patternwith azimuth) is related to applied stress and elastic propertiesThe intensity variations with azimuth are indicative of preferredorientation For example there is a strong maximum for 004(fourth order diffraction on the lattice plane 001) in the compres-sion direction This image illustrates why radial diffraction geome-try has to be used to display CPO as function of angle to thecompression direction In axial geometry (X-rays parallel to thediamond axis) Debye-rings have uniform intensity since alldiffracting lattice planes have the same angle to the compressiondirection

A qualitative interpretation of a diffraction image is illustratedin Fig 19 for an experiment with MgGeO3 post-perovskite(Miyagi et al 2011) and used to construct an inverse pole figureof the compression direction (arrow) MgGeO3 is an analog ofMgSiO3 but transforms to pPv at lower pressure There is a maxi-mum for 002 and a minimum for 020 in the compression directionwhich can be plotted in the inverse pole figure (Fig 19 right side)The quantitative deconvolution of diffraction images is not trivialand most often an iterative Rietveld method is applied (egLutterotti et al 2014 Wenk et al 2014) The high pressure syn-chrotron X-ray diffraction deformation images provide quantita-tive information about phases crystal structures density stresselastic properties and preferred orientation

Fig 20a-c shows experimental inverse pole figures of MgSiO3

pPv documenting increasing texture development with pressure-stressndashstrain with a maximum at (001) From the orientation pat-tern active slip systems can be derived by comparing experimentalinverse pole figures with results from polycrystal plasticity calcu-lations that assume certain combinations of slip systems(Fig 20d) Based on the good agreement it can be concluded thatpPv deformed in the experiment by dominant (001)[100] slip(Miyagi et al 2010)

With similar experiments it was suggested that MgSiO3 bridg-manite deforms dominantly by slip on (001) planes in [100][010] and h1 1 0i directions (eg Miyagi and Wenk 2016) but sim-

Fig 18 (a) Diffraction image of MgSiO3 post-perovskite at 150 GPa (b) Unrolled diffractiochanges in Q are due to elastic distortion of the crystal lattice under compression Botquantitative information such as inverse pole figures

Fig 17 Diamond anvil cell for radial diffraction experiments The X-ray beam ishorizontal (a) illustrates the cell and the insert is an enlargement with diamondsand gasket to contain the sample (b c) illustrate that diamonds not only applypressure but also compressive stress that deforms the sample and produces CPO

B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90 71

ple shear experiments in a D-DIA apparatus indicate (100)[001]slip (Tsujino et al 2016) Ferropericlase likely deforms by 110h110i slip (eg Stretton et al 2001 Merkel et al 2002 Linet al 2009) at high pressure conditions For Ca-perovskite domi-nant 110h110i slip was proposed (Miyagi et al 2006 2009)

So far most DAC high-pressure deformation experimentsextracted COD information from intensity variations along Debyerings (eg Fig 18) A new method called multigrain is still underdevelopment It obtains orientation information from individualgrain diffractions (eg Barton and Bernier 2012 Rosa et al2015 Langrand et al 2017) and is especially applicable to coarseraggregates Nisr et al (2012) used information about dislocationsfrom distortion of single crystal diffraction patterns of the post-perovskite analog MgGeO3 and suggested dominant slip on 110and (001) planes

It should be mentioned that information from such high pres-sure experiments is by no means unambiguous Obviously defor-mation conditions in experiments and simulations differconsiderably from those in the deep Earth just to mention temper-ature grain size strain rate interaction of dislocations and interac-tion between grains Furthermore not all CPO patterns that areobserved are due to deformation but could be inherited from orien-tation patterns of precursor phases such as for pPv from perovskite(Dobson et al 2013) or enstatite (Merkel et al 2006 2007 Miyagiet al 2011) Also slip systems may not be the same for pPv phasesof different compositions such as MgGeO3 CaIrO3 NaMgF3 orMn2O3

A different approach has become very important computationof Peierlrsquos stresses and lattice friction for dislocation systems basedon bonding characteristics It was originally developed for metals(eg Kubin et al 1992 Devincre and Kubin 1997) and has morerecently been applied to minerals in the mantle where it allowsto predict slip system activities for a wide range of temperaturendashpressurendashstrain rate conditions (eg Carrez et al 2007Mainprice et al 2008 Cordier et al 2012) Amodeo et al (20122014 2016) propose a switch from 110h010i slip to 100h0 1 1i slip in periclase with pressure Kraych et al (2016) suggest(010)[100] slip in bridgmanite at high pressure According tothese calculations the strength of bridgmanite increases greatlywith pressure and at 60 GPa bridgmanite appears 20 times stron-ger than periclase The critical resolved shear stress decreasesabout 20 from strain rates of 105 s1 (which corresponds to

n image as function of Q (Q = 1d) Intensity variations with azimuth illustrate CPOtom experimental data above fit of the data with the Rietveld method to extract

Fig 19 Explanation of the relationship between DAC diffraction image and inverse pole figure Left Unrolled diffraction image of MgGeO3 post-perovskite Some diffractionlines are labeled The sinusoidal variations are due to imposed stress High stress (high Q low d) is indicated by arrows On the right side is a conceptual construction of theinverse pole figure of the compression axis based on relative diffraction intensities (Miyagi et al 2011)

Fig 20 Inverse pole figures for MgSiO3 post-perovskite (AndashC) experiments (D) Plasticity model with dominant (001) slip equal area projection (Miyagi et al 2010)

72 B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90

experimental values) to 1014 s1 corresponding to likely values atdeep mantle conditions (Fig 21a) The opposite is the case for pPvwhich appears much weaker than periclase at high pressure hightemperature and slow strain rates (Fig 21b Goryaeva et al 20152016) Also the predicted weakest calculated slip system for post-perovskite at deep mantle conditions is (010)[100] correspondingto the layered crystal structure (Fig 21c) but different from thatobserved in DAC experiments (Miyagi et al 2010 Wu et al 2017)

It should be mentioned that a single slip system is not sufficientto deform a polycrystal In the case of the Taylor model at least 5systems have to be active to produce an arbitrary strain (Mises1928) This is relaxed for the self-consistent model but also hereseveral slip systems are active The choice of activity depends onthe crystal orientation relative to the applied stress (Schmid fac-tor) TEM investigations confirm this though some slip systemsusually dominate and the literature refers to the lsquolsquodominantrdquo slipsystem Some dominant slip systems for deep Earth minerals aresummarized in Table 2

34 Elastic properties

Elastic properties of crystals at conditions pertaining to thelower mantle are critical to link microstructural properties of therock with seismic observations The most straightforward experi-mental method that has been applied to many lower mantle min-erals is Brillouin scattering (see review by Speziale et al 2014) andenergy-dispersive X-ray diffraction (eg for calcium silicate per-ovskite Shieh et al 2004) A different approach is with first prin-ciples calculations at high pressure and temperature (for someapplications to bridgmanite CaSiO3 perovskite and pPv see egZhang et al 2013 Wentzcovitch et al 2005 Kawai and

Tsuchiya 2015) First principles results look fairly consistent forminerals at lower mantle conditions but as we will see in Sec-tion 62 predictions for iron at inner core conditions are stillambiguous Furthermore the actual composition of the mineralsparticularly the iron content can be significant (eg Koci et al2007) Values of stiffness coefficients and P-wave anisotropy (An = 200(Pmax Pmin)(Pmax + Pmin) for some low mantle mineralsat lowermost mantle conditions are listed in Table 3 Fig 22 givescorresponding S velocities of single crystals with black lines corre-sponding to the orientation of the fast S-wave polarization As canbe seen in Table 1 periclase and pPv have the highest P-wave ani-sotropy and Ca-perovskite is least anisotropic The S-wave aniso-tropy is considerably higher for pPv and periclase than forbridgmanite and particularly CaSiO3 perovskite

To obtain elastic properties of aggregates one has to averageover all orientations and corresponding elastic tensors takingphase fractions into account Simple averages are upper bound(Voigt 1887) and lower bound (Reuss 1929) Generally an inter-mediate arithmetic mean (Hill 1952) or a geometric mean(Matthies and Humbert 1995) are preferred All these models donot take grain shape into account which is not very significantfor crystalline phases but becomes important for systems withplaty minerals such as graphite or sheet-silicate containing rocksand aggregates with flat oriented pores For such cases a self-consistent (Matthies 2012 Vasin et al 2013) or differential effec-tive medium approach (eg Hornby et al 1994) should be consid-ered It is probably not important for the lower mantle

Note that S-waves passing through anisotropic media have arbi-trary polarization directions in the plane perpendicular to thedirection of propagation as is best displayed for the fast directionof single crystals in Fig 22 but applies also to aggregations of ori-

Fig 21 Critical resolved shear stress CRSS for dislocation glide activities as functionof temperature of (a) bridgmanite at 60 GPa (from Kraych et al 2016) and MgO(from Amodeo et al 2016) at strain rates 105 s1 and 1014 s1 (b) post-perovskiteat 120 GPa at strain rate 1016 s1 (from Goryaeva et al 2016) compared with MgO(from Amodeo et al 2012) Courtesy of P Cordier

B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90 73

ented crystals Seismologists generally consider the projection ofthat polarization direction onto horizontal and vertical axes Thisis convenient because differences in arrival times and waveformsin this representation can be expressed in terms of apparent verti-cal transverse isotropy (VTI) which because of limited azimuthalsampling is often the only anisotropic constraint that can beobtained

4 Linking seismology and mineral physics through predictionsof anisotropy in geodynamic models

41 Isotropic geodynamic models for upper mantle convection

Ever since the concept of plate tectonics became accepted in the1960s convective movements in the Earthrsquos mantle have been pro-posed such as upwelling along oceanic ridges (eg Hess 1964Cann 1968 Fig 1b) The first quantitative models based on hydro-dynamics emerged in the eighties (eg Hager and OrsquoConnell 1981)

Table 2Proposed dominant slip systems in deep Earth minerals

Ferropericlase Lower P 110110High PT also 100011

Bridgmanite Low P (001)[100] [010] 110High P (100)[001](010)[100]

pPv (001)[100](010)[100]

Ca-perovskite 110110e-iron (0001)1120 subordinate 1010

Geodynamic models have been mainly applied to the upper mantleand we will not discuss them here in detail (see eg review by Longand Becker 2010)

Many convection models have been developed to understandthe evolution of the deep Earth Calculations generally assume aviscous fluid and use non-dimensional equations for the conserva-tion of mass momentum and energy applying the Boussineqapproximation Critical parameters are Rayleigh number viscosityboundary temperatures In order to evaluate the strain evolutionduring the convection process tracers are introduced that recordthe velocity gradient tensor at each time step along the path ofthe tracer If the deformation mechanisms are known (eg disloca-tion glide) polycrystal plasticity calculations can be used to calcu-late the evolution of crystal preferred orientation based on thestrain recorded by tracers

Most geodynamic models assume a viscous isotropic mediumwith a smoothly varying viscosity structure and the microstruc-tural processes leading to preferred orientation are introducedpost-mortem Considering an anisotropic medium that constantlychanges its properties greatly increases the complexity of geody-namic calculations However there are models in metallurgy suchas extrusion of an aggregate that illustrate the importance of ananisotropic material behavior (eg Beyerlein et al 2003)

42 Review of upper mantle anisotropic models

We will start the discussion of anisotropic convection byreturning to a simple 2D model (Dawson and Wenk 2000) thatwas originally issued as an educational video by AGU (1999) andcan now be downloaded in digital form (httpepsberkeleyedu~wenkTexturePageMantle-Videohtm) At high Rayleigh number(low viscosity) heat transfer occurs by convection rather than con-duction corresponding to conditions in the Earthrsquos mantle Convec-tion is driven by temperature gradients As aggregates move alongstreamlines the orientation of grains is constantly updated and thelocal texture affects the next deformation step which introducesconsiderable heterogeneities It was surprising to find locallyheterogeneous CPO patterns in the 2D convection cell representingthe upper mantle shown as [100] pole figures of olivine after100 my (Fig 23) Some regions have strong and others very weakpatterns that can be attributed to heterogeneous deformation dueto CPO development and result in lsquolsquoanisotropicrdquo viscosity

Some complexities of different plasticity models for a simplecase of upwelling have been investigated by Blackman et al(1996 2002) and Castelnau et al (2009) If a lower bound behavioris assumed (Sachs 1928) there is very strong CPO developmentFor self-consistent models (Lebensohn and Tomeacute 1993) rotationsare reduced If dislocation glide is combined with dynamic recrys-tallization both grain growth and grain growth combined withnucleation resulting orientation patterns can be very differentRecrystallization is likely in the deep Earth with high temperatureand large strains where grain boundary migration is likely tooccur We will return to the issue of recrystallization in Section 48

Merkel et al (2002) and Lin et al (2009)Amodeo et al (2016)Miyagi and Wenk 2016Tsujino et al (2016)Kraych et al (2016)Miyagi et al (2010) and Wu et al (2017)Goryaeva et al (2016)Miyagi et al (2009) and Ferreacute et al (2009)

Merkel et al (2004) and Miyagi et al (2008)

Fig 8 Comparison of 6 recent models of lateral variations in the radial anisotropy parameter n = (VshVsv)2 plotted in terms of dlnn referred to isotropy While the modelsdisagree in detail common features are Vsh gt Vsv (blue) in the circum Pacific ring (roughly in agreement with local studies) and pronounced Vsv gt Vsh (orange) in the Fiji-TongaIndonesia region and under southernmost Africa (except SAVANI) Models plotted are (a) SAW642ANb (Panning et al 2010) (b) SAW642AN (Panning andRomanowicz 2006) (c) SAVANI (Auer et al 2014) (d) SGLOBE-rani (Chang et al 2015) (e) S362WANI + M (Moulik and Ekstroumlm 2014) (f) SEMUCB_WM1 (French andRomanowicz 2014)

Fig 9 (a) Experimentally determined PT phase diagram for perovskitebridgmanite (Pv)-post-perovskite (Murakami et al 2004) (b) T-Depth phase diagram plotting the pv-ppv phase boundary and cold and warm geotherms (after Hernlund et al 2005)

B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90 67

because some produce crystal rotations and thus crystallographicpreferred orientation (notably dislocation glide and ndash to someextent ndash dynamic recrystallization) while others generate random

orientations (such as grain boundary sliding in fine-grained mate-rials and dislocation climb) We will return to these issues inSection 48

Fig 10 Crystal structures of (a) periclase (b) bridgmanite and (c) post-perovskite the latter two with octahedrally coordinated silicon

Fig 11 Lower mantle composition for different models (a) pyrolite (b) MORB(from Irifune and Tsuchiya 2015) Pv perovskitebridgmanite Ppv post-perovskiteMw magnesiowuestiteferropericlase Mj majorite Rw ringwoodite SiO2 Ststishovite CC CaCl2 phase AP a-PbO2 phase Al2O Hex CF calcium-ferrite phaseCT calcium-titanate phase

68 B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90

In a polycrystalline aggregate stresses are transmitted acrossgrain boundaries causing heterogeneities even within grains Thisis most realistically approached with finite element methods (egMika and Dawson 1999) but these are still extremely demandingand rarely applied Simpler models have been used in materialsscience for a long time The Taylor (1938) theory developed bythe same Taylor who discovered dislocations (1934) assumeshomogeneous strain All grains undergo the same shape changeirrespective of orientation This leaves grain boundaries intact(Fig 14 left side) The Taylor model is very applicable to cubic met-als with many symmetrically related slip systems Slip on 111h

1 1 0i in fcc metals or cubic periclase has 12 equivalent systemsAnother model (Sachs 1928) assumes stress equilibrium and morefavorably oriented grains deform more than others In the modelthis causes overlaps and gaps at grain boundaries In principle thiswould be more adequate for low symmetry minerals (such asorthorhombic) but of course overlaps and gaps do not exist A com-promise between homogeneous strain and stress equilibrium is aself-consistent model that treats grains as ellipsoidal inclusionsdeforming in an anisotropic viscous medium (Fig 14 centerMolinari et al 1987) It is most widely applied in the Los Alamoscode VPSC (Lebensohn and Tomeacute 1993) and it can be used bothto understand preferred orientation in high pressure experimentsand to predict anisotropy in geodynamic models In the viscoplas-tic self-consistent model grains deform without knowledge of theirneighborhood In a finite element model (Fig 14 right) grains areconstrained by the orientation of neighbors In this sketch it isassumed that each grain has a single orientation In more sophisti-cated FEM models there are strain and orientation gradients devel-oping within grains (eg Mika and Dawson 1999)

When crystals are deformed in a polycrystalline medium theyundergo systematic rotations (Fig 12) and the material attains ananisotropic pattern We need to describe the orientation of a crys-tal relative to the macroscopic sample This is efficiently done byrelating two orthogonal coordinate systems (sample x y z crystal[100] [010] [001]) by three rotations Most frequently the so-called Euler angles are used U is the distance from z to [001]1 is the azimuth of [001] from y (around z) 2 is the azimuthof [100] around [001] (Fig 15) The 3-dimensional crystal orienta-tion distribution (COD) is conventionally described by a continuousorientation distribution function (ODF) The ODF is required to cal-culate anisotropic elastic properties of an aggregate from crystalorientations

For graphical representations of orientation patterns generally2-dimensional spherical projections of the ODF are used Depend-ing on the application one can either use the macroscopic sample xy z as reference and plot crystal directions (pole figures) or use thecrystal as reference and plot sample directions (inverse pole fig-ures) Inverse pole figures are useful if only a single sample direc-tion is of interest eg the compression direction in a compressionexperiment The symmetry of pole figures reflects the symmetry ofthe deformation path In compression experiments pole figures areaxially symmetric The density of poles on the sphere is contouredand then expressed as continuous pole densities usually normal-ized relative to a random distribution and defined as multiples ofa random distribution (mrd) 2ndash5 mrd are moderate CODs20ndash50 mrd very strong CODs The strongest crystal alignmentsin rocks that have been observed are muscovite in slates exceeding100 mrd Fig 16a is a 111 pole figure of rolled copper with roll-

Fig 12 Under stress imposed by pistons a crystal deforms to a new shape by slip of dislocations on a glide plane Since pistons remain in contact with the crystal surfacethere is an effective rotation b In a polycrystal neighboring grains act as effective pistons to transmit the stress

Fig 13 Stress-temperature deformation mechanism map (Langdon and Mohamed1978)

B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90 69

ing R transverse T and normal N sample directions indicatedFig 16b is the corresponding inverse pole figure of the normaldirection Inverse pole figures display the crystal symmetry Bothrepresentations will be used in the following discussion

33 Deformation experiments and rheology

The experiments on plasticity of metals were not applicable tomost minerals because even at elevated temperatures theirdeformation behavior at ambient pressure is generally brittleOne had to wait until high pressure deformation experiments weredeveloped by Griggs (1936) and applied on a wide scale includingolivine (eg Raleigh 1968) Since then sophisticated deformationapparati have been constructed in many laboratories making itpossible to deform rocks at a wide range of pressures and temper-atures They were applied to many minerals and rocks in the crustand upper mantle Studies on olivine (eg Jung and Karato 2001

Hansen et al 2012 Jackson and Faul 2010) documented the com-plex influence of temperature pressure composition (such aswater and iron content) The most sophisticated apparatus wasdeveloped at the Australian National University (Paterson andOlgaard 2000) It allows for deformation experiments on relativelylarge samples (1 cm) in compression tension and torsion Pres-sures are limited to 03 GPa and the limitation in pressure pre-vents these instruments to be used for experiments relevant tothe lower mantle (20ndash150 GPa) and inner core (320ndash360 GPa)

Higher pressure deformation experiments have been reviewedby Weidner and Li (2015) The multi-anvil apparatus called DIAwith three pairs of octahedral pistons (Onodera 1987) has beenmodified to apply stress by preferentially advancing one pistonpair (D-DIA for deformation DIA) The sample can be heated inter-nally Changes in phase structure preferred orientation andmicrostructure can be recorded in situ if the D-DIA apparatus iscombined with a monochromatic synchrotron X-ray beam fordiffraction and imaging (eg Wang et al 2003 2011) The conven-tional D-DIA apparatus has been used to 20 GPa and samples arecylinders 1 mm in diameter (eg Kawazoe et al 2010) A moreadvanced D-DIA (Kawai-type) reaching gt110 GPa with sintereddiamond anvils and smaller samples has been introduced atSPring8 in Japan (Yamazaki et al 2014)

Shear deformation at high pressure can be performed with arotational Drickamer apparatus (RDA) (eg Yamasaki and Karato2001) Shear deformation of a bridgmanite-ferropericlase aggre-gate at 25 GPa and 2100 K has been achieved to large strains(Girard et al 2016) In such torsion experiments the strain variesgreatly as a function of sample radius The experiment documentedthat most of the plastic deformation is accommodated by theweaker ferropericlase

Currently the most accessible method to deform samples atultrahigh pressures (gt500 GPa) is with diamond anvil cells (DAC)where diamonds are used as pistons compressing a small sample(30ndash80 lm in diameter and 50 lm thick) (eg Merkel et al2002 Fig 17) The diamonds are used not only to induce pressurebut also to cause compressive deformation (Fig 17 b c) and theevolution of preferred orientation can be observed in situ if hori-zontal X-rays transmit the sample in radial diffraction geometry(r-DAC) Strong textures have been observed in ferropericlase(eg Merkel et al 2002 Lin et al 2009) perovskitebridgmanite(eg Merkel et al 2003 Wenk et al 2006 Miyagi and Wenk2016 Tsujino et al 2016) and pPv the phase likely to be presentat the core-mantle boundary (eg Merkel et al 2006 2007

Fig 14 2D Sketches of polycrystal plasticity models Gray shades express orien-tation (Left) For the full constraints Taylor model all grains undergo the samedeformation regardless of orientation (Center) The viscoplastic model VPSC treatsgrains as inclusions in an anisotropic viscous medium (Right) In finite elementmodels grains deform differently depending on the orientation of neighbors

Fig 15 Definition of crystal orientation relative to sample coordinates with threerotations (Euler angles) 1 U 2 Projection based on sample coordinate system xy z (pole figure) Crystal coordinate system is defined by axes [100] [010] and[001]

Fig 16 Comparison of (a) 111 pole figure relative to sample coordinates and (b) Ninverse pole figure relative to crystal coordinates for rolled copper Equal areaprojection red colors are high and blue colors are low pole densities N normaldirection R rolling direction and T transverse direction Note the equivalentinformation In the 111 pole figure a maximum in the N direction and in the NDinverse pole figure a maximum in 111

70 B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90

Miyagi et al 2010 2011 Wu et al 2017) Shear deformation canbe induced in rotational DACs (eg Levitas et al 2006) Thismethod has been mainly used to induce phase transformationsand has not yet been applied to study texture evolution at highpressure

In addition to pressure and stress temperature can be inducedin DAC experiments by resistive (eg Liermann et al 2009) andlaser heating (eg Prakapenka et al 2008 Dubrovinsky et al2009) or a combination of the two (Miyagi et al 2013) Tatenoet al (2015) reached temperatures of 6000 K at gt400 GPa on exper-iments on Fe and Fe-Si corresponding to conditions of the Earthrsquos

inner core Obviously there are limitations to DAC experimentssamples are extremely small strain is always compressive andstrain rates are difficult to control

It was surprising to see that silicates and oxides that are brittleat ambient conditions including olivine become ductile at pres-sures of 10GPa even at room temperature and deform by dislo-cation glide (eg Wenk et al 2004) The diffraction image ofMgSiO3 post-perovskite at 150 GPa (Fig 18a) is lsquolsquounrolledrdquo andthe compression direction is indicated by arrows (large 2h smalld Q=1d) (Fig 18b) The elastic lattice distortion (wave-like patternwith azimuth) is related to applied stress and elastic propertiesThe intensity variations with azimuth are indicative of preferredorientation For example there is a strong maximum for 004(fourth order diffraction on the lattice plane 001) in the compres-sion direction This image illustrates why radial diffraction geome-try has to be used to display CPO as function of angle to thecompression direction In axial geometry (X-rays parallel to thediamond axis) Debye-rings have uniform intensity since alldiffracting lattice planes have the same angle to the compressiondirection

A qualitative interpretation of a diffraction image is illustratedin Fig 19 for an experiment with MgGeO3 post-perovskite(Miyagi et al 2011) and used to construct an inverse pole figureof the compression direction (arrow) MgGeO3 is an analog ofMgSiO3 but transforms to pPv at lower pressure There is a maxi-mum for 002 and a minimum for 020 in the compression directionwhich can be plotted in the inverse pole figure (Fig 19 right side)The quantitative deconvolution of diffraction images is not trivialand most often an iterative Rietveld method is applied (egLutterotti et al 2014 Wenk et al 2014) The high pressure syn-chrotron X-ray diffraction deformation images provide quantita-tive information about phases crystal structures density stresselastic properties and preferred orientation

Fig 20a-c shows experimental inverse pole figures of MgSiO3

pPv documenting increasing texture development with pressure-stressndashstrain with a maximum at (001) From the orientation pat-tern active slip systems can be derived by comparing experimentalinverse pole figures with results from polycrystal plasticity calcu-lations that assume certain combinations of slip systems(Fig 20d) Based on the good agreement it can be concluded thatpPv deformed in the experiment by dominant (001)[100] slip(Miyagi et al 2010)

With similar experiments it was suggested that MgSiO3 bridg-manite deforms dominantly by slip on (001) planes in [100][010] and h1 1 0i directions (eg Miyagi and Wenk 2016) but sim-

Fig 18 (a) Diffraction image of MgSiO3 post-perovskite at 150 GPa (b) Unrolled diffractiochanges in Q are due to elastic distortion of the crystal lattice under compression Botquantitative information such as inverse pole figures

Fig 17 Diamond anvil cell for radial diffraction experiments The X-ray beam ishorizontal (a) illustrates the cell and the insert is an enlargement with diamondsand gasket to contain the sample (b c) illustrate that diamonds not only applypressure but also compressive stress that deforms the sample and produces CPO

B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90 71

ple shear experiments in a D-DIA apparatus indicate (100)[001]slip (Tsujino et al 2016) Ferropericlase likely deforms by 110h110i slip (eg Stretton et al 2001 Merkel et al 2002 Linet al 2009) at high pressure conditions For Ca-perovskite domi-nant 110h110i slip was proposed (Miyagi et al 2006 2009)

So far most DAC high-pressure deformation experimentsextracted COD information from intensity variations along Debyerings (eg Fig 18) A new method called multigrain is still underdevelopment It obtains orientation information from individualgrain diffractions (eg Barton and Bernier 2012 Rosa et al2015 Langrand et al 2017) and is especially applicable to coarseraggregates Nisr et al (2012) used information about dislocationsfrom distortion of single crystal diffraction patterns of the post-perovskite analog MgGeO3 and suggested dominant slip on 110and (001) planes

It should be mentioned that information from such high pres-sure experiments is by no means unambiguous Obviously defor-mation conditions in experiments and simulations differconsiderably from those in the deep Earth just to mention temper-ature grain size strain rate interaction of dislocations and interac-tion between grains Furthermore not all CPO patterns that areobserved are due to deformation but could be inherited from orien-tation patterns of precursor phases such as for pPv from perovskite(Dobson et al 2013) or enstatite (Merkel et al 2006 2007 Miyagiet al 2011) Also slip systems may not be the same for pPv phasesof different compositions such as MgGeO3 CaIrO3 NaMgF3 orMn2O3

A different approach has become very important computationof Peierlrsquos stresses and lattice friction for dislocation systems basedon bonding characteristics It was originally developed for metals(eg Kubin et al 1992 Devincre and Kubin 1997) and has morerecently been applied to minerals in the mantle where it allowsto predict slip system activities for a wide range of temperaturendashpressurendashstrain rate conditions (eg Carrez et al 2007Mainprice et al 2008 Cordier et al 2012) Amodeo et al (20122014 2016) propose a switch from 110h010i slip to 100h0 1 1i slip in periclase with pressure Kraych et al (2016) suggest(010)[100] slip in bridgmanite at high pressure According tothese calculations the strength of bridgmanite increases greatlywith pressure and at 60 GPa bridgmanite appears 20 times stron-ger than periclase The critical resolved shear stress decreasesabout 20 from strain rates of 105 s1 (which corresponds to

n image as function of Q (Q = 1d) Intensity variations with azimuth illustrate CPOtom experimental data above fit of the data with the Rietveld method to extract

Fig 19 Explanation of the relationship between DAC diffraction image and inverse pole figure Left Unrolled diffraction image of MgGeO3 post-perovskite Some diffractionlines are labeled The sinusoidal variations are due to imposed stress High stress (high Q low d) is indicated by arrows On the right side is a conceptual construction of theinverse pole figure of the compression axis based on relative diffraction intensities (Miyagi et al 2011)

Fig 20 Inverse pole figures for MgSiO3 post-perovskite (AndashC) experiments (D) Plasticity model with dominant (001) slip equal area projection (Miyagi et al 2010)

72 B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90

experimental values) to 1014 s1 corresponding to likely values atdeep mantle conditions (Fig 21a) The opposite is the case for pPvwhich appears much weaker than periclase at high pressure hightemperature and slow strain rates (Fig 21b Goryaeva et al 20152016) Also the predicted weakest calculated slip system for post-perovskite at deep mantle conditions is (010)[100] correspondingto the layered crystal structure (Fig 21c) but different from thatobserved in DAC experiments (Miyagi et al 2010 Wu et al 2017)

It should be mentioned that a single slip system is not sufficientto deform a polycrystal In the case of the Taylor model at least 5systems have to be active to produce an arbitrary strain (Mises1928) This is relaxed for the self-consistent model but also hereseveral slip systems are active The choice of activity depends onthe crystal orientation relative to the applied stress (Schmid fac-tor) TEM investigations confirm this though some slip systemsusually dominate and the literature refers to the lsquolsquodominantrdquo slipsystem Some dominant slip systems for deep Earth minerals aresummarized in Table 2

34 Elastic properties

Elastic properties of crystals at conditions pertaining to thelower mantle are critical to link microstructural properties of therock with seismic observations The most straightforward experi-mental method that has been applied to many lower mantle min-erals is Brillouin scattering (see review by Speziale et al 2014) andenergy-dispersive X-ray diffraction (eg for calcium silicate per-ovskite Shieh et al 2004) A different approach is with first prin-ciples calculations at high pressure and temperature (for someapplications to bridgmanite CaSiO3 perovskite and pPv see egZhang et al 2013 Wentzcovitch et al 2005 Kawai and

Tsuchiya 2015) First principles results look fairly consistent forminerals at lower mantle conditions but as we will see in Sec-tion 62 predictions for iron at inner core conditions are stillambiguous Furthermore the actual composition of the mineralsparticularly the iron content can be significant (eg Koci et al2007) Values of stiffness coefficients and P-wave anisotropy (An = 200(Pmax Pmin)(Pmax + Pmin) for some low mantle mineralsat lowermost mantle conditions are listed in Table 3 Fig 22 givescorresponding S velocities of single crystals with black lines corre-sponding to the orientation of the fast S-wave polarization As canbe seen in Table 1 periclase and pPv have the highest P-wave ani-sotropy and Ca-perovskite is least anisotropic The S-wave aniso-tropy is considerably higher for pPv and periclase than forbridgmanite and particularly CaSiO3 perovskite

To obtain elastic properties of aggregates one has to averageover all orientations and corresponding elastic tensors takingphase fractions into account Simple averages are upper bound(Voigt 1887) and lower bound (Reuss 1929) Generally an inter-mediate arithmetic mean (Hill 1952) or a geometric mean(Matthies and Humbert 1995) are preferred All these models donot take grain shape into account which is not very significantfor crystalline phases but becomes important for systems withplaty minerals such as graphite or sheet-silicate containing rocksand aggregates with flat oriented pores For such cases a self-consistent (Matthies 2012 Vasin et al 2013) or differential effec-tive medium approach (eg Hornby et al 1994) should be consid-ered It is probably not important for the lower mantle

Note that S-waves passing through anisotropic media have arbi-trary polarization directions in the plane perpendicular to thedirection of propagation as is best displayed for the fast directionof single crystals in Fig 22 but applies also to aggregations of ori-

Fig 21 Critical resolved shear stress CRSS for dislocation glide activities as functionof temperature of (a) bridgmanite at 60 GPa (from Kraych et al 2016) and MgO(from Amodeo et al 2016) at strain rates 105 s1 and 1014 s1 (b) post-perovskiteat 120 GPa at strain rate 1016 s1 (from Goryaeva et al 2016) compared with MgO(from Amodeo et al 2012) Courtesy of P Cordier

B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90 73

ented crystals Seismologists generally consider the projection ofthat polarization direction onto horizontal and vertical axes Thisis convenient because differences in arrival times and waveformsin this representation can be expressed in terms of apparent verti-cal transverse isotropy (VTI) which because of limited azimuthalsampling is often the only anisotropic constraint that can beobtained

4 Linking seismology and mineral physics through predictionsof anisotropy in geodynamic models

41 Isotropic geodynamic models for upper mantle convection

Ever since the concept of plate tectonics became accepted in the1960s convective movements in the Earthrsquos mantle have been pro-posed such as upwelling along oceanic ridges (eg Hess 1964Cann 1968 Fig 1b) The first quantitative models based on hydro-dynamics emerged in the eighties (eg Hager and OrsquoConnell 1981)

Table 2Proposed dominant slip systems in deep Earth minerals

Ferropericlase Lower P 110110High PT also 100011

Bridgmanite Low P (001)[100] [010] 110High P (100)[001](010)[100]

pPv (001)[100](010)[100]

Ca-perovskite 110110e-iron (0001)1120 subordinate 1010

Geodynamic models have been mainly applied to the upper mantleand we will not discuss them here in detail (see eg review by Longand Becker 2010)

Many convection models have been developed to understandthe evolution of the deep Earth Calculations generally assume aviscous fluid and use non-dimensional equations for the conserva-tion of mass momentum and energy applying the Boussineqapproximation Critical parameters are Rayleigh number viscosityboundary temperatures In order to evaluate the strain evolutionduring the convection process tracers are introduced that recordthe velocity gradient tensor at each time step along the path ofthe tracer If the deformation mechanisms are known (eg disloca-tion glide) polycrystal plasticity calculations can be used to calcu-late the evolution of crystal preferred orientation based on thestrain recorded by tracers

Most geodynamic models assume a viscous isotropic mediumwith a smoothly varying viscosity structure and the microstruc-tural processes leading to preferred orientation are introducedpost-mortem Considering an anisotropic medium that constantlychanges its properties greatly increases the complexity of geody-namic calculations However there are models in metallurgy suchas extrusion of an aggregate that illustrate the importance of ananisotropic material behavior (eg Beyerlein et al 2003)

42 Review of upper mantle anisotropic models

We will start the discussion of anisotropic convection byreturning to a simple 2D model (Dawson and Wenk 2000) thatwas originally issued as an educational video by AGU (1999) andcan now be downloaded in digital form (httpepsberkeleyedu~wenkTexturePageMantle-Videohtm) At high Rayleigh number(low viscosity) heat transfer occurs by convection rather than con-duction corresponding to conditions in the Earthrsquos mantle Convec-tion is driven by temperature gradients As aggregates move alongstreamlines the orientation of grains is constantly updated and thelocal texture affects the next deformation step which introducesconsiderable heterogeneities It was surprising to find locallyheterogeneous CPO patterns in the 2D convection cell representingthe upper mantle shown as [100] pole figures of olivine after100 my (Fig 23) Some regions have strong and others very weakpatterns that can be attributed to heterogeneous deformation dueto CPO development and result in lsquolsquoanisotropicrdquo viscosity

Some complexities of different plasticity models for a simplecase of upwelling have been investigated by Blackman et al(1996 2002) and Castelnau et al (2009) If a lower bound behavioris assumed (Sachs 1928) there is very strong CPO developmentFor self-consistent models (Lebensohn and Tomeacute 1993) rotationsare reduced If dislocation glide is combined with dynamic recrys-tallization both grain growth and grain growth combined withnucleation resulting orientation patterns can be very differentRecrystallization is likely in the deep Earth with high temperatureand large strains where grain boundary migration is likely tooccur We will return to the issue of recrystallization in Section 48

Merkel et al (2002) and Lin et al (2009)Amodeo et al (2016)Miyagi and Wenk 2016Tsujino et al (2016)Kraych et al (2016)Miyagi et al (2010) and Wu et al (2017)Goryaeva et al (2016)Miyagi et al (2009) and Ferreacute et al (2009)

Merkel et al (2004) and Miyagi et al (2008)

Fig 10 Crystal structures of (a) periclase (b) bridgmanite and (c) post-perovskite the latter two with octahedrally coordinated silicon

Fig 11 Lower mantle composition for different models (a) pyrolite (b) MORB(from Irifune and Tsuchiya 2015) Pv perovskitebridgmanite Ppv post-perovskiteMw magnesiowuestiteferropericlase Mj majorite Rw ringwoodite SiO2 Ststishovite CC CaCl2 phase AP a-PbO2 phase Al2O Hex CF calcium-ferrite phaseCT calcium-titanate phase

68 B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90

In a polycrystalline aggregate stresses are transmitted acrossgrain boundaries causing heterogeneities even within grains Thisis most realistically approached with finite element methods (egMika and Dawson 1999) but these are still extremely demandingand rarely applied Simpler models have been used in materialsscience for a long time The Taylor (1938) theory developed bythe same Taylor who discovered dislocations (1934) assumeshomogeneous strain All grains undergo the same shape changeirrespective of orientation This leaves grain boundaries intact(Fig 14 left side) The Taylor model is very applicable to cubic met-als with many symmetrically related slip systems Slip on 111h

1 1 0i in fcc metals or cubic periclase has 12 equivalent systemsAnother model (Sachs 1928) assumes stress equilibrium and morefavorably oriented grains deform more than others In the modelthis causes overlaps and gaps at grain boundaries In principle thiswould be more adequate for low symmetry minerals (such asorthorhombic) but of course overlaps and gaps do not exist A com-promise between homogeneous strain and stress equilibrium is aself-consistent model that treats grains as ellipsoidal inclusionsdeforming in an anisotropic viscous medium (Fig 14 centerMolinari et al 1987) It is most widely applied in the Los Alamoscode VPSC (Lebensohn and Tomeacute 1993) and it can be used bothto understand preferred orientation in high pressure experimentsand to predict anisotropy in geodynamic models In the viscoplas-tic self-consistent model grains deform without knowledge of theirneighborhood In a finite element model (Fig 14 right) grains areconstrained by the orientation of neighbors In this sketch it isassumed that each grain has a single orientation In more sophisti-cated FEM models there are strain and orientation gradients devel-oping within grains (eg Mika and Dawson 1999)

When crystals are deformed in a polycrystalline medium theyundergo systematic rotations (Fig 12) and the material attains ananisotropic pattern We need to describe the orientation of a crys-tal relative to the macroscopic sample This is efficiently done byrelating two orthogonal coordinate systems (sample x y z crystal[100] [010] [001]) by three rotations Most frequently the so-called Euler angles are used U is the distance from z to [001]1 is the azimuth of [001] from y (around z) 2 is the azimuthof [100] around [001] (Fig 15) The 3-dimensional crystal orienta-tion distribution (COD) is conventionally described by a continuousorientation distribution function (ODF) The ODF is required to cal-culate anisotropic elastic properties of an aggregate from crystalorientations

For graphical representations of orientation patterns generally2-dimensional spherical projections of the ODF are used Depend-ing on the application one can either use the macroscopic sample xy z as reference and plot crystal directions (pole figures) or use thecrystal as reference and plot sample directions (inverse pole fig-ures) Inverse pole figures are useful if only a single sample direc-tion is of interest eg the compression direction in a compressionexperiment The symmetry of pole figures reflects the symmetry ofthe deformation path In compression experiments pole figures areaxially symmetric The density of poles on the sphere is contouredand then expressed as continuous pole densities usually normal-ized relative to a random distribution and defined as multiples ofa random distribution (mrd) 2ndash5 mrd are moderate CODs20ndash50 mrd very strong CODs The strongest crystal alignmentsin rocks that have been observed are muscovite in slates exceeding100 mrd Fig 16a is a 111 pole figure of rolled copper with roll-

Fig 12 Under stress imposed by pistons a crystal deforms to a new shape by slip of dislocations on a glide plane Since pistons remain in contact with the crystal surfacethere is an effective rotation b In a polycrystal neighboring grains act as effective pistons to transmit the stress

Fig 13 Stress-temperature deformation mechanism map (Langdon and Mohamed1978)

B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90 69

ing R transverse T and normal N sample directions indicatedFig 16b is the corresponding inverse pole figure of the normaldirection Inverse pole figures display the crystal symmetry Bothrepresentations will be used in the following discussion

33 Deformation experiments and rheology

The experiments on plasticity of metals were not applicable tomost minerals because even at elevated temperatures theirdeformation behavior at ambient pressure is generally brittleOne had to wait until high pressure deformation experiments weredeveloped by Griggs (1936) and applied on a wide scale includingolivine (eg Raleigh 1968) Since then sophisticated deformationapparati have been constructed in many laboratories making itpossible to deform rocks at a wide range of pressures and temper-atures They were applied to many minerals and rocks in the crustand upper mantle Studies on olivine (eg Jung and Karato 2001

Hansen et al 2012 Jackson and Faul 2010) documented the com-plex influence of temperature pressure composition (such aswater and iron content) The most sophisticated apparatus wasdeveloped at the Australian National University (Paterson andOlgaard 2000) It allows for deformation experiments on relativelylarge samples (1 cm) in compression tension and torsion Pres-sures are limited to 03 GPa and the limitation in pressure pre-vents these instruments to be used for experiments relevant tothe lower mantle (20ndash150 GPa) and inner core (320ndash360 GPa)

Higher pressure deformation experiments have been reviewedby Weidner and Li (2015) The multi-anvil apparatus called DIAwith three pairs of octahedral pistons (Onodera 1987) has beenmodified to apply stress by preferentially advancing one pistonpair (D-DIA for deformation DIA) The sample can be heated inter-nally Changes in phase structure preferred orientation andmicrostructure can be recorded in situ if the D-DIA apparatus iscombined with a monochromatic synchrotron X-ray beam fordiffraction and imaging (eg Wang et al 2003 2011) The conven-tional D-DIA apparatus has been used to 20 GPa and samples arecylinders 1 mm in diameter (eg Kawazoe et al 2010) A moreadvanced D-DIA (Kawai-type) reaching gt110 GPa with sintereddiamond anvils and smaller samples has been introduced atSPring8 in Japan (Yamazaki et al 2014)

Shear deformation at high pressure can be performed with arotational Drickamer apparatus (RDA) (eg Yamasaki and Karato2001) Shear deformation of a bridgmanite-ferropericlase aggre-gate at 25 GPa and 2100 K has been achieved to large strains(Girard et al 2016) In such torsion experiments the strain variesgreatly as a function of sample radius The experiment documentedthat most of the plastic deformation is accommodated by theweaker ferropericlase

Currently the most accessible method to deform samples atultrahigh pressures (gt500 GPa) is with diamond anvil cells (DAC)where diamonds are used as pistons compressing a small sample(30ndash80 lm in diameter and 50 lm thick) (eg Merkel et al2002 Fig 17) The diamonds are used not only to induce pressurebut also to cause compressive deformation (Fig 17 b c) and theevolution of preferred orientation can be observed in situ if hori-zontal X-rays transmit the sample in radial diffraction geometry(r-DAC) Strong textures have been observed in ferropericlase(eg Merkel et al 2002 Lin et al 2009) perovskitebridgmanite(eg Merkel et al 2003 Wenk et al 2006 Miyagi and Wenk2016 Tsujino et al 2016) and pPv the phase likely to be presentat the core-mantle boundary (eg Merkel et al 2006 2007

Fig 14 2D Sketches of polycrystal plasticity models Gray shades express orien-tation (Left) For the full constraints Taylor model all grains undergo the samedeformation regardless of orientation (Center) The viscoplastic model VPSC treatsgrains as inclusions in an anisotropic viscous medium (Right) In finite elementmodels grains deform differently depending on the orientation of neighbors

Fig 15 Definition of crystal orientation relative to sample coordinates with threerotations (Euler angles) 1 U 2 Projection based on sample coordinate system xy z (pole figure) Crystal coordinate system is defined by axes [100] [010] and[001]

Fig 16 Comparison of (a) 111 pole figure relative to sample coordinates and (b) Ninverse pole figure relative to crystal coordinates for rolled copper Equal areaprojection red colors are high and blue colors are low pole densities N normaldirection R rolling direction and T transverse direction Note the equivalentinformation In the 111 pole figure a maximum in the N direction and in the NDinverse pole figure a maximum in 111

70 B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90

Miyagi et al 2010 2011 Wu et al 2017) Shear deformation canbe induced in rotational DACs (eg Levitas et al 2006) Thismethod has been mainly used to induce phase transformationsand has not yet been applied to study texture evolution at highpressure

In addition to pressure and stress temperature can be inducedin DAC experiments by resistive (eg Liermann et al 2009) andlaser heating (eg Prakapenka et al 2008 Dubrovinsky et al2009) or a combination of the two (Miyagi et al 2013) Tatenoet al (2015) reached temperatures of 6000 K at gt400 GPa on exper-iments on Fe and Fe-Si corresponding to conditions of the Earthrsquos

inner core Obviously there are limitations to DAC experimentssamples are extremely small strain is always compressive andstrain rates are difficult to control

It was surprising to see that silicates and oxides that are brittleat ambient conditions including olivine become ductile at pres-sures of 10GPa even at room temperature and deform by dislo-cation glide (eg Wenk et al 2004) The diffraction image ofMgSiO3 post-perovskite at 150 GPa (Fig 18a) is lsquolsquounrolledrdquo andthe compression direction is indicated by arrows (large 2h smalld Q=1d) (Fig 18b) The elastic lattice distortion (wave-like patternwith azimuth) is related to applied stress and elastic propertiesThe intensity variations with azimuth are indicative of preferredorientation For example there is a strong maximum for 004(fourth order diffraction on the lattice plane 001) in the compres-sion direction This image illustrates why radial diffraction geome-try has to be used to display CPO as function of angle to thecompression direction In axial geometry (X-rays parallel to thediamond axis) Debye-rings have uniform intensity since alldiffracting lattice planes have the same angle to the compressiondirection

A qualitative interpretation of a diffraction image is illustratedin Fig 19 for an experiment with MgGeO3 post-perovskite(Miyagi et al 2011) and used to construct an inverse pole figureof the compression direction (arrow) MgGeO3 is an analog ofMgSiO3 but transforms to pPv at lower pressure There is a maxi-mum for 002 and a minimum for 020 in the compression directionwhich can be plotted in the inverse pole figure (Fig 19 right side)The quantitative deconvolution of diffraction images is not trivialand most often an iterative Rietveld method is applied (egLutterotti et al 2014 Wenk et al 2014) The high pressure syn-chrotron X-ray diffraction deformation images provide quantita-tive information about phases crystal structures density stresselastic properties and preferred orientation

Fig 20a-c shows experimental inverse pole figures of MgSiO3

pPv documenting increasing texture development with pressure-stressndashstrain with a maximum at (001) From the orientation pat-tern active slip systems can be derived by comparing experimentalinverse pole figures with results from polycrystal plasticity calcu-lations that assume certain combinations of slip systems(Fig 20d) Based on the good agreement it can be concluded thatpPv deformed in the experiment by dominant (001)[100] slip(Miyagi et al 2010)

With similar experiments it was suggested that MgSiO3 bridg-manite deforms dominantly by slip on (001) planes in [100][010] and h1 1 0i directions (eg Miyagi and Wenk 2016) but sim-

Fig 18 (a) Diffraction image of MgSiO3 post-perovskite at 150 GPa (b) Unrolled diffractiochanges in Q are due to elastic distortion of the crystal lattice under compression Botquantitative information such as inverse pole figures

Fig 17 Diamond anvil cell for radial diffraction experiments The X-ray beam ishorizontal (a) illustrates the cell and the insert is an enlargement with diamondsand gasket to contain the sample (b c) illustrate that diamonds not only applypressure but also compressive stress that deforms the sample and produces CPO

B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90 71

ple shear experiments in a D-DIA apparatus indicate (100)[001]slip (Tsujino et al 2016) Ferropericlase likely deforms by 110h110i slip (eg Stretton et al 2001 Merkel et al 2002 Linet al 2009) at high pressure conditions For Ca-perovskite domi-nant 110h110i slip was proposed (Miyagi et al 2006 2009)

So far most DAC high-pressure deformation experimentsextracted COD information from intensity variations along Debyerings (eg Fig 18) A new method called multigrain is still underdevelopment It obtains orientation information from individualgrain diffractions (eg Barton and Bernier 2012 Rosa et al2015 Langrand et al 2017) and is especially applicable to coarseraggregates Nisr et al (2012) used information about dislocationsfrom distortion of single crystal diffraction patterns of the post-perovskite analog MgGeO3 and suggested dominant slip on 110and (001) planes

It should be mentioned that information from such high pres-sure experiments is by no means unambiguous Obviously defor-mation conditions in experiments and simulations differconsiderably from those in the deep Earth just to mention temper-ature grain size strain rate interaction of dislocations and interac-tion between grains Furthermore not all CPO patterns that areobserved are due to deformation but could be inherited from orien-tation patterns of precursor phases such as for pPv from perovskite(Dobson et al 2013) or enstatite (Merkel et al 2006 2007 Miyagiet al 2011) Also slip systems may not be the same for pPv phasesof different compositions such as MgGeO3 CaIrO3 NaMgF3 orMn2O3

A different approach has become very important computationof Peierlrsquos stresses and lattice friction for dislocation systems basedon bonding characteristics It was originally developed for metals(eg Kubin et al 1992 Devincre and Kubin 1997) and has morerecently been applied to minerals in the mantle where it allowsto predict slip system activities for a wide range of temperaturendashpressurendashstrain rate conditions (eg Carrez et al 2007Mainprice et al 2008 Cordier et al 2012) Amodeo et al (20122014 2016) propose a switch from 110h010i slip to 100h0 1 1i slip in periclase with pressure Kraych et al (2016) suggest(010)[100] slip in bridgmanite at high pressure According tothese calculations the strength of bridgmanite increases greatlywith pressure and at 60 GPa bridgmanite appears 20 times stron-ger than periclase The critical resolved shear stress decreasesabout 20 from strain rates of 105 s1 (which corresponds to

n image as function of Q (Q = 1d) Intensity variations with azimuth illustrate CPOtom experimental data above fit of the data with the Rietveld method to extract

Fig 19 Explanation of the relationship between DAC diffraction image and inverse pole figure Left Unrolled diffraction image of MgGeO3 post-perovskite Some diffractionlines are labeled The sinusoidal variations are due to imposed stress High stress (high Q low d) is indicated by arrows On the right side is a conceptual construction of theinverse pole figure of the compression axis based on relative diffraction intensities (Miyagi et al 2011)

Fig 20 Inverse pole figures for MgSiO3 post-perovskite (AndashC) experiments (D) Plasticity model with dominant (001) slip equal area projection (Miyagi et al 2010)

72 B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90

experimental values) to 1014 s1 corresponding to likely values atdeep mantle conditions (Fig 21a) The opposite is the case for pPvwhich appears much weaker than periclase at high pressure hightemperature and slow strain rates (Fig 21b Goryaeva et al 20152016) Also the predicted weakest calculated slip system for post-perovskite at deep mantle conditions is (010)[100] correspondingto the layered crystal structure (Fig 21c) but different from thatobserved in DAC experiments (Miyagi et al 2010 Wu et al 2017)

It should be mentioned that a single slip system is not sufficientto deform a polycrystal In the case of the Taylor model at least 5systems have to be active to produce an arbitrary strain (Mises1928) This is relaxed for the self-consistent model but also hereseveral slip systems are active The choice of activity depends onthe crystal orientation relative to the applied stress (Schmid fac-tor) TEM investigations confirm this though some slip systemsusually dominate and the literature refers to the lsquolsquodominantrdquo slipsystem Some dominant slip systems for deep Earth minerals aresummarized in Table 2

34 Elastic properties

Elastic properties of crystals at conditions pertaining to thelower mantle are critical to link microstructural properties of therock with seismic observations The most straightforward experi-mental method that has been applied to many lower mantle min-erals is Brillouin scattering (see review by Speziale et al 2014) andenergy-dispersive X-ray diffraction (eg for calcium silicate per-ovskite Shieh et al 2004) A different approach is with first prin-ciples calculations at high pressure and temperature (for someapplications to bridgmanite CaSiO3 perovskite and pPv see egZhang et al 2013 Wentzcovitch et al 2005 Kawai and

Tsuchiya 2015) First principles results look fairly consistent forminerals at lower mantle conditions but as we will see in Sec-tion 62 predictions for iron at inner core conditions are stillambiguous Furthermore the actual composition of the mineralsparticularly the iron content can be significant (eg Koci et al2007) Values of stiffness coefficients and P-wave anisotropy (An = 200(Pmax Pmin)(Pmax + Pmin) for some low mantle mineralsat lowermost mantle conditions are listed in Table 3 Fig 22 givescorresponding S velocities of single crystals with black lines corre-sponding to the orientation of the fast S-wave polarization As canbe seen in Table 1 periclase and pPv have the highest P-wave ani-sotropy and Ca-perovskite is least anisotropic The S-wave aniso-tropy is considerably higher for pPv and periclase than forbridgmanite and particularly CaSiO3 perovskite

To obtain elastic properties of aggregates one has to averageover all orientations and corresponding elastic tensors takingphase fractions into account Simple averages are upper bound(Voigt 1887) and lower bound (Reuss 1929) Generally an inter-mediate arithmetic mean (Hill 1952) or a geometric mean(Matthies and Humbert 1995) are preferred All these models donot take grain shape into account which is not very significantfor crystalline phases but becomes important for systems withplaty minerals such as graphite or sheet-silicate containing rocksand aggregates with flat oriented pores For such cases a self-consistent (Matthies 2012 Vasin et al 2013) or differential effec-tive medium approach (eg Hornby et al 1994) should be consid-ered It is probably not important for the lower mantle

Note that S-waves passing through anisotropic media have arbi-trary polarization directions in the plane perpendicular to thedirection of propagation as is best displayed for the fast directionof single crystals in Fig 22 but applies also to aggregations of ori-

Fig 21 Critical resolved shear stress CRSS for dislocation glide activities as functionof temperature of (a) bridgmanite at 60 GPa (from Kraych et al 2016) and MgO(from Amodeo et al 2016) at strain rates 105 s1 and 1014 s1 (b) post-perovskiteat 120 GPa at strain rate 1016 s1 (from Goryaeva et al 2016) compared with MgO(from Amodeo et al 2012) Courtesy of P Cordier

B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90 73

ented crystals Seismologists generally consider the projection ofthat polarization direction onto horizontal and vertical axes Thisis convenient because differences in arrival times and waveformsin this representation can be expressed in terms of apparent verti-cal transverse isotropy (VTI) which because of limited azimuthalsampling is often the only anisotropic constraint that can beobtained

4 Linking seismology and mineral physics through predictionsof anisotropy in geodynamic models

41 Isotropic geodynamic models for upper mantle convection

Ever since the concept of plate tectonics became accepted in the1960s convective movements in the Earthrsquos mantle have been pro-posed such as upwelling along oceanic ridges (eg Hess 1964Cann 1968 Fig 1b) The first quantitative models based on hydro-dynamics emerged in the eighties (eg Hager and OrsquoConnell 1981)

Table 2Proposed dominant slip systems in deep Earth minerals

Ferropericlase Lower P 110110High PT also 100011

Bridgmanite Low P (001)[100] [010] 110High P (100)[001](010)[100]

pPv (001)[100](010)[100]

Ca-perovskite 110110e-iron (0001)1120 subordinate 1010

Geodynamic models have been mainly applied to the upper mantleand we will not discuss them here in detail (see eg review by Longand Becker 2010)

Many convection models have been developed to understandthe evolution of the deep Earth Calculations generally assume aviscous fluid and use non-dimensional equations for the conserva-tion of mass momentum and energy applying the Boussineqapproximation Critical parameters are Rayleigh number viscosityboundary temperatures In order to evaluate the strain evolutionduring the convection process tracers are introduced that recordthe velocity gradient tensor at each time step along the path ofthe tracer If the deformation mechanisms are known (eg disloca-tion glide) polycrystal plasticity calculations can be used to calcu-late the evolution of crystal preferred orientation based on thestrain recorded by tracers

Most geodynamic models assume a viscous isotropic mediumwith a smoothly varying viscosity structure and the microstruc-tural processes leading to preferred orientation are introducedpost-mortem Considering an anisotropic medium that constantlychanges its properties greatly increases the complexity of geody-namic calculations However there are models in metallurgy suchas extrusion of an aggregate that illustrate the importance of ananisotropic material behavior (eg Beyerlein et al 2003)

42 Review of upper mantle anisotropic models

We will start the discussion of anisotropic convection byreturning to a simple 2D model (Dawson and Wenk 2000) thatwas originally issued as an educational video by AGU (1999) andcan now be downloaded in digital form (httpepsberkeleyedu~wenkTexturePageMantle-Videohtm) At high Rayleigh number(low viscosity) heat transfer occurs by convection rather than con-duction corresponding to conditions in the Earthrsquos mantle Convec-tion is driven by temperature gradients As aggregates move alongstreamlines the orientation of grains is constantly updated and thelocal texture affects the next deformation step which introducesconsiderable heterogeneities It was surprising to find locallyheterogeneous CPO patterns in the 2D convection cell representingthe upper mantle shown as [100] pole figures of olivine after100 my (Fig 23) Some regions have strong and others very weakpatterns that can be attributed to heterogeneous deformation dueto CPO development and result in lsquolsquoanisotropicrdquo viscosity

Some complexities of different plasticity models for a simplecase of upwelling have been investigated by Blackman et al(1996 2002) and Castelnau et al (2009) If a lower bound behavioris assumed (Sachs 1928) there is very strong CPO developmentFor self-consistent models (Lebensohn and Tomeacute 1993) rotationsare reduced If dislocation glide is combined with dynamic recrys-tallization both grain growth and grain growth combined withnucleation resulting orientation patterns can be very differentRecrystallization is likely in the deep Earth with high temperatureand large strains where grain boundary migration is likely tooccur We will return to the issue of recrystallization in Section 48

Merkel et al (2002) and Lin et al (2009)Amodeo et al (2016)Miyagi and Wenk 2016Tsujino et al (2016)Kraych et al (2016)Miyagi et al (2010) and Wu et al (2017)Goryaeva et al (2016)Miyagi et al (2009) and Ferreacute et al (2009)

Merkel et al (2004) and Miyagi et al (2008)

Fig 12 Under stress imposed by pistons a crystal deforms to a new shape by slip of dislocations on a glide plane Since pistons remain in contact with the crystal surfacethere is an effective rotation b In a polycrystal neighboring grains act as effective pistons to transmit the stress

Fig 13 Stress-temperature deformation mechanism map (Langdon and Mohamed1978)

B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90 69

ing R transverse T and normal N sample directions indicatedFig 16b is the corresponding inverse pole figure of the normaldirection Inverse pole figures display the crystal symmetry Bothrepresentations will be used in the following discussion

33 Deformation experiments and rheology

The experiments on plasticity of metals were not applicable tomost minerals because even at elevated temperatures theirdeformation behavior at ambient pressure is generally brittleOne had to wait until high pressure deformation experiments weredeveloped by Griggs (1936) and applied on a wide scale includingolivine (eg Raleigh 1968) Since then sophisticated deformationapparati have been constructed in many laboratories making itpossible to deform rocks at a wide range of pressures and temper-atures They were applied to many minerals and rocks in the crustand upper mantle Studies on olivine (eg Jung and Karato 2001

Hansen et al 2012 Jackson and Faul 2010) documented the com-plex influence of temperature pressure composition (such aswater and iron content) The most sophisticated apparatus wasdeveloped at the Australian National University (Paterson andOlgaard 2000) It allows for deformation experiments on relativelylarge samples (1 cm) in compression tension and torsion Pres-sures are limited to 03 GPa and the limitation in pressure pre-vents these instruments to be used for experiments relevant tothe lower mantle (20ndash150 GPa) and inner core (320ndash360 GPa)

Higher pressure deformation experiments have been reviewedby Weidner and Li (2015) The multi-anvil apparatus called DIAwith three pairs of octahedral pistons (Onodera 1987) has beenmodified to apply stress by preferentially advancing one pistonpair (D-DIA for deformation DIA) The sample can be heated inter-nally Changes in phase structure preferred orientation andmicrostructure can be recorded in situ if the D-DIA apparatus iscombined with a monochromatic synchrotron X-ray beam fordiffraction and imaging (eg Wang et al 2003 2011) The conven-tional D-DIA apparatus has been used to 20 GPa and samples arecylinders 1 mm in diameter (eg Kawazoe et al 2010) A moreadvanced D-DIA (Kawai-type) reaching gt110 GPa with sintereddiamond anvils and smaller samples has been introduced atSPring8 in Japan (Yamazaki et al 2014)

Shear deformation at high pressure can be performed with arotational Drickamer apparatus (RDA) (eg Yamasaki and Karato2001) Shear deformation of a bridgmanite-ferropericlase aggre-gate at 25 GPa and 2100 K has been achieved to large strains(Girard et al 2016) In such torsion experiments the strain variesgreatly as a function of sample radius The experiment documentedthat most of the plastic deformation is accommodated by theweaker ferropericlase

Currently the most accessible method to deform samples atultrahigh pressures (gt500 GPa) is with diamond anvil cells (DAC)where diamonds are used as pistons compressing a small sample(30ndash80 lm in diameter and 50 lm thick) (eg Merkel et al2002 Fig 17) The diamonds are used not only to induce pressurebut also to cause compressive deformation (Fig 17 b c) and theevolution of preferred orientation can be observed in situ if hori-zontal X-rays transmit the sample in radial diffraction geometry(r-DAC) Strong textures have been observed in ferropericlase(eg Merkel et al 2002 Lin et al 2009) perovskitebridgmanite(eg Merkel et al 2003 Wenk et al 2006 Miyagi and Wenk2016 Tsujino et al 2016) and pPv the phase likely to be presentat the core-mantle boundary (eg Merkel et al 2006 2007

Fig 14 2D Sketches of polycrystal plasticity models Gray shades express orien-tation (Left) For the full constraints Taylor model all grains undergo the samedeformation regardless of orientation (Center) The viscoplastic model VPSC treatsgrains as inclusions in an anisotropic viscous medium (Right) In finite elementmodels grains deform differently depending on the orientation of neighbors

Fig 15 Definition of crystal orientation relative to sample coordinates with threerotations (Euler angles) 1 U 2 Projection based on sample coordinate system xy z (pole figure) Crystal coordinate system is defined by axes [100] [010] and[001]

Fig 16 Comparison of (a) 111 pole figure relative to sample coordinates and (b) Ninverse pole figure relative to crystal coordinates for rolled copper Equal areaprojection red colors are high and blue colors are low pole densities N normaldirection R rolling direction and T transverse direction Note the equivalentinformation In the 111 pole figure a maximum in the N direction and in the NDinverse pole figure a maximum in 111

70 B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90

Miyagi et al 2010 2011 Wu et al 2017) Shear deformation canbe induced in rotational DACs (eg Levitas et al 2006) Thismethod has been mainly used to induce phase transformationsand has not yet been applied to study texture evolution at highpressure

In addition to pressure and stress temperature can be inducedin DAC experiments by resistive (eg Liermann et al 2009) andlaser heating (eg Prakapenka et al 2008 Dubrovinsky et al2009) or a combination of the two (Miyagi et al 2013) Tatenoet al (2015) reached temperatures of 6000 K at gt400 GPa on exper-iments on Fe and Fe-Si corresponding to conditions of the Earthrsquos

inner core Obviously there are limitations to DAC experimentssamples are extremely small strain is always compressive andstrain rates are difficult to control

It was surprising to see that silicates and oxides that are brittleat ambient conditions including olivine become ductile at pres-sures of 10GPa even at room temperature and deform by dislo-cation glide (eg Wenk et al 2004) The diffraction image ofMgSiO3 post-perovskite at 150 GPa (Fig 18a) is lsquolsquounrolledrdquo andthe compression direction is indicated by arrows (large 2h smalld Q=1d) (Fig 18b) The elastic lattice distortion (wave-like patternwith azimuth) is related to applied stress and elastic propertiesThe intensity variations with azimuth are indicative of preferredorientation For example there is a strong maximum for 004(fourth order diffraction on the lattice plane 001) in the compres-sion direction This image illustrates why radial diffraction geome-try has to be used to display CPO as function of angle to thecompression direction In axial geometry (X-rays parallel to thediamond axis) Debye-rings have uniform intensity since alldiffracting lattice planes have the same angle to the compressiondirection

A qualitative interpretation of a diffraction image is illustratedin Fig 19 for an experiment with MgGeO3 post-perovskite(Miyagi et al 2011) and used to construct an inverse pole figureof the compression direction (arrow) MgGeO3 is an analog ofMgSiO3 but transforms to pPv at lower pressure There is a maxi-mum for 002 and a minimum for 020 in the compression directionwhich can be plotted in the inverse pole figure (Fig 19 right side)The quantitative deconvolution of diffraction images is not trivialand most often an iterative Rietveld method is applied (egLutterotti et al 2014 Wenk et al 2014) The high pressure syn-chrotron X-ray diffraction deformation images provide quantita-tive information about phases crystal structures density stresselastic properties and preferred orientation

Fig 20a-c shows experimental inverse pole figures of MgSiO3

pPv documenting increasing texture development with pressure-stressndashstrain with a maximum at (001) From the orientation pat-tern active slip systems can be derived by comparing experimentalinverse pole figures with results from polycrystal plasticity calcu-lations that assume certain combinations of slip systems(Fig 20d) Based on the good agreement it can be concluded thatpPv deformed in the experiment by dominant (001)[100] slip(Miyagi et al 2010)

With similar experiments it was suggested that MgSiO3 bridg-manite deforms dominantly by slip on (001) planes in [100][010] and h1 1 0i directions (eg Miyagi and Wenk 2016) but sim-

Fig 18 (a) Diffraction image of MgSiO3 post-perovskite at 150 GPa (b) Unrolled diffractiochanges in Q are due to elastic distortion of the crystal lattice under compression Botquantitative information such as inverse pole figures

Fig 17 Diamond anvil cell for radial diffraction experiments The X-ray beam ishorizontal (a) illustrates the cell and the insert is an enlargement with diamondsand gasket to contain the sample (b c) illustrate that diamonds not only applypressure but also compressive stress that deforms the sample and produces CPO

B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90 71

ple shear experiments in a D-DIA apparatus indicate (100)[001]slip (Tsujino et al 2016) Ferropericlase likely deforms by 110h110i slip (eg Stretton et al 2001 Merkel et al 2002 Linet al 2009) at high pressure conditions For Ca-perovskite domi-nant 110h110i slip was proposed (Miyagi et al 2006 2009)

So far most DAC high-pressure deformation experimentsextracted COD information from intensity variations along Debyerings (eg Fig 18) A new method called multigrain is still underdevelopment It obtains orientation information from individualgrain diffractions (eg Barton and Bernier 2012 Rosa et al2015 Langrand et al 2017) and is especially applicable to coarseraggregates Nisr et al (2012) used information about dislocationsfrom distortion of single crystal diffraction patterns of the post-perovskite analog MgGeO3 and suggested dominant slip on 110and (001) planes

It should be mentioned that information from such high pres-sure experiments is by no means unambiguous Obviously defor-mation conditions in experiments and simulations differconsiderably from those in the deep Earth just to mention temper-ature grain size strain rate interaction of dislocations and interac-tion between grains Furthermore not all CPO patterns that areobserved are due to deformation but could be inherited from orien-tation patterns of precursor phases such as for pPv from perovskite(Dobson et al 2013) or enstatite (Merkel et al 2006 2007 Miyagiet al 2011) Also slip systems may not be the same for pPv phasesof different compositions such as MgGeO3 CaIrO3 NaMgF3 orMn2O3

A different approach has become very important computationof Peierlrsquos stresses and lattice friction for dislocation systems basedon bonding characteristics It was originally developed for metals(eg Kubin et al 1992 Devincre and Kubin 1997) and has morerecently been applied to minerals in the mantle where it allowsto predict slip system activities for a wide range of temperaturendashpressurendashstrain rate conditions (eg Carrez et al 2007Mainprice et al 2008 Cordier et al 2012) Amodeo et al (20122014 2016) propose a switch from 110h010i slip to 100h0 1 1i slip in periclase with pressure Kraych et al (2016) suggest(010)[100] slip in bridgmanite at high pressure According tothese calculations the strength of bridgmanite increases greatlywith pressure and at 60 GPa bridgmanite appears 20 times stron-ger than periclase The critical resolved shear stress decreasesabout 20 from strain rates of 105 s1 (which corresponds to

n image as function of Q (Q = 1d) Intensity variations with azimuth illustrate CPOtom experimental data above fit of the data with the Rietveld method to extract

Fig 19 Explanation of the relationship between DAC diffraction image and inverse pole figure Left Unrolled diffraction image of MgGeO3 post-perovskite Some diffractionlines are labeled The sinusoidal variations are due to imposed stress High stress (high Q low d) is indicated by arrows On the right side is a conceptual construction of theinverse pole figure of the compression axis based on relative diffraction intensities (Miyagi et al 2011)

Fig 20 Inverse pole figures for MgSiO3 post-perovskite (AndashC) experiments (D) Plasticity model with dominant (001) slip equal area projection (Miyagi et al 2010)

72 B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90

experimental values) to 1014 s1 corresponding to likely values atdeep mantle conditions (Fig 21a) The opposite is the case for pPvwhich appears much weaker than periclase at high pressure hightemperature and slow strain rates (Fig 21b Goryaeva et al 20152016) Also the predicted weakest calculated slip system for post-perovskite at deep mantle conditions is (010)[100] correspondingto the layered crystal structure (Fig 21c) but different from thatobserved in DAC experiments (Miyagi et al 2010 Wu et al 2017)

It should be mentioned that a single slip system is not sufficientto deform a polycrystal In the case of the Taylor model at least 5systems have to be active to produce an arbitrary strain (Mises1928) This is relaxed for the self-consistent model but also hereseveral slip systems are active The choice of activity depends onthe crystal orientation relative to the applied stress (Schmid fac-tor) TEM investigations confirm this though some slip systemsusually dominate and the literature refers to the lsquolsquodominantrdquo slipsystem Some dominant slip systems for deep Earth minerals aresummarized in Table 2

34 Elastic properties

Elastic properties of crystals at conditions pertaining to thelower mantle are critical to link microstructural properties of therock with seismic observations The most straightforward experi-mental method that has been applied to many lower mantle min-erals is Brillouin scattering (see review by Speziale et al 2014) andenergy-dispersive X-ray diffraction (eg for calcium silicate per-ovskite Shieh et al 2004) A different approach is with first prin-ciples calculations at high pressure and temperature (for someapplications to bridgmanite CaSiO3 perovskite and pPv see egZhang et al 2013 Wentzcovitch et al 2005 Kawai and

Tsuchiya 2015) First principles results look fairly consistent forminerals at lower mantle conditions but as we will see in Sec-tion 62 predictions for iron at inner core conditions are stillambiguous Furthermore the actual composition of the mineralsparticularly the iron content can be significant (eg Koci et al2007) Values of stiffness coefficients and P-wave anisotropy (An = 200(Pmax Pmin)(Pmax + Pmin) for some low mantle mineralsat lowermost mantle conditions are listed in Table 3 Fig 22 givescorresponding S velocities of single crystals with black lines corre-sponding to the orientation of the fast S-wave polarization As canbe seen in Table 1 periclase and pPv have the highest P-wave ani-sotropy and Ca-perovskite is least anisotropic The S-wave aniso-tropy is considerably higher for pPv and periclase than forbridgmanite and particularly CaSiO3 perovskite

To obtain elastic properties of aggregates one has to averageover all orientations and corresponding elastic tensors takingphase fractions into account Simple averages are upper bound(Voigt 1887) and lower bound (Reuss 1929) Generally an inter-mediate arithmetic mean (Hill 1952) or a geometric mean(Matthies and Humbert 1995) are preferred All these models donot take grain shape into account which is not very significantfor crystalline phases but becomes important for systems withplaty minerals such as graphite or sheet-silicate containing rocksand aggregates with flat oriented pores For such cases a self-consistent (Matthies 2012 Vasin et al 2013) or differential effec-tive medium approach (eg Hornby et al 1994) should be consid-ered It is probably not important for the lower mantle

Note that S-waves passing through anisotropic media have arbi-trary polarization directions in the plane perpendicular to thedirection of propagation as is best displayed for the fast directionof single crystals in Fig 22 but applies also to aggregations of ori-

Fig 21 Critical resolved shear stress CRSS for dislocation glide activities as functionof temperature of (a) bridgmanite at 60 GPa (from Kraych et al 2016) and MgO(from Amodeo et al 2016) at strain rates 105 s1 and 1014 s1 (b) post-perovskiteat 120 GPa at strain rate 1016 s1 (from Goryaeva et al 2016) compared with MgO(from Amodeo et al 2012) Courtesy of P Cordier

B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90 73

ented crystals Seismologists generally consider the projection ofthat polarization direction onto horizontal and vertical axes Thisis convenient because differences in arrival times and waveformsin this representation can be expressed in terms of apparent verti-cal transverse isotropy (VTI) which because of limited azimuthalsampling is often the only anisotropic constraint that can beobtained

4 Linking seismology and mineral physics through predictionsof anisotropy in geodynamic models

41 Isotropic geodynamic models for upper mantle convection

Ever since the concept of plate tectonics became accepted in the1960s convective movements in the Earthrsquos mantle have been pro-posed such as upwelling along oceanic ridges (eg Hess 1964Cann 1968 Fig 1b) The first quantitative models based on hydro-dynamics emerged in the eighties (eg Hager and OrsquoConnell 1981)

Table 2Proposed dominant slip systems in deep Earth minerals

Ferropericlase Lower P 110110High PT also 100011

Bridgmanite Low P (001)[100] [010] 110High P (100)[001](010)[100]

pPv (001)[100](010)[100]

Ca-perovskite 110110e-iron (0001)1120 subordinate 1010

Geodynamic models have been mainly applied to the upper mantleand we will not discuss them here in detail (see eg review by Longand Becker 2010)

Many convection models have been developed to understandthe evolution of the deep Earth Calculations generally assume aviscous fluid and use non-dimensional equations for the conserva-tion of mass momentum and energy applying the Boussineqapproximation Critical parameters are Rayleigh number viscosityboundary temperatures In order to evaluate the strain evolutionduring the convection process tracers are introduced that recordthe velocity gradient tensor at each time step along the path ofthe tracer If the deformation mechanisms are known (eg disloca-tion glide) polycrystal plasticity calculations can be used to calcu-late the evolution of crystal preferred orientation based on thestrain recorded by tracers

Most geodynamic models assume a viscous isotropic mediumwith a smoothly varying viscosity structure and the microstruc-tural processes leading to preferred orientation are introducedpost-mortem Considering an anisotropic medium that constantlychanges its properties greatly increases the complexity of geody-namic calculations However there are models in metallurgy suchas extrusion of an aggregate that illustrate the importance of ananisotropic material behavior (eg Beyerlein et al 2003)

42 Review of upper mantle anisotropic models

We will start the discussion of anisotropic convection byreturning to a simple 2D model (Dawson and Wenk 2000) thatwas originally issued as an educational video by AGU (1999) andcan now be downloaded in digital form (httpepsberkeleyedu~wenkTexturePageMantle-Videohtm) At high Rayleigh number(low viscosity) heat transfer occurs by convection rather than con-duction corresponding to conditions in the Earthrsquos mantle Convec-tion is driven by temperature gradients As aggregates move alongstreamlines the orientation of grains is constantly updated and thelocal texture affects the next deformation step which introducesconsiderable heterogeneities It was surprising to find locallyheterogeneous CPO patterns in the 2D convection cell representingthe upper mantle shown as [100] pole figures of olivine after100 my (Fig 23) Some regions have strong and others very weakpatterns that can be attributed to heterogeneous deformation dueto CPO development and result in lsquolsquoanisotropicrdquo viscosity

Some complexities of different plasticity models for a simplecase of upwelling have been investigated by Blackman et al(1996 2002) and Castelnau et al (2009) If a lower bound behavioris assumed (Sachs 1928) there is very strong CPO developmentFor self-consistent models (Lebensohn and Tomeacute 1993) rotationsare reduced If dislocation glide is combined with dynamic recrys-tallization both grain growth and grain growth combined withnucleation resulting orientation patterns can be very differentRecrystallization is likely in the deep Earth with high temperatureand large strains where grain boundary migration is likely tooccur We will return to the issue of recrystallization in Section 48

Merkel et al (2002) and Lin et al (2009)Amodeo et al (2016)Miyagi and Wenk 2016Tsujino et al (2016)Kraych et al (2016)Miyagi et al (2010) and Wu et al (2017)Goryaeva et al (2016)Miyagi et al (2009) and Ferreacute et al (2009)

Merkel et al (2004) and Miyagi et al (2008)

Fig 14 2D Sketches of polycrystal plasticity models Gray shades express orien-tation (Left) For the full constraints Taylor model all grains undergo the samedeformation regardless of orientation (Center) The viscoplastic model VPSC treatsgrains as inclusions in an anisotropic viscous medium (Right) In finite elementmodels grains deform differently depending on the orientation of neighbors

Fig 15 Definition of crystal orientation relative to sample coordinates with threerotations (Euler angles) 1 U 2 Projection based on sample coordinate system xy z (pole figure) Crystal coordinate system is defined by axes [100] [010] and[001]

Fig 16 Comparison of (a) 111 pole figure relative to sample coordinates and (b) Ninverse pole figure relative to crystal coordinates for rolled copper Equal areaprojection red colors are high and blue colors are low pole densities N normaldirection R rolling direction and T transverse direction Note the equivalentinformation In the 111 pole figure a maximum in the N direction and in the NDinverse pole figure a maximum in 111

70 B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90

Miyagi et al 2010 2011 Wu et al 2017) Shear deformation canbe induced in rotational DACs (eg Levitas et al 2006) Thismethod has been mainly used to induce phase transformationsand has not yet been applied to study texture evolution at highpressure

In addition to pressure and stress temperature can be inducedin DAC experiments by resistive (eg Liermann et al 2009) andlaser heating (eg Prakapenka et al 2008 Dubrovinsky et al2009) or a combination of the two (Miyagi et al 2013) Tatenoet al (2015) reached temperatures of 6000 K at gt400 GPa on exper-iments on Fe and Fe-Si corresponding to conditions of the Earthrsquos

inner core Obviously there are limitations to DAC experimentssamples are extremely small strain is always compressive andstrain rates are difficult to control

It was surprising to see that silicates and oxides that are brittleat ambient conditions including olivine become ductile at pres-sures of 10GPa even at room temperature and deform by dislo-cation glide (eg Wenk et al 2004) The diffraction image ofMgSiO3 post-perovskite at 150 GPa (Fig 18a) is lsquolsquounrolledrdquo andthe compression direction is indicated by arrows (large 2h smalld Q=1d) (Fig 18b) The elastic lattice distortion (wave-like patternwith azimuth) is related to applied stress and elastic propertiesThe intensity variations with azimuth are indicative of preferredorientation For example there is a strong maximum for 004(fourth order diffraction on the lattice plane 001) in the compres-sion direction This image illustrates why radial diffraction geome-try has to be used to display CPO as function of angle to thecompression direction In axial geometry (X-rays parallel to thediamond axis) Debye-rings have uniform intensity since alldiffracting lattice planes have the same angle to the compressiondirection

A qualitative interpretation of a diffraction image is illustratedin Fig 19 for an experiment with MgGeO3 post-perovskite(Miyagi et al 2011) and used to construct an inverse pole figureof the compression direction (arrow) MgGeO3 is an analog ofMgSiO3 but transforms to pPv at lower pressure There is a maxi-mum for 002 and a minimum for 020 in the compression directionwhich can be plotted in the inverse pole figure (Fig 19 right side)The quantitative deconvolution of diffraction images is not trivialand most often an iterative Rietveld method is applied (egLutterotti et al 2014 Wenk et al 2014) The high pressure syn-chrotron X-ray diffraction deformation images provide quantita-tive information about phases crystal structures density stresselastic properties and preferred orientation

Fig 20a-c shows experimental inverse pole figures of MgSiO3

pPv documenting increasing texture development with pressure-stressndashstrain with a maximum at (001) From the orientation pat-tern active slip systems can be derived by comparing experimentalinverse pole figures with results from polycrystal plasticity calcu-lations that assume certain combinations of slip systems(Fig 20d) Based on the good agreement it can be concluded thatpPv deformed in the experiment by dominant (001)[100] slip(Miyagi et al 2010)

With similar experiments it was suggested that MgSiO3 bridg-manite deforms dominantly by slip on (001) planes in [100][010] and h1 1 0i directions (eg Miyagi and Wenk 2016) but sim-

Fig 18 (a) Diffraction image of MgSiO3 post-perovskite at 150 GPa (b) Unrolled diffractiochanges in Q are due to elastic distortion of the crystal lattice under compression Botquantitative information such as inverse pole figures

Fig 17 Diamond anvil cell for radial diffraction experiments The X-ray beam ishorizontal (a) illustrates the cell and the insert is an enlargement with diamondsand gasket to contain the sample (b c) illustrate that diamonds not only applypressure but also compressive stress that deforms the sample and produces CPO

B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90 71

ple shear experiments in a D-DIA apparatus indicate (100)[001]slip (Tsujino et al 2016) Ferropericlase likely deforms by 110h110i slip (eg Stretton et al 2001 Merkel et al 2002 Linet al 2009) at high pressure conditions For Ca-perovskite domi-nant 110h110i slip was proposed (Miyagi et al 2006 2009)

So far most DAC high-pressure deformation experimentsextracted COD information from intensity variations along Debyerings (eg Fig 18) A new method called multigrain is still underdevelopment It obtains orientation information from individualgrain diffractions (eg Barton and Bernier 2012 Rosa et al2015 Langrand et al 2017) and is especially applicable to coarseraggregates Nisr et al (2012) used information about dislocationsfrom distortion of single crystal diffraction patterns of the post-perovskite analog MgGeO3 and suggested dominant slip on 110and (001) planes

It should be mentioned that information from such high pres-sure experiments is by no means unambiguous Obviously defor-mation conditions in experiments and simulations differconsiderably from those in the deep Earth just to mention temper-ature grain size strain rate interaction of dislocations and interac-tion between grains Furthermore not all CPO patterns that areobserved are due to deformation but could be inherited from orien-tation patterns of precursor phases such as for pPv from perovskite(Dobson et al 2013) or enstatite (Merkel et al 2006 2007 Miyagiet al 2011) Also slip systems may not be the same for pPv phasesof different compositions such as MgGeO3 CaIrO3 NaMgF3 orMn2O3

A different approach has become very important computationof Peierlrsquos stresses and lattice friction for dislocation systems basedon bonding characteristics It was originally developed for metals(eg Kubin et al 1992 Devincre and Kubin 1997) and has morerecently been applied to minerals in the mantle where it allowsto predict slip system activities for a wide range of temperaturendashpressurendashstrain rate conditions (eg Carrez et al 2007Mainprice et al 2008 Cordier et al 2012) Amodeo et al (20122014 2016) propose a switch from 110h010i slip to 100h0 1 1i slip in periclase with pressure Kraych et al (2016) suggest(010)[100] slip in bridgmanite at high pressure According tothese calculations the strength of bridgmanite increases greatlywith pressure and at 60 GPa bridgmanite appears 20 times stron-ger than periclase The critical resolved shear stress decreasesabout 20 from strain rates of 105 s1 (which corresponds to

n image as function of Q (Q = 1d) Intensity variations with azimuth illustrate CPOtom experimental data above fit of the data with the Rietveld method to extract

Fig 19 Explanation of the relationship between DAC diffraction image and inverse pole figure Left Unrolled diffraction image of MgGeO3 post-perovskite Some diffractionlines are labeled The sinusoidal variations are due to imposed stress High stress (high Q low d) is indicated by arrows On the right side is a conceptual construction of theinverse pole figure of the compression axis based on relative diffraction intensities (Miyagi et al 2011)

Fig 20 Inverse pole figures for MgSiO3 post-perovskite (AndashC) experiments (D) Plasticity model with dominant (001) slip equal area projection (Miyagi et al 2010)

72 B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90

experimental values) to 1014 s1 corresponding to likely values atdeep mantle conditions (Fig 21a) The opposite is the case for pPvwhich appears much weaker than periclase at high pressure hightemperature and slow strain rates (Fig 21b Goryaeva et al 20152016) Also the predicted weakest calculated slip system for post-perovskite at deep mantle conditions is (010)[100] correspondingto the layered crystal structure (Fig 21c) but different from thatobserved in DAC experiments (Miyagi et al 2010 Wu et al 2017)

It should be mentioned that a single slip system is not sufficientto deform a polycrystal In the case of the Taylor model at least 5systems have to be active to produce an arbitrary strain (Mises1928) This is relaxed for the self-consistent model but also hereseveral slip systems are active The choice of activity depends onthe crystal orientation relative to the applied stress (Schmid fac-tor) TEM investigations confirm this though some slip systemsusually dominate and the literature refers to the lsquolsquodominantrdquo slipsystem Some dominant slip systems for deep Earth minerals aresummarized in Table 2

34 Elastic properties

Elastic properties of crystals at conditions pertaining to thelower mantle are critical to link microstructural properties of therock with seismic observations The most straightforward experi-mental method that has been applied to many lower mantle min-erals is Brillouin scattering (see review by Speziale et al 2014) andenergy-dispersive X-ray diffraction (eg for calcium silicate per-ovskite Shieh et al 2004) A different approach is with first prin-ciples calculations at high pressure and temperature (for someapplications to bridgmanite CaSiO3 perovskite and pPv see egZhang et al 2013 Wentzcovitch et al 2005 Kawai and

Tsuchiya 2015) First principles results look fairly consistent forminerals at lower mantle conditions but as we will see in Sec-tion 62 predictions for iron at inner core conditions are stillambiguous Furthermore the actual composition of the mineralsparticularly the iron content can be significant (eg Koci et al2007) Values of stiffness coefficients and P-wave anisotropy (An = 200(Pmax Pmin)(Pmax + Pmin) for some low mantle mineralsat lowermost mantle conditions are listed in Table 3 Fig 22 givescorresponding S velocities of single crystals with black lines corre-sponding to the orientation of the fast S-wave polarization As canbe seen in Table 1 periclase and pPv have the highest P-wave ani-sotropy and Ca-perovskite is least anisotropic The S-wave aniso-tropy is considerably higher for pPv and periclase than forbridgmanite and particularly CaSiO3 perovskite

To obtain elastic properties of aggregates one has to averageover all orientations and corresponding elastic tensors takingphase fractions into account Simple averages are upper bound(Voigt 1887) and lower bound (Reuss 1929) Generally an inter-mediate arithmetic mean (Hill 1952) or a geometric mean(Matthies and Humbert 1995) are preferred All these models donot take grain shape into account which is not very significantfor crystalline phases but becomes important for systems withplaty minerals such as graphite or sheet-silicate containing rocksand aggregates with flat oriented pores For such cases a self-consistent (Matthies 2012 Vasin et al 2013) or differential effec-tive medium approach (eg Hornby et al 1994) should be consid-ered It is probably not important for the lower mantle

Note that S-waves passing through anisotropic media have arbi-trary polarization directions in the plane perpendicular to thedirection of propagation as is best displayed for the fast directionof single crystals in Fig 22 but applies also to aggregations of ori-

Fig 21 Critical resolved shear stress CRSS for dislocation glide activities as functionof temperature of (a) bridgmanite at 60 GPa (from Kraych et al 2016) and MgO(from Amodeo et al 2016) at strain rates 105 s1 and 1014 s1 (b) post-perovskiteat 120 GPa at strain rate 1016 s1 (from Goryaeva et al 2016) compared with MgO(from Amodeo et al 2012) Courtesy of P Cordier

B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90 73

ented crystals Seismologists generally consider the projection ofthat polarization direction onto horizontal and vertical axes Thisis convenient because differences in arrival times and waveformsin this representation can be expressed in terms of apparent verti-cal transverse isotropy (VTI) which because of limited azimuthalsampling is often the only anisotropic constraint that can beobtained

4 Linking seismology and mineral physics through predictionsof anisotropy in geodynamic models

41 Isotropic geodynamic models for upper mantle convection

Ever since the concept of plate tectonics became accepted in the1960s convective movements in the Earthrsquos mantle have been pro-posed such as upwelling along oceanic ridges (eg Hess 1964Cann 1968 Fig 1b) The first quantitative models based on hydro-dynamics emerged in the eighties (eg Hager and OrsquoConnell 1981)

Table 2Proposed dominant slip systems in deep Earth minerals

Ferropericlase Lower P 110110High PT also 100011

Bridgmanite Low P (001)[100] [010] 110High P (100)[001](010)[100]

pPv (001)[100](010)[100]

Ca-perovskite 110110e-iron (0001)1120 subordinate 1010

Geodynamic models have been mainly applied to the upper mantleand we will not discuss them here in detail (see eg review by Longand Becker 2010)

Many convection models have been developed to understandthe evolution of the deep Earth Calculations generally assume aviscous fluid and use non-dimensional equations for the conserva-tion of mass momentum and energy applying the Boussineqapproximation Critical parameters are Rayleigh number viscosityboundary temperatures In order to evaluate the strain evolutionduring the convection process tracers are introduced that recordthe velocity gradient tensor at each time step along the path ofthe tracer If the deformation mechanisms are known (eg disloca-tion glide) polycrystal plasticity calculations can be used to calcu-late the evolution of crystal preferred orientation based on thestrain recorded by tracers

Most geodynamic models assume a viscous isotropic mediumwith a smoothly varying viscosity structure and the microstruc-tural processes leading to preferred orientation are introducedpost-mortem Considering an anisotropic medium that constantlychanges its properties greatly increases the complexity of geody-namic calculations However there are models in metallurgy suchas extrusion of an aggregate that illustrate the importance of ananisotropic material behavior (eg Beyerlein et al 2003)

42 Review of upper mantle anisotropic models

We will start the discussion of anisotropic convection byreturning to a simple 2D model (Dawson and Wenk 2000) thatwas originally issued as an educational video by AGU (1999) andcan now be downloaded in digital form (httpepsberkeleyedu~wenkTexturePageMantle-Videohtm) At high Rayleigh number(low viscosity) heat transfer occurs by convection rather than con-duction corresponding to conditions in the Earthrsquos mantle Convec-tion is driven by temperature gradients As aggregates move alongstreamlines the orientation of grains is constantly updated and thelocal texture affects the next deformation step which introducesconsiderable heterogeneities It was surprising to find locallyheterogeneous CPO patterns in the 2D convection cell representingthe upper mantle shown as [100] pole figures of olivine after100 my (Fig 23) Some regions have strong and others very weakpatterns that can be attributed to heterogeneous deformation dueto CPO development and result in lsquolsquoanisotropicrdquo viscosity

Some complexities of different plasticity models for a simplecase of upwelling have been investigated by Blackman et al(1996 2002) and Castelnau et al (2009) If a lower bound behavioris assumed (Sachs 1928) there is very strong CPO developmentFor self-consistent models (Lebensohn and Tomeacute 1993) rotationsare reduced If dislocation glide is combined with dynamic recrys-tallization both grain growth and grain growth combined withnucleation resulting orientation patterns can be very differentRecrystallization is likely in the deep Earth with high temperatureand large strains where grain boundary migration is likely tooccur We will return to the issue of recrystallization in Section 48

Merkel et al (2002) and Lin et al (2009)Amodeo et al (2016)Miyagi and Wenk 2016Tsujino et al (2016)Kraych et al (2016)Miyagi et al (2010) and Wu et al (2017)Goryaeva et al (2016)Miyagi et al (2009) and Ferreacute et al (2009)

Merkel et al (2004) and Miyagi et al (2008)

Fig 18 (a) Diffraction image of MgSiO3 post-perovskite at 150 GPa (b) Unrolled diffractiochanges in Q are due to elastic distortion of the crystal lattice under compression Botquantitative information such as inverse pole figures

Fig 17 Diamond anvil cell for radial diffraction experiments The X-ray beam ishorizontal (a) illustrates the cell and the insert is an enlargement with diamondsand gasket to contain the sample (b c) illustrate that diamonds not only applypressure but also compressive stress that deforms the sample and produces CPO

B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90 71

ple shear experiments in a D-DIA apparatus indicate (100)[001]slip (Tsujino et al 2016) Ferropericlase likely deforms by 110h110i slip (eg Stretton et al 2001 Merkel et al 2002 Linet al 2009) at high pressure conditions For Ca-perovskite domi-nant 110h110i slip was proposed (Miyagi et al 2006 2009)

So far most DAC high-pressure deformation experimentsextracted COD information from intensity variations along Debyerings (eg Fig 18) A new method called multigrain is still underdevelopment It obtains orientation information from individualgrain diffractions (eg Barton and Bernier 2012 Rosa et al2015 Langrand et al 2017) and is especially applicable to coarseraggregates Nisr et al (2012) used information about dislocationsfrom distortion of single crystal diffraction patterns of the post-perovskite analog MgGeO3 and suggested dominant slip on 110and (001) planes

It should be mentioned that information from such high pres-sure experiments is by no means unambiguous Obviously defor-mation conditions in experiments and simulations differconsiderably from those in the deep Earth just to mention temper-ature grain size strain rate interaction of dislocations and interac-tion between grains Furthermore not all CPO patterns that areobserved are due to deformation but could be inherited from orien-tation patterns of precursor phases such as for pPv from perovskite(Dobson et al 2013) or enstatite (Merkel et al 2006 2007 Miyagiet al 2011) Also slip systems may not be the same for pPv phasesof different compositions such as MgGeO3 CaIrO3 NaMgF3 orMn2O3

A different approach has become very important computationof Peierlrsquos stresses and lattice friction for dislocation systems basedon bonding characteristics It was originally developed for metals(eg Kubin et al 1992 Devincre and Kubin 1997) and has morerecently been applied to minerals in the mantle where it allowsto predict slip system activities for a wide range of temperaturendashpressurendashstrain rate conditions (eg Carrez et al 2007Mainprice et al 2008 Cordier et al 2012) Amodeo et al (20122014 2016) propose a switch from 110h010i slip to 100h0 1 1i slip in periclase with pressure Kraych et al (2016) suggest(010)[100] slip in bridgmanite at high pressure According tothese calculations the strength of bridgmanite increases greatlywith pressure and at 60 GPa bridgmanite appears 20 times stron-ger than periclase The critical resolved shear stress decreasesabout 20 from strain rates of 105 s1 (which corresponds to

n image as function of Q (Q = 1d) Intensity variations with azimuth illustrate CPOtom experimental data above fit of the data with the Rietveld method to extract

Fig 19 Explanation of the relationship between DAC diffraction image and inverse pole figure Left Unrolled diffraction image of MgGeO3 post-perovskite Some diffractionlines are labeled The sinusoidal variations are due to imposed stress High stress (high Q low d) is indicated by arrows On the right side is a conceptual construction of theinverse pole figure of the compression axis based on relative diffraction intensities (Miyagi et al 2011)

Fig 20 Inverse pole figures for MgSiO3 post-perovskite (AndashC) experiments (D) Plasticity model with dominant (001) slip equal area projection (Miyagi et al 2010)

72 B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90

experimental values) to 1014 s1 corresponding to likely values atdeep mantle conditions (Fig 21a) The opposite is the case for pPvwhich appears much weaker than periclase at high pressure hightemperature and slow strain rates (Fig 21b Goryaeva et al 20152016) Also the predicted weakest calculated slip system for post-perovskite at deep mantle conditions is (010)[100] correspondingto the layered crystal structure (Fig 21c) but different from thatobserved in DAC experiments (Miyagi et al 2010 Wu et al 2017)

It should be mentioned that a single slip system is not sufficientto deform a polycrystal In the case of the Taylor model at least 5systems have to be active to produce an arbitrary strain (Mises1928) This is relaxed for the self-consistent model but also hereseveral slip systems are active The choice of activity depends onthe crystal orientation relative to the applied stress (Schmid fac-tor) TEM investigations confirm this though some slip systemsusually dominate and the literature refers to the lsquolsquodominantrdquo slipsystem Some dominant slip systems for deep Earth minerals aresummarized in Table 2

34 Elastic properties

Elastic properties of crystals at conditions pertaining to thelower mantle are critical to link microstructural properties of therock with seismic observations The most straightforward experi-mental method that has been applied to many lower mantle min-erals is Brillouin scattering (see review by Speziale et al 2014) andenergy-dispersive X-ray diffraction (eg for calcium silicate per-ovskite Shieh et al 2004) A different approach is with first prin-ciples calculations at high pressure and temperature (for someapplications to bridgmanite CaSiO3 perovskite and pPv see egZhang et al 2013 Wentzcovitch et al 2005 Kawai and

Tsuchiya 2015) First principles results look fairly consistent forminerals at lower mantle conditions but as we will see in Sec-tion 62 predictions for iron at inner core conditions are stillambiguous Furthermore the actual composition of the mineralsparticularly the iron content can be significant (eg Koci et al2007) Values of stiffness coefficients and P-wave anisotropy (An = 200(Pmax Pmin)(Pmax + Pmin) for some low mantle mineralsat lowermost mantle conditions are listed in Table 3 Fig 22 givescorresponding S velocities of single crystals with black lines corre-sponding to the orientation of the fast S-wave polarization As canbe seen in Table 1 periclase and pPv have the highest P-wave ani-sotropy and Ca-perovskite is least anisotropic The S-wave aniso-tropy is considerably higher for pPv and periclase than forbridgmanite and particularly CaSiO3 perovskite

To obtain elastic properties of aggregates one has to averageover all orientations and corresponding elastic tensors takingphase fractions into account Simple averages are upper bound(Voigt 1887) and lower bound (Reuss 1929) Generally an inter-mediate arithmetic mean (Hill 1952) or a geometric mean(Matthies and Humbert 1995) are preferred All these models donot take grain shape into account which is not very significantfor crystalline phases but becomes important for systems withplaty minerals such as graphite or sheet-silicate containing rocksand aggregates with flat oriented pores For such cases a self-consistent (Matthies 2012 Vasin et al 2013) or differential effec-tive medium approach (eg Hornby et al 1994) should be consid-ered It is probably not important for the lower mantle

Note that S-waves passing through anisotropic media have arbi-trary polarization directions in the plane perpendicular to thedirection of propagation as is best displayed for the fast directionof single crystals in Fig 22 but applies also to aggregations of ori-

Fig 21 Critical resolved shear stress CRSS for dislocation glide activities as functionof temperature of (a) bridgmanite at 60 GPa (from Kraych et al 2016) and MgO(from Amodeo et al 2016) at strain rates 105 s1 and 1014 s1 (b) post-perovskiteat 120 GPa at strain rate 1016 s1 (from Goryaeva et al 2016) compared with MgO(from Amodeo et al 2012) Courtesy of P Cordier

B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90 73

ented crystals Seismologists generally consider the projection ofthat polarization direction onto horizontal and vertical axes Thisis convenient because differences in arrival times and waveformsin this representation can be expressed in terms of apparent verti-cal transverse isotropy (VTI) which because of limited azimuthalsampling is often the only anisotropic constraint that can beobtained

4 Linking seismology and mineral physics through predictionsof anisotropy in geodynamic models

41 Isotropic geodynamic models for upper mantle convection

Ever since the concept of plate tectonics became accepted in the1960s convective movements in the Earthrsquos mantle have been pro-posed such as upwelling along oceanic ridges (eg Hess 1964Cann 1968 Fig 1b) The first quantitative models based on hydro-dynamics emerged in the eighties (eg Hager and OrsquoConnell 1981)

Table 2Proposed dominant slip systems in deep Earth minerals

Ferropericlase Lower P 110110High PT also 100011

Bridgmanite Low P (001)[100] [010] 110High P (100)[001](010)[100]

pPv (001)[100](010)[100]

Ca-perovskite 110110e-iron (0001)1120 subordinate 1010

Geodynamic models have been mainly applied to the upper mantleand we will not discuss them here in detail (see eg review by Longand Becker 2010)

Many convection models have been developed to understandthe evolution of the deep Earth Calculations generally assume aviscous fluid and use non-dimensional equations for the conserva-tion of mass momentum and energy applying the Boussineqapproximation Critical parameters are Rayleigh number viscosityboundary temperatures In order to evaluate the strain evolutionduring the convection process tracers are introduced that recordthe velocity gradient tensor at each time step along the path ofthe tracer If the deformation mechanisms are known (eg disloca-tion glide) polycrystal plasticity calculations can be used to calcu-late the evolution of crystal preferred orientation based on thestrain recorded by tracers

Most geodynamic models assume a viscous isotropic mediumwith a smoothly varying viscosity structure and the microstruc-tural processes leading to preferred orientation are introducedpost-mortem Considering an anisotropic medium that constantlychanges its properties greatly increases the complexity of geody-namic calculations However there are models in metallurgy suchas extrusion of an aggregate that illustrate the importance of ananisotropic material behavior (eg Beyerlein et al 2003)

42 Review of upper mantle anisotropic models

We will start the discussion of anisotropic convection byreturning to a simple 2D model (Dawson and Wenk 2000) thatwas originally issued as an educational video by AGU (1999) andcan now be downloaded in digital form (httpepsberkeleyedu~wenkTexturePageMantle-Videohtm) At high Rayleigh number(low viscosity) heat transfer occurs by convection rather than con-duction corresponding to conditions in the Earthrsquos mantle Convec-tion is driven by temperature gradients As aggregates move alongstreamlines the orientation of grains is constantly updated and thelocal texture affects the next deformation step which introducesconsiderable heterogeneities It was surprising to find locallyheterogeneous CPO patterns in the 2D convection cell representingthe upper mantle shown as [100] pole figures of olivine after100 my (Fig 23) Some regions have strong and others very weakpatterns that can be attributed to heterogeneous deformation dueto CPO development and result in lsquolsquoanisotropicrdquo viscosity

Some complexities of different plasticity models for a simplecase of upwelling have been investigated by Blackman et al(1996 2002) and Castelnau et al (2009) If a lower bound behavioris assumed (Sachs 1928) there is very strong CPO developmentFor self-consistent models (Lebensohn and Tomeacute 1993) rotationsare reduced If dislocation glide is combined with dynamic recrys-tallization both grain growth and grain growth combined withnucleation resulting orientation patterns can be very differentRecrystallization is likely in the deep Earth with high temperatureand large strains where grain boundary migration is likely tooccur We will return to the issue of recrystallization in Section 48

Merkel et al (2002) and Lin et al (2009)Amodeo et al (2016)Miyagi and Wenk 2016Tsujino et al (2016)Kraych et al (2016)Miyagi et al (2010) and Wu et al (2017)Goryaeva et al (2016)Miyagi et al (2009) and Ferreacute et al (2009)

Merkel et al (2004) and Miyagi et al (2008)

Fig 19 Explanation of the relationship between DAC diffraction image and inverse pole figure Left Unrolled diffraction image of MgGeO3 post-perovskite Some diffractionlines are labeled The sinusoidal variations are due to imposed stress High stress (high Q low d) is indicated by arrows On the right side is a conceptual construction of theinverse pole figure of the compression axis based on relative diffraction intensities (Miyagi et al 2011)

Fig 20 Inverse pole figures for MgSiO3 post-perovskite (AndashC) experiments (D) Plasticity model with dominant (001) slip equal area projection (Miyagi et al 2010)

72 B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90

experimental values) to 1014 s1 corresponding to likely values atdeep mantle conditions (Fig 21a) The opposite is the case for pPvwhich appears much weaker than periclase at high pressure hightemperature and slow strain rates (Fig 21b Goryaeva et al 20152016) Also the predicted weakest calculated slip system for post-perovskite at deep mantle conditions is (010)[100] correspondingto the layered crystal structure (Fig 21c) but different from thatobserved in DAC experiments (Miyagi et al 2010 Wu et al 2017)

It should be mentioned that a single slip system is not sufficientto deform a polycrystal In the case of the Taylor model at least 5systems have to be active to produce an arbitrary strain (Mises1928) This is relaxed for the self-consistent model but also hereseveral slip systems are active The choice of activity depends onthe crystal orientation relative to the applied stress (Schmid fac-tor) TEM investigations confirm this though some slip systemsusually dominate and the literature refers to the lsquolsquodominantrdquo slipsystem Some dominant slip systems for deep Earth minerals aresummarized in Table 2

34 Elastic properties

Elastic properties of crystals at conditions pertaining to thelower mantle are critical to link microstructural properties of therock with seismic observations The most straightforward experi-mental method that has been applied to many lower mantle min-erals is Brillouin scattering (see review by Speziale et al 2014) andenergy-dispersive X-ray diffraction (eg for calcium silicate per-ovskite Shieh et al 2004) A different approach is with first prin-ciples calculations at high pressure and temperature (for someapplications to bridgmanite CaSiO3 perovskite and pPv see egZhang et al 2013 Wentzcovitch et al 2005 Kawai and

Tsuchiya 2015) First principles results look fairly consistent forminerals at lower mantle conditions but as we will see in Sec-tion 62 predictions for iron at inner core conditions are stillambiguous Furthermore the actual composition of the mineralsparticularly the iron content can be significant (eg Koci et al2007) Values of stiffness coefficients and P-wave anisotropy (An = 200(Pmax Pmin)(Pmax + Pmin) for some low mantle mineralsat lowermost mantle conditions are listed in Table 3 Fig 22 givescorresponding S velocities of single crystals with black lines corre-sponding to the orientation of the fast S-wave polarization As canbe seen in Table 1 periclase and pPv have the highest P-wave ani-sotropy and Ca-perovskite is least anisotropic The S-wave aniso-tropy is considerably higher for pPv and periclase than forbridgmanite and particularly CaSiO3 perovskite

To obtain elastic properties of aggregates one has to averageover all orientations and corresponding elastic tensors takingphase fractions into account Simple averages are upper bound(Voigt 1887) and lower bound (Reuss 1929) Generally an inter-mediate arithmetic mean (Hill 1952) or a geometric mean(Matthies and Humbert 1995) are preferred All these models donot take grain shape into account which is not very significantfor crystalline phases but becomes important for systems withplaty minerals such as graphite or sheet-silicate containing rocksand aggregates with flat oriented pores For such cases a self-consistent (Matthies 2012 Vasin et al 2013) or differential effec-tive medium approach (eg Hornby et al 1994) should be consid-ered It is probably not important for the lower mantle

Note that S-waves passing through anisotropic media have arbi-trary polarization directions in the plane perpendicular to thedirection of propagation as is best displayed for the fast directionof single crystals in Fig 22 but applies also to aggregations of ori-

Fig 21 Critical resolved shear stress CRSS for dislocation glide activities as functionof temperature of (a) bridgmanite at 60 GPa (from Kraych et al 2016) and MgO(from Amodeo et al 2016) at strain rates 105 s1 and 1014 s1 (b) post-perovskiteat 120 GPa at strain rate 1016 s1 (from Goryaeva et al 2016) compared with MgO(from Amodeo et al 2012) Courtesy of P Cordier

B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90 73

ented crystals Seismologists generally consider the projection ofthat polarization direction onto horizontal and vertical axes Thisis convenient because differences in arrival times and waveformsin this representation can be expressed in terms of apparent verti-cal transverse isotropy (VTI) which because of limited azimuthalsampling is often the only anisotropic constraint that can beobtained

4 Linking seismology and mineral physics through predictionsof anisotropy in geodynamic models

41 Isotropic geodynamic models for upper mantle convection

Ever since the concept of plate tectonics became accepted in the1960s convective movements in the Earthrsquos mantle have been pro-posed such as upwelling along oceanic ridges (eg Hess 1964Cann 1968 Fig 1b) The first quantitative models based on hydro-dynamics emerged in the eighties (eg Hager and OrsquoConnell 1981)

Table 2Proposed dominant slip systems in deep Earth minerals

Ferropericlase Lower P 110110High PT also 100011

Bridgmanite Low P (001)[100] [010] 110High P (100)[001](010)[100]

pPv (001)[100](010)[100]

Ca-perovskite 110110e-iron (0001)1120 subordinate 1010

Geodynamic models have been mainly applied to the upper mantleand we will not discuss them here in detail (see eg review by Longand Becker 2010)

Many convection models have been developed to understandthe evolution of the deep Earth Calculations generally assume aviscous fluid and use non-dimensional equations for the conserva-tion of mass momentum and energy applying the Boussineqapproximation Critical parameters are Rayleigh number viscosityboundary temperatures In order to evaluate the strain evolutionduring the convection process tracers are introduced that recordthe velocity gradient tensor at each time step along the path ofthe tracer If the deformation mechanisms are known (eg disloca-tion glide) polycrystal plasticity calculations can be used to calcu-late the evolution of crystal preferred orientation based on thestrain recorded by tracers

Most geodynamic models assume a viscous isotropic mediumwith a smoothly varying viscosity structure and the microstruc-tural processes leading to preferred orientation are introducedpost-mortem Considering an anisotropic medium that constantlychanges its properties greatly increases the complexity of geody-namic calculations However there are models in metallurgy suchas extrusion of an aggregate that illustrate the importance of ananisotropic material behavior (eg Beyerlein et al 2003)

42 Review of upper mantle anisotropic models

We will start the discussion of anisotropic convection byreturning to a simple 2D model (Dawson and Wenk 2000) thatwas originally issued as an educational video by AGU (1999) andcan now be downloaded in digital form (httpepsberkeleyedu~wenkTexturePageMantle-Videohtm) At high Rayleigh number(low viscosity) heat transfer occurs by convection rather than con-duction corresponding to conditions in the Earthrsquos mantle Convec-tion is driven by temperature gradients As aggregates move alongstreamlines the orientation of grains is constantly updated and thelocal texture affects the next deformation step which introducesconsiderable heterogeneities It was surprising to find locallyheterogeneous CPO patterns in the 2D convection cell representingthe upper mantle shown as [100] pole figures of olivine after100 my (Fig 23) Some regions have strong and others very weakpatterns that can be attributed to heterogeneous deformation dueto CPO development and result in lsquolsquoanisotropicrdquo viscosity

Some complexities of different plasticity models for a simplecase of upwelling have been investigated by Blackman et al(1996 2002) and Castelnau et al (2009) If a lower bound behavioris assumed (Sachs 1928) there is very strong CPO developmentFor self-consistent models (Lebensohn and Tomeacute 1993) rotationsare reduced If dislocation glide is combined with dynamic recrys-tallization both grain growth and grain growth combined withnucleation resulting orientation patterns can be very differentRecrystallization is likely in the deep Earth with high temperatureand large strains where grain boundary migration is likely tooccur We will return to the issue of recrystallization in Section 48

Merkel et al (2002) and Lin et al (2009)Amodeo et al (2016)Miyagi and Wenk 2016Tsujino et al (2016)Kraych et al (2016)Miyagi et al (2010) and Wu et al (2017)Goryaeva et al (2016)Miyagi et al (2009) and Ferreacute et al (2009)

Merkel et al (2004) and Miyagi et al (2008)

Fig 21 Critical resolved shear stress CRSS for dislocation glide activities as functionof temperature of (a) bridgmanite at 60 GPa (from Kraych et al 2016) and MgO(from Amodeo et al 2016) at strain rates 105 s1 and 1014 s1 (b) post-perovskiteat 120 GPa at strain rate 1016 s1 (from Goryaeva et al 2016) compared with MgO(from Amodeo et al 2012) Courtesy of P Cordier

B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90 73

ented crystals Seismologists generally consider the projection ofthat polarization direction onto horizontal and vertical axes Thisis convenient because differences in arrival times and waveformsin this representation can be expressed in terms of apparent verti-cal transverse isotropy (VTI) which because of limited azimuthalsampling is often the only anisotropic constraint that can beobtained

4 Linking seismology and mineral physics through predictionsof anisotropy in geodynamic models

41 Isotropic geodynamic models for upper mantle convection

Ever since the concept of plate tectonics became accepted in the1960s convective movements in the Earthrsquos mantle have been pro-posed such as upwelling along oceanic ridges (eg Hess 1964Cann 1968 Fig 1b) The first quantitative models based on hydro-dynamics emerged in the eighties (eg Hager and OrsquoConnell 1981)

Table 2Proposed dominant slip systems in deep Earth minerals

Ferropericlase Lower P 110110High PT also 100011

Bridgmanite Low P (001)[100] [010] 110High P (100)[001](010)[100]

pPv (001)[100](010)[100]

Ca-perovskite 110110e-iron (0001)1120 subordinate 1010

Geodynamic models have been mainly applied to the upper mantleand we will not discuss them here in detail (see eg review by Longand Becker 2010)

Many convection models have been developed to understandthe evolution of the deep Earth Calculations generally assume aviscous fluid and use non-dimensional equations for the conserva-tion of mass momentum and energy applying the Boussineqapproximation Critical parameters are Rayleigh number viscosityboundary temperatures In order to evaluate the strain evolutionduring the convection process tracers are introduced that recordthe velocity gradient tensor at each time step along the path ofthe tracer If the deformation mechanisms are known (eg disloca-tion glide) polycrystal plasticity calculations can be used to calcu-late the evolution of crystal preferred orientation based on thestrain recorded by tracers

Most geodynamic models assume a viscous isotropic mediumwith a smoothly varying viscosity structure and the microstruc-tural processes leading to preferred orientation are introducedpost-mortem Considering an anisotropic medium that constantlychanges its properties greatly increases the complexity of geody-namic calculations However there are models in metallurgy suchas extrusion of an aggregate that illustrate the importance of ananisotropic material behavior (eg Beyerlein et al 2003)

42 Review of upper mantle anisotropic models

We will start the discussion of anisotropic convection byreturning to a simple 2D model (Dawson and Wenk 2000) thatwas originally issued as an educational video by AGU (1999) andcan now be downloaded in digital form (httpepsberkeleyedu~wenkTexturePageMantle-Videohtm) At high Rayleigh number(low viscosity) heat transfer occurs by convection rather than con-duction corresponding to conditions in the Earthrsquos mantle Convec-tion is driven by temperature gradients As aggregates move alongstreamlines the orientation of grains is constantly updated and thelocal texture affects the next deformation step which introducesconsiderable heterogeneities It was surprising to find locallyheterogeneous CPO patterns in the 2D convection cell representingthe upper mantle shown as [100] pole figures of olivine after100 my (Fig 23) Some regions have strong and others very weakpatterns that can be attributed to heterogeneous deformation dueto CPO development and result in lsquolsquoanisotropicrdquo viscosity

Some complexities of different plasticity models for a simplecase of upwelling have been investigated by Blackman et al(1996 2002) and Castelnau et al (2009) If a lower bound behavioris assumed (Sachs 1928) there is very strong CPO developmentFor self-consistent models (Lebensohn and Tomeacute 1993) rotationsare reduced If dislocation glide is combined with dynamic recrys-tallization both grain growth and grain growth combined withnucleation resulting orientation patterns can be very differentRecrystallization is likely in the deep Earth with high temperatureand large strains where grain boundary migration is likely tooccur We will return to the issue of recrystallization in Section 48

Merkel et al (2002) and Lin et al (2009)Amodeo et al (2016)Miyagi and Wenk 2016Tsujino et al (2016)Kraych et al (2016)Miyagi et al (2010) and Wu et al (2017)Goryaeva et al (2016)Miyagi et al (2009) and Ferreacute et al (2009)

Merkel et al (2004) and Miyagi et al (2008)

Table 3Density (gcm3) elastic stiffness (GPa) and P-wave anisotropy (An) of periclase bridgmanite post-perovskite and Ca-perovskite at conditions of the lowermost mantle (3000 K125 GPa)

Periclase Bridgmanite pPv Ca-perovskite

Karki et al (2000) Wentzcovitch et al (2004) Stackhouse et al (2005) Kawai and Tscuchiya (2015)q 507 525 535 56C11 11540 8600 12200 970C12 2655 5355 4740 505C13 2655 4370 3590 505C22 11540 10675 8990 970C23 2655 4675 4930 505C33 11540 10530 11760 970C44 1980 2940 2730 305C55 1980 2495 2450 305C66 1980 2845 3760 305An 167 110 152 47

Fig 22 Spherical representation of shear-wave splitting (in ms) of main minerals at lowermost mantle conditions and corresponding to elastic properties in Table 1 Valuesare in ms black lines illustrate polarization of the fast S-wave

Fig 23 (001) pole figures of olivine for a finite element model of homogeneous upper mantle convection that takes anisotropy development into account Upwelling on leftsubduction on the right (Dawson and Wenk 2000)

74 B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90

43 Anisotropic models for the lowermost mantle

As explained earlier seismic imaging of the D00 zone hasrevealed an anisotropic velocity structure particularly expressedin fast S-wave velocities for polarization parallel to the core-mantle boundary in regions that are thought to correspond to slabgraveyards (Fig 8) This seismic anisotropy depends on the elasticproperties of the rocks Elastic properties are due to the mineralphases that are present the orientation of crystals and the elasticproperties of single crystals at D00 conditions If we know the defor-mation mechanisms of crystals at conditions of the lower mantle(from high pressuretemperature deformation experiments orbonding calculations) we can predict the alignment of crystals inan aggregate that has undergone a strain path recorded by tracersin a geodynamic model

An isotropic viscous medium approach was used by McNamaraet al (2002) and then extended to include texture development byWenk et al (2006) and Wenk et al (2011) in 2D and Cottaar et al

(2014) in 3D to predict patterns of seismic anisotropy in andaround slabs as they impinge on the core-mantle boundary

In another approach the flow field is derived from an instanta-neous flow calculation based on the consideration of an existing3D mantle global tomographic model a 1D mantle viscositymodel as well as constraints from geodynamic observables suchas the gravity field and surface plate motions (eg Simmonset al 2009) This was used by Walker et al (2011) and Nowackiet al (2013) to predict global anisotropy patterns The advantageof this model is that it applies to the whole Earth but it may bebiased by the tomographic seismic structure and assumptionson the conversion of seismic velocities to density to establishthe flow field

In both approaches particle paths are tracked by tracers allow-ing the computation of the strain field Texture development isthen modelled in polycrystalline aggregates starting from a largesample of randomly oriented grains and applying polycrystal plas-ticity theory (Section 32) followed by computation of the elastic

B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90 75

tensor of the aggregate by averaging over crystal orientations andcorresponding single crystal elastic properties

44 Isotropic viscosity medium approach for lower mantle anisotropy

This type of model investigates the characteristics of a subduc-tiong cold slab descending through the lower mantle to the core-mantle boundary The model is isochemical and isotropic viscosityis assumed The calculations solve non-dimensional equations forthe conservation of mass momentum and energy using theBoussinesq approximation (McNamara et al 2003) The strain evo-lution is evaluated by inserting tracers into the isotropic convec-tive medium This strain is then used to calculate development ofpreferred orientation using the viscoplastic self-consistent method(Lebensohn and Tomeacute 1993) which was introduced in Section 32for evaluating slip systems in high pressure deformationexperiments

We will explain the general procedure for a 2D model of a sub-ducting slab into the D00 zone (Wenk et al 2011) Fig 24 (top) is asnapshot of a section of the upper mantle with downwelling coldslabs (blue) und upwelling hot plumes (red) Below (Fig 24 bot-tom) is an enlarged section of D00 extending 300 km above thecore-mantle boundary It indicates the path of some streamlinesWe are following the lowest tracer 189 Post-perovskite and fer-ropericlase are likely the main components in the cooler parts ofthe enigmatic D00 zone and texture calculations were done withsuch a 2-phase system In addition significant amounts of cubicCaSiO3 perovskite may be present but this was not considered inthis model because of relatively low anisotropy

Plasticity calculations were performed by assuming differentcombinations of dominant slip systems for pPv since there is someambiguity (Section 32 and Table 2) (100) (010) (001) (egMerkel et al 2004 2007 Miyagi et al 2010 2011 Wu et al2017 Goryaeva et al 2015 2016) They are shown in Fig 25 fordominant (001)[100] slip for pPv and dominant 110h1 1 0islip for periclase (MgO) (eg Merkel et al 2002 Miyajima et al2009) at three step increments There is moderate CPO at 1200steps but it becomes very strong at 3600 steps For periclase thereis a significant rotation of the pattern due to simple shear similarto what was observed in halite with the same crystal structure(Wenk et al 2009) The simple shear rotation is less pronouncedfor orthorhombic pPv than for cubic periclase

Below the pole figures are corresponding maps of P-velocitiesagain expressing significant rotations for periclase Post-perovskite shows very low P-velocities parallel to the core-mantle boundary For two-phase materials the combination mayadd or reduce overall anisotropy It should be mentioned that plas-ticity models assume deformation by dislocation slip At deepmantle conditions other mechanisms are likely active that do notcontribute crystal rotations such as dislocation climb grain

Fig 24 2D convection model illustrating subduction of a cold slab (blue) into the lowe(reproduced from Wenk et al 2011)

boundary sliding and to some extent dynamic recrystallizationWe will return to some of these issues in Section 45 For this cal-culation it was assumed that only half of the strain is accommo-dated by dislocation glide

Following this procedure for many streamlines we can mapanisotropic velocity patterns over the whole region of the geody-namic model Fig 26 shows five simulations one for ferropericlaseand perovskite and three for post-perovskite assuming differentdominant slip systems Only the pattern for dominant (001) dislo-cation glide of post-perovskite compares well with seismic obser-vations of fast SH waves in regions of faster than averageisotropic Vs (eg Fig 3) The anti-correlation of anisotropy in Sand P is consistent with a seismic study of the average profile withdepth of VTI parameters constrained by normal mode data(Beghein et al 2006) Perovskite was also considered but did notmatch the seismic observations One additional argument in favorof (001) slip is the strong splitting and prediction of a tilted fastaxis This is also more compatible in both direction and strengthwith the observations of splitting in Sdiff at the edge of the AfricanLLSVP (Cottaar and Romanowicz 2013)

This is an interesting example linking microscopic and macro-scopic observations Deformation mechanisms at the crystal scale(dislocations) derived from laboratory experiments predict defor-mation mechanisms and are then applied to Earth processes overlarge volumes and long time-scales Comparing the geodynamicresults with seismic observations in this case seems to confirmthe assumptions about microscopic processes ie the type of dislo-cations that are active However the interpretation relies heavilyon the very tentative seismic observation of anti-correlation of Sand P anisotropy in the deep mantle

45 Flow calculation based on a global tomographic model

This type of flow model is based on the joint inversion of globalS-wave travel times the global gravity field dynamic surfacetopography tectonic plate motions and the excess ellipticity ofthe core-mantle boundary (Walker et al 2011) A theory of viscousflow in a compressible self-gravitating spherical mantle is used tocalculate the mantle convective flow predicted on the basis of thetomographically-inferred 3D density anomalies (Mitrovica andForte 2004) Fig 27 shows a map of the horizontal flow vectors(arrows) and radial components of flow velocity (color blue nega-tive red positive) illustrating upwelling in the Pacific and in SouthAfrica for one model From the 3D mantle flow field polycrystalplasticity calculations similar to themodel discussed in Section 43are used to calculate orientation patterns and corresponding aniso-tropic elastic properties

In tomographic models of radial anisotropy in P (Boschi andDziewonski 2000) and instantaneous flow calculations globalmaps of VTI inferred from different pPv models are compared with

rmost mantle The insert illustrates some tracers and temperatures in the D00 zone

Fig 25 (001) Pole figures and P-wave velocities for three positions along tracer 189 marked on Fig Equal area projection Core-mantle boundary is horizontal

76 B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90

global seismic VTI models of D00 (Walker et al 2011) They suggesta preference for slip of dislocations on (010) or (100) and 110rather than on (001) However this preference is based on the cal-culation of correlations that are dominated by regions within theLLSVPs where in fact pPv might not be present since the LLSVPsare very likely hotter than average regions and the pPv-bridgmanite transition may occur at pressures corresponding tothe core (Fig 9b) The correlation is dominated by the centers ofthe Pacific and African LLSVP where actually one might not expect

Fig 26 D00 zone with plots of squared ratios of horizontally and vertically polarizedS waves (left side) and horizontal and vertical P-waves for different phases (ppvpost-perovskite pv perovskite and MgO) and different dominant slip systems(Wenk et al 2011)

pPv to be present (Fig 9b) Clearly further constraints on P aniso-tropy in the deep mantle are necessary to better discriminateamong possible pPv slip systems

Whereas Walker et al (2011) restricted their analysis to the VTIportion of their predicted anisotropic structure in a follow-upstudy Nowacki et al (2013) extended this approach to allow amost general form of anisotropy albeit focused on three regionsof paleo-subduction where differential S-ScS shear wave splittingmeasurements indicate the presence of azimuthal anisotropy in

Fig 27 Tomographic inversion model for mantle flow Map showing the radial(color red positive blue negative) and horizontal flow (arrows) 150 km above theCMB (from Walker et al 2011)

B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90 77

D00 Testing as previously the predictions of anisotropy from thesame flow models as in Walker et al (2011) they confirmed thatthe (010) slip system of pPv provided the best fit to the seismicdata Still only the fast axis directions were tested disregardingthe amplitude of splitting arguing that the latter may be unrealis-tically strong in plasticity calculations while imposing any scalingwould be arbitrary

We note that Ford and Long (2015) have independently testedthe seismic anisotropy predictions of the Walker et al (2011) flowmodels on a set of measurements of shear wave splitting at theeastern edge of the African LLSVP They concluded that none ofthe flow models and pPv slip system combinations provided satis-factory predictions of their dataset although when they relax con-straints on the fast axis orientations the (010) slip model isfavored

46 Compositional heterogeneities

Neither the 2D and 3D convection models nor the instantaneousflow model constrained by tomography include the presence ofthermo-chemical piles as have been hypothesized to explainLLSVPs The presence of such piles could significantly modify theflow patterns and focus deformation at the border of the pileswhich seems to be observed in some local shear wave splittingstudies (eg Fig 4) Also it appears that the lowermost mantlemay be compositionally considerably heterogeneous (eg White2015) Subduction of lithospheric slabs is a major contribution toheterogeneity including in the D00 zone (van den Berg et al2010 cf Fig 11a and b) Additional phases are likely presentamong them cubic CaSiO3 perovskite silica and perhaps metalliciron (eg Shi et al 2013) (see Fig 11) Upwelling plumes displaychemical heterogeneity and characteristic isotope signatures weredocumented at hotspots such as Hawaii (Weis et al 2011 NobreSilva et al 2013 Li Y et al 2014) but this does not explain theprevalent seismic anisotropy in the D00 zone expressed in S-wavesplitting patterns with SHgtSV (eg Table 1 Fig 3) and for thiscrystal alignment during subduction is the most obvious explana-tion at present (eg Cottaar et al 2014)

47 Viscosity changes

There are some complications that have not been taken intoaccount in any of these models Changes in viscosity do occureg during phase transformations with strong increases in thetransition zone between the upper and lower mantle (410ndash660 km) The viscosity is assumed to be low in the upper mantle(radial viscosity of reference model 011021 Pa s Becker 2006)increases in the transition zone (11021 Pa s) and then again asminerals transform to denser lower mantle phases (501021Pa s) There is considerable complexity as some slabs descend intothe lower mantle (eg Conrad and Lithgow-Bertelloni 2004)

Recently seismic heterogeneities were attributed to higher vis-cosities in the mid-mantle region (1000 km) leading to a stagna-tion of subducting slabs (Rudolph et al 2015) and this could bedue to composition (eg Bolfan-Casanova et al 2003 suggestedthat the solubility of water decreases) iron fractionation and ironspin transitions (eg Lin et al 2012 Vilella et al 2015) or changesin mechanical properties with pressure of ferropericlase (egMarquardt and Miyagi 2015) and post-perovskite (Catalli et al2009) First principle calculations of Kraych et al (2016) suggesta strong strength increase for bridgmanite with pressure(Fig 21a) and a dramatic decrease for post-perovskite (Goryaevaet al 2016 Fig 21b) The geodynamic models described here donot take changes in viscosity into account nor do they consider ani-sotropic viscosity (eg Christensen 1987)

48 Active deformation mechanisms

The models described in this section attribute anisotropy toplastic deformation of crystals by dislocation glide that inducesrotations and resulting preferred orientation In Section 32 we dis-cussed deformation mechanisms and clearly at lower mantle con-ditions other mechanisms are likely active The deformationmechanism map (Fig 13) suggests a creep regime with a combina-tion of dislocation glide and diffusional dislocation climb (egAmmann et al 2010) Also grain boundary mechanisms may beactive at low stress (eg Chen and Argon 1979) with grain bound-ary sliding grain-size reduction but there are no experimental datafor lower mantle conditions (eg Sun et al 2016 describe disclina-tions in olivine) Recent bonding calculations suggest that disloca-tion climb may dominate in olivine (Boioli et al 2015) andparticularly in bridgmanite (Boioli et al 2017) Since only glidegenerates CPO this may explain why most of the lower mantleappears isotropic To account for these other mechanisms in somegeodynamic convection models only half of the strain was attribu-ted to glide but this limit is arbitrary

Many deformation mechanism maps have been introduced forgeological systems with emphasis on the upper mantle and theinfluences of temperature pressure stress and strain rate (egHansen et al 2011 2012 Kohlstedt and Goetze 1974 Linckenset al 2011) Extrapolating results to the lower mantle is morespeculative but with new models such as Boioli et al (2017)Goryaeva et al (2016) and Kraych et al (2016) this domain maycome within reach

Another mechanism that is likely active in the deep mantle isdynamic recrystallization It has been approached with thermody-namic theory of grain growth under stress (eg Kamb 1961Paterson 1973 Green 1980 Shimizu 1999 2008 Rozel et al2011) While recrystallization can result in grain growth it moreoften produces grain size reduction which has an effect on the rhe-ology (eg De Bresser et al 2001) But evidence from materialsscience suggests that in deformed aggregates recrystallization isoften controlled by crystal defects Grains with high dislocationdensities are less stable and nucleation may occur On the otherhand a grain with low dislocation density may grow and replacea highly strained grain by grain boundary migration (egHaessner 1978) These concepts can be introduced in plasticitymodels and were able to explain orientation patterns observed inexperimentally deformed quartzite halite and ice (Wenk et al1997) and olivine (Wenk and Tomeacute 1999 Kaminski and Ribe2001) but there are too many unknown parameters to predictrecrystallization mechanisms in lower mantle rocks Oftendynamic recrystallization randomizes orientation patterns

49 Complications in polyphase systems

Perhaps the most important complication for anisotropic geo-dynamics is that the lower mantle is a system with two majorphases of different strength The interaction of these phases isnot taken into account in most polycrystal plasticity models Suchsystems are common yet there is not much work neither in mate-rial science nor geological environments and recommendationsformulated at an interdisciplinary polyphase polycrystal plasticityworkshop still apply (Breacutechet et al 1994)

Most rocks in the Earthrsquos crust and mantle are polymineralicyet most experimental and theoretical investigations were doneon monomineralic systems and for example in quartz-mica mix-tures CPO of quartz is greatly reduced compared with a purequartz aggregate (Canova et al 1992 Tullis and Wenk 1994)Under metamorphic conditions complex reactions may occur atgrain boundaries and change the fabric (eg Abart et al 2004Gaidies et al 2017)

78 B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90

In most recrystallized gneisses feldspar and quartz show barelyany preferred orientation (eg Kern et al 2008 Ullemeyer et al2006) This becomes particularly pronounced if rocks have under-gone large secondary deformation resulting in mylonites (egHandy 1994 Kern and Wenk 1990 Herwegh et al 2011Linckens et al 2011 Bercovici and Ricard 2016) In mylonites ofgranitic composition the much stronger and dominant feldsparphase barely deforms and grains tumble in the much weaker andrecrystallizing quartz phase (Fig 28) A similar microstructuremay be expected in highly deformed parts of the lower mantlewith strong bridgmanite in a matrix of weak ferropericlase(Fig 21a) and could explain the lack of significant anisotropy

For the analog system neighborite-halite Kaercher et al (2016)have documented that for single phase systems strong CPO devel-ops but for mixtures CPO is greatly reduced caused by locallyheterogeneous deformation This is also confirmed by DAC experi-ments for perovskite-ferropericlase mixtures (eg Miyagi andWenk 2016 Girard et al 2016)

For the 2-phase problem with local heterogeneities there is nostraightforward polycrystal plasticity model Canova et al (1992)have developed an n-site viscoplastic formulation and applied itto muscovite quartz mixtures There have been attempts withfinite element approaches (eg Mika and Dawson 1999) and Four-ier transform methods (eg Lebensohn 2001) but they are notapplicable to large geophysical systems at least for now and par-

Fig 28 (a) Thin section image of granite mylonite from the Santa Rosa mylonitezone in Southern California with rigid strong plagioclase crystals floating in finegrained recrystallized quartz creating a viscous matrix This represents probably asimilar microstructure as bridgmanite and periclase in the lower mantle (b) Imageof deformed quartzite with feldspar inclusions from the Bergell Alps This pervasiveductile deformation may be similar to sheared post-perovskite in the lowermostmantle Width of images is 10 mm crossed polarizers

ticularly do not account for grain boundary sliding which may bevery significant

For the D00 zone this is likely different because post-perovskiteis of similar strength or weaker than ferropericlase (Fig 21b) andthus deforms with a significant contribution of dislocation glideThe microstructure of highly strained D00 material may be moreanalogous to deformed quartzite with some feldspar inclusionsand extremely strong preferred orientation (Fig 28b)

5 Seismic anisotropy in the inner core

We conclude this review with a brief discussion about seismicanisotropy in the solid inner core While the presence of a densepossibly fluid core had been suggested long ago based on the highaverage density of the Earth as well as measurements of tides itspresence was confirmed by seismology in the early 20th century(Oldham 1906 Gutenberg 1913) An iron-nickel compositionwas assigned in analogy to iron meteorites In 1936 Inge Lehmanndiscovered the presence of an inner core of different elastic proper-ties within the fluid outer core (Lehmann 1936) Several decadeslater the solidity of the inner core was demonstrated byDziewonski and Gilbert (1971) based on the measurements ofeigenfrequencies of inner core-sensitive free oscillations Birch(1952) showed that the density of an iron-nickel alloy is too highcompared to seismological estimates and proposed the presenceof 10 of lighter elements Since then the structure and compo-sition of the core was refined based on seismic gravitational andmagnetic evidence (eg Hirose et al 2013)

The presence of cylindrical anisotropy in the inner core withthe fast axis aligned with the Earthrsquos rotation axis was first pro-posed thirty years ago to explain two types of independent seismicobservations (1) travel time anomalies of P waves that traversethe inner core (denoted PKIKP or PKP(DF)) on polar paths (ie ina direction quasi parallel to the Earthrsquos rotation axis) arriving upto 5 s earlier than those travelling on equatorial paths (Morelliet al 1986) and (2) anomalous splitting of inner core sensitive freeoscillations (Woodhouse et al 1986) Neither of these observationscould be explained by long-wavelength heterogeneous structure inthe earthrsquos mantle It was suggested that this anisotropy couldlikely be due to the alignment of intrinsically anisotropic iron crys-tals and in the following decade several models for the physicalcause of such alignment were proposed (Jeanloz and Wenk1988 Romanowicz et al 1996 Bergman 1997 Karato 1999Wenk et al 2000b Buffett and Wenk 2001 Yoshida et al 1996see review by Sumita and Bergman 2015)

In the decades since its discovery many seismic studies haveconfirmed these early observations from ever increasing datasetsleading to a current landscape of the distribution of inner core ani-sotropy that is surprisingly complex for such a small volume of theEarth (eg Tkalcic 2015) The top 100 km of the 1220 km-thickinner core have been found to be isotropic while deeper there isevidence for a hemispherical pattern of anisotropy (Tanaka andHamaguchi 1997 Creager 1999 Niu and Wen 2002 Garcia2002 Waszek et al 2011 Irving and Deuss 2011 Lythgoe et al2014) with weaker anisotropy in the eastern hemisphere than inthe western hemisphere There is also evidence for depth depen-dence with increased strength of anisotropy towards the center(Creager 1992 Vinnik et al 1994) and more recently the sugges-tion of a different orientation of anisotropy in the central part ofthe inner core (Ishii and Dziewonski 2002 Beghein andTrampert 2003) dubbed lsquolsquoInner Most Inner Corerdquo (IMIC Ishii andDziewonski 2002) The IMIC as reexamined in more recent stud-ies would have a radius of about 550 km (eg Cormier andStroujkova 2005 Cao and Romanowicz 2007 Lythgoe et al2014 Wang et al 2015 Romanowicz et al 2016) The signature

B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90 79

of a hemispherical anisotropic structure has also been found fromthe modeling of coupling of pairs of modes sensitive to such struc-ture (Deuss et al 2010) In addition regional variations in thedirection of the fast axis and strength of anisotropy have been doc-umented (eg Breacuteger et al 1999 Sun and Song 2008ab Irving2016) To explain this complexity Tkalcic (2010) suggested thatthe inner core may be made of a patchwork of anisotropic domainsof different orientations Attenuation of PKIKP waves also presentsanisotropic variations with higher attenuation correlated withearly arrivals along quasi-polar paths (Souriau and Romanowicz1996 1997 Oreshin and Vinnik 2004) We refer the reader tomore complete reviews of seismological studies of inner core ani-sotropy (Deuss 2014 Souriau 2015 Tkalcic 2015) Here webriefly describe some of the seismological challenges that are stillpreventing us from a full understanding of these intriguingobservations

One of the main challenges in fully resolving the pattern ofinner core anisotropy is the poor directional sampling availabledue to the limited distribution of sources and receivers in polarregions (eg Tkalcic 2015) Thus paths sampling the inner coreat a given location from different directions which is necessaryto confirm the presence of anisotropy are frequently lacking mak-ing it difficult to image inner core anisotropy in three dimensionswithout imposing strong a priori-constraints (eg Sun and Song2008a Lythgoe et al 2014) The strongest anisotropy in PKIKPdata is found primarily along paths from events in South SandwichIslands (SSI) to Alaska which dominate the set of observations inthe strongly anisotropic western hemisphere that contribute tothe n angle range between 10-30o where n is the angle of the ray-path in the inner core with the Earthrsquos axis of rotation At shorterdistances (lt155) the PKP(DF) phase can be referred to PKP(BC) which is a core phase that does not traverse the inner core(Fig 29) This makes it possible to eliminate contributions fromuncertainties in the source parameters as well as a significant partof the effects of 3D mantle structure given that PKP(BC) and PKP

Fig 29 Raypaths of main body wave phases used in the study of inner-corestructure and anisotropy at an epicentral distance of 155o At this distance all threecore phases PKIKP (also called PKP(DF)) PKP(BC) and PKP(AB) are observed Thephase PKJKP (a shear wave in the inner core) is very difficult to observe and isplotted here only for reference

(DF) have very similar paths throughout the mantle diverging onlyin the vicinity of the inner core

In fact the SSI dataset shows a wide range of travel timeanomalies ranging from 0 to gt5 s when referred to the PKP(BC)phase suggesting a strong local anomaly (eg Tkalcic et al2002) When plotted as a function of the angle n the global PKP(BC)-PKP(DF) travel time dataset (which covers epicentral dis-tances between 150o and 160) forms an L-shaped curve which isnot well explained by best fitting simple models of inner core ani-sotropy with fast axis aligned with the Earthrsquos rotation axis(Fig 30) for which one would expect a parabolic shape accordingto the equation

dt frac14 athorn bcos2nthorn ccos4n

where a b c are related to integrals of elastic anisotropic parame-ters along the path in the inner core

At larger distances the reference outer core phase is PKP(AB)which spends significant time in the highly heterogeneous D00

region at the base of the mantle Therefore absolute travel timeanomalies of PKP(DF) are preferred although in that case contri-butions from mantle 3D structure and uncertainties in sourceparameters can bias the data (eg Breacuteger et al 2000) Most studieswill therefore only consider events from the high quality relocatedEHB catalog (Engdahl et al 1998) which presently exists onlythrough 2010 Still analysis of these PKP(DF) data indicate thatin the western hemisphere a similar trend is observed in the abso-lute PKP(DF) travel time residuals as in the PKP(DF)-PKP(AB) resid-uals as a function of angle n (Fig 30b) Most recent estimates of thecorresponding anisotropy are on the order of 3ndash4 in the IMICwhich is considerable and difficult to reconcile with current pre-dictions from mineral physics (see Section 6) let alone the esti-mate of 3ndash88 of Lythgoe et al (2014)

To explain this trend and other aspects of complexity in traveltime measurements of core sensitive phases that cannot beexplained by mantle structure Romanowicz et al (2003) proposedalternative models that would involve structure in the outer corewith either faster than average velocities in the inner core tangentcylinder or in polar caps at the top of the outer core that couldrepresent an increased concentration of light elements For exam-ple Fig 31 shows the pattern obtained when plotting absolutetravel time anomalies for DFBC and AB plotted at the entry pointof the corresponding raypath into the outer core on the Alaskaside for south-Sandwich to Alaska paths as well as paths fromAlaska to Antarctica When plotted in this manner the travel-time anomalies form a coherent pattern suggesting a localizedanomaly that may originate near the core-mantle boundary onthe Alaska side compatible with both a polar cap in the outer coreor heterogeneity within at least part of the tangent cylinder Mostanomalously split inner core sensitive normal modes could beexplained by either of these models except for mode 3S2 whichexhibits particularly strong splitting (Romanowicz and Breacuteger2000) These results have been reexamined critically by Ishii andDziewonski (2005)

Putting structure in the outer core remains controversial (egSouriau et al 2003) as significant density anomalies in the vigor-ously convecting outer core appear to be ruled out (eg Stevenson1987) However recent work suggesting the possibility of stagnantlayers at the top of the outer core from magneto-hydrodynamicsconsiderations (eg Buffett 2014) indicates that at least the polarcap hypothesis should perhaps remain on the table as alternativeto a strongly anisotropic region in the inner core On the otherhand Tkalcic (2010) found that differential travel time anomaliesof similar amplitude are observed on PcP-P data in the vicinity ofSSI Because such data do not sample the inner core at all Tkalcic(2010) proposed that a significant part of the SSI anomaly could

Fig 30 Travel time anomalies of core phases as a function of angle n of the ray path in the inner core with respect to the Earthrsquos rotation axis from the combined Berkeleydata collection (Tkalcic et al 2002) and from Leykam et al (2010) Left (DFndashBC) ndash Right absolute DF a) and d) all data b) and e) for events in the south-Sandwich Islands c)and f) for events in Alaska

80 B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90

be located in the deep mantle although no such structure has beenidentified yet tomographically Therefore explaining the broadspread of PKP(DF) travel time anomalies on SSI paths to Alaskaremains an open question which needs to be answered beforerobust bounds on the strength of anisotropy in the inner corersquoswestern hemisphere can be provided to mineral physicists Accu-mulation of data from the current deployment of USArray in Alaskamay shed more light on this question

This leads us to the second and possibly related challenge thathas come to light recently (Lincot et al 2015 2016 Romanowiczet al 2016) which is how to reconcile the 3ndash8 seismic anisotropyinferred in the inner corersquos western hemisphere with currentknowledge from mineral physics

6 Mineral physics of the inner core

61 Phase relations

From the mineral physics point of view a first order questionhas been the phase in which iron is present in the inner coreThe high pressure e phase of iron was first confirmed by X-raydiffraction by Mao et al (1967) and a hexagonal close-packed(hcp) structure was identified Since then many high pressureexperiments have been conducted Most important are those per-tinent to conditions of the inner core (Fig 32) They includedynamic shock compression with relatively large error margins(eg Alfegrave et al 2002 Anzellini et al 2013 Brown 2001 Ping

Fig 31 Absolute travel time anomalies for DF (circles and triangles) BC (crosses)and AB (squares) for events at latitudes lower than 50S or higher than 50Nplotted as a function of the location of the entry point of the ray path into the outercore Triangles are for events at latitude gt50N observed at stations at latitudeslt50S Expanded from Romanowicz et al (2003) to include data from Leykamet al (2010) as also shown in Fig 34bndashf This collection of travel time anomaliesforms a coherent pattern with a sharp gradient delineating a localized boundarybetween very fast paths to the northwest and normal paths to the southeastsuggesting a lsquolsquopolar caprdquo pattern that may or may not originate in the inner coreNote that the color code is centered at dt = 35 s

Fig 32 Pressurendashtemperature phase diagram for iron at high pressure illustratingdiamond anvil and shock experiments as well as ab initio simulations The linescorrespond to melting curves (courtesy of BK Godwal)

B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90 81

et al 2013) and DAC experiments at high pressure and tempera-ture up to 380 GPa and 6000 K (eg Tateno et al 2010) Basedon theoretical calculations some authors have suggested thatbody-centered cubic (bcc) iron could be stable just below the melt-ing point at core pressures (eg Vocadlo et al 2003 Belonoshkoet al 2003 2006 Dubrovinsky et al 2007 Bouchet et al 2013)but most recent studies indicate that bcc is unstable at these con-ditions (eg Godwal et al 2015)

An important aspect is that the inner core may not be chemi-cally and structurally homogeneous It is likely that nickel a com-ponent in iron meteorites is also present in the core (Sakai et al2011 Tateno et al 2012) Furthermore to account for the lowerdensity implied by seismic data suggests that lighter elementsmay be present and a good candidate is silicon The Fe-Si systemhas been studied at intermediate pressure-temperatures (egSakai et al 2011 Fischer et al 2013 Fig 33) and inner core con-ditions (Tateno et al 2015) At high pressure and high tempera-ture FeSi crystallizes in the cubic B2 structure (CsCl structure)which is an ordered bcc structure Fe3Si forms a DO3 structure withdoubling of the B2 unit cell and ordering At lower pressures FeSiforms the B20 structure which is partially disordered bcc with alack of inversion symmetry (eg Jeong and Pickett 2004) Elasticproperties of FeSi have been investigated by Petrova et al (2010)Badro et al (2014) explored a range of possible elements in thecore (O S Si Ni) and concluded that oxygen is required in the outercore

62 Causes of anisotropy in the inner core

Potential mechanisms for alignment of crystals in the inner coreare dislocation-plasticity (eg Jeanloz andWenk 1988 Wenk et al2000a Lincot et al 2015 2016) growth from a melt (eg Bergman1997 Deguen 2012) magnetic Maxwell stresses (eg Karato1999 Buffett and Wenk 2001)

Radial DAC experiments (eg Wenk et al 2000a Merkel et al2004 2013 Miyagi et al 2008) documented texture developmentin e iron at high pressure and inferred (0001) and subordinatef11 20g slip combined with mechanical twinning as potentialmechanisms However these experiments were not at inner coreconditions

Elastic properties at core conditions rely on first principle calcu-lations and various groups have been involved (eg Vocadlo et al2008 2009 Mattesini et al 2010) It is interesting to find thatresults are quite contradictory as expressed in P-wave velocityprofiles for hcp single crystals with the c-axis at n = 0 (Fig 34b)While Vocadlo et al (2009) predict maximum velocities perpendic-ular to the c-axis Mattesini et al (2010) suggest maximum veloc-ities parallel to the c-axis (the elastic tensor of hexagonal crystals isaxially symmetric about the c-axis) Estimates of inner core seismicanisotropy are very high ((Vp-fast Vp-slow)Vp-iso = 3ndash8 Fig 34a)compared with the rather small P-wave anisotropy obtained fromfirst principles calculations for single crystals (eg 49 for Vocadloet al 2009 at 308 GPa and 5000 K or 57 for Mattesini et al 2010at 346 GPa and 6000 K) and the best fit with seismic data would bea hexagonal single crystal aligned with the c-axis more or less par-allel to the N-S axis A huge single crystal seems unlikely giventhat the largest documented crystals on Earth are about 20 m insize and with pressurendashtemperature gradients it is likely thathuge crystals at high temperature would undergo transformationsand recrystallization over geologic times

A recent study (Lincot et al 2016) constructed a multi-scalemodel combining self-consistent polycrystal plasticity inner-core formation models and Monte Carlo simulations of elasticparameters to predict travel times of inner core PKP waves andconfront them with observations These authors found that theycould explain as much as 3 seismic anisotropy with an hcp-ironstructure with fast c axis and with anomalous single crystal aniso-tropies near the melting point of up to 20 (Martorell et al 2013)with dominant pyramidal hc + ai slip and crystal alignment pro-vided by a low degree boundary condition for crystallization atthe ICB While this model might account for the faster PKP traveltimes on polar compared to equatorial paths it does not reproducethe L-shaped travel time anomaly curve as a function of angle n(Fig 30)

Fig 33 Phase diagrams of the Fe-Si system (Fischer et al 2013) (a) Pressurendashtemperature phase diagram illustrating stability fields of the various phases for Fe-9Si (b)Temperature-composition diagram at 145 GPa illustrating the transition from hcp to B2

Fig 34 (a) Comparison of relative velocity variations (in) as a function of angle n of the ray path in the inner core with respect to the Earthrsquos rotation axis for severalseismological models Black OIC model of Wang et al (2003) Grey OIC model of Beghein and Trampert (2003) Blue best fitting IMIC model using Wang et alrsquos model forOIC anisotropy corrections Green best fitting IMIC model using Beghein and Trampertrsquos (2003) OIC model for anisotropy corrections in the OIC In the latter two cases theIMIC radius is held at 600 km The IMIC model obtained is only slightly sensitive to the radius in the range 500ndash600 km Dashed lines indicate the range of uncertainty on theIMIC model (b) Calculated normalized P-wave velocities of hexagonal single crystals based on first principle elastic properties at various temperatures and pressures An isstrength of anisotropy The polar angle n is zero parallel to the hexagonal c-axis Mat Mattesini et al 2010 Voc Vocadlo et al (2009) Based on Romanowicz et al (2016)

82 B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90

7 Conclusions and future directions

71 Anisotropy in the deep mantle

In the last ten years global seismic tomography has providedincreasingly refined images of seismic heterogeneity in the deepEarth There is now agreement on the long wavelength structuredominated by the presence of two low shear velocity provinces(LLSVPs) under Africa and the central Pacific which may requirecompositional heterogeneity at least at their base There is alsoevidence for smaller scale structures suggestive of subductingslabs and upwelling plumes in the lower mantle While the bulkof the lower mantle appears largely isotropic the long wavelengthpattern of VTI anisotropy detected in D00 from shear wave tomo-graphic studies seems to track that of isotropic velocity with SHfaster than SV outside of the LLSVPs and SV faster than SH withinthem However the agreement among different models is limited

to the very longest wavelengths (lsquolsquodegree 200) and there are stilldebates about trade-offs between isotropic and anisotropicstructure

On the other hand recent local studies of shear wave splittingare consistently showing the presence of strong seismic anisotropy(both radial and azimuthal) at the edges of the LLSVPs primarily onthe fast side Because anisotropy in post-perovskite (pPv) isthought to be much stronger than in perovskite and pPv is likelymore widely present outside of the LLSVP (ie colder regions man-ifested by faster than average shear velocity) than inside theLLSVPs (which are likely warmer) these observations suggest thatCPO of pPv may be the cause indicating the presence of strongdeformation due to constrained flow at the base of the mantlewith a change of direction towards the vertical at the border ofthe LLSVP and more vertically oriented flow within it While veryattractive because it can also explain opposite polarity behavior inreflections of P and S waves on the discontinuity at the top of D00

B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90 83

(Thomas et al 2011 Cobden et al 2015) the interpretation interms of pPv must be considered with caution given the uncertain-ties on whether pPv is actually present at deep mantle depths

A priority for future seismic studies is to continue investigatingthe patterns of anisotropy on the borders of the LLSVPs as well as inthe vicinity of upwelling plumes where high concentrations ofstrain are expected This would be greatly helped by installationsof large aperture broadband arrays on the ocean floor collectinghigh quality horizontal component data for at least 1 year to covergaps in the available sampling of D00 in these regions We also lackrobust constraints on deep mantle P anisotropy which would helpdifferentiate between dominant (001) and (010) slip systems inpost-perovskite

Also mineral physics has added a lot of new information mostsignificantly the discovery of post-perovskite (Oganov and Ono2004) and derivation of deformation mechanisms both by experi-ments and theoretical models But as the anisotropic seismic struc-ture of the Earth has become more complex over the last ten yearsso has the interpretation with mineral physics concepts opening awide range of opportunities for new investigations Perhaps mostsignificant have been the recent advances in modeling crystaldeformation based on bonding characteristics at a wide range ofconditions that are relevant for the mantle but cannot beapproached with experiments like slow strain rates It will beimportant to apply theory to experimental conditions and thismight explain why DAC experiments at high pressure suggest(001) slip for MgSiO3 post-perovskite (Miyagi et al 2010 Wuet al 2017) while bonding models predict (010) slip at deep man-tle conditions (Goryaeva et al 2016)

High pressure experiments will remain crucial With advancesin multi-anvil technology it will become possible to reach lowermantle conditions (Yamazaki et al 2014) with larger samplesand better defined deformation geometry than DAC which isrestricted to the 50 lm range) with large gradients in pressuredeformation rates and temperature In addition D-DIA experi-ments can provide tomographic information about microstructuralevolution eg during phase transitions and recrystallization (Wanget al 2011) Also DAC technology is adding new possibilities suchas resistive heating for high temperature experiments multigraintexture analysis for coarser aggregates (eg Barton and Bernier2012 Langrand et al 2017) and the possibility of using DAC withLaue microdiffraction (Tamura 2014) to perform orientation andmicrostructural mapping in situ at high pressure

In the future also a larger range of compositions needs to beexplored experimentally for example iron-magnesium contentmultiphase systems (pPv ferropericlase and CaSiO3 perovskite)and the significance of perovskitepost-perovskite transformations

Geodynamic models need refinements New 3D models withtracers (eg Cottaar et al 2014 Li M et al 2014) still do notaccount for the very significant viscosity changes implied by min-eral physics And following texture evolution along streamlinesprovides results at different times for the advancing tracers whilerelating anisotropy results to the Earth assumes that the stream-line does not change which is clearly not the case

The issue of deformation mechanisms was addressed in Sec-tion 48 All models for lower mantle anisotropy assume disloca-tion glide of post-perovskite and ferropericlase as the cause ofcrystal alignment and use a self-consistent viscoplastic plasticitymodel Some arbitrary strain fraction corrections are introducedto account for mechanisms such as climb grain boundary migra-tion grain boundary sliding that do not contribute to texture Inthe future the significance of these mechanisms should be studiedmore systematically both with experiments and models There arestrong indications that the activity of different mechanisms is thecause for lack of significant anisotropy in large parts of the lowermantle

72 Inner core anisotropy

While the complexities of the lower mantle are developing intoa realistic and solvable puzzle inner core anisotropy is becomingmore enigmatic As we learn more about the large seismic aniso-tropy it is not clear what the origin of this signal is and how muchoriginates in the inner core There is room for many possible inter-pretations including a layered inner core with a bcc iron structurein the innermost inner core and an outer shell with an hcp struc-ture (Wang et al 2015) While such a structure is not impossibleit is quite unlikely (eg Romanowicz et al 2016) and not presentlyresolvable from seismological observations The high axial veloci-ties compared with equatorial velocities are difficult to explainand particularly the striking L-shape of the PKP travel time residualas a function of angle of the raypath in the inner core with respectto the rotation axis It is not impossible that heterogeneous struc-tures in the outer liquid core particularly columnar convectionwith a characteristic seismic pattern (eg Jones 2011 Soderlundet al 2012) influence the apparent seismic signature of the innercore A priority for future seismic studies in our view is to achieveconsensus on the origin of the observed L-shape mentioned aboveThe dense temporary broadband arrays recently installed in Alaska(as part of the Earthscope program) and in Antarctica should helpin that endeavor

On the mineral physics side there is general agreement thathexagonal close-packed iron is the most likely component butthe actual composition is still debated and an iron-silicon alloymay exist There is uncertainty and disagreement about elasticproperties of pure iron at inner core conditions derived with firstprinciples calculations (eg Vocadlo et al 2009 versus Mattesiniet al 2010) and no information about elastic properties of iron-silicon alloys While there are many experiments documentingphase relations both of Fe and Fe-Si at high pressure and temper-ature (eg Tateno et al 2010 2015) there is still considerableuncertainty about the melting temperature

These studies highlight the chemical and structural complexi-ties of the core with likely heterogeneities in the inner core vari-able elastic properties and anisotropy A multi-disciplinaryapproach including seismologists geodynamicists mineral physi-cists and material scientists is required to make progress Such col-laborations have been initiated and show great promise for thenear future

Acknowledgements

We are grateful to Mark Jellinek and Tim Horscroft for invitingus to prepare this review It was an opportunity for us to explorethe extensive literature on the subject and also to discover that alot of work remains to be done Particularly interesting was inter-action with colleagues and students at the 2016 CIDER Workshopin Santa Barbara HRW is appreciative of discussions with RainerAbart Sanne Cottaar Patrick Cordier Thorne Lay Sebastien MerkelLowell Miyagi and Kaiqing Yuan CIDER is funded through NSF(FESD grant EAR 1135452) We acknowledge support from NSF(EAR 1343908 1417229 CSEDI-106751) DOE (DE-FG02-05ER15637) CDAC We acknowledge constructive reviews by MarkJellinek and Maureen Long

References

Abart R Kunze K Milke R Sperb R Heinrich W et al 2004 Silicon and oxygenself diffusion in enstatite polycrystals the Milke (2001) rim growthexperiments revisited Contrib Mineral Petrol 147 633ndash646 httpdxdoiorg101007s00410-004-0596-9

Alfegrave D Price GD Gillan MJ 2002 Iron under Earthrsquos core conditions Liquid-state thermodynamics and high pressure melting curve from ab initio

B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90 75

tensor of the aggregate by averaging over crystal orientations andcorresponding single crystal elastic properties

44 Isotropic viscosity medium approach for lower mantle anisotropy

This type of model investigates the characteristics of a subduc-tiong cold slab descending through the lower mantle to the core-mantle boundary The model is isochemical and isotropic viscosityis assumed The calculations solve non-dimensional equations forthe conservation of mass momentum and energy using theBoussinesq approximation (McNamara et al 2003) The strain evo-lution is evaluated by inserting tracers into the isotropic convec-tive medium This strain is then used to calculate development ofpreferred orientation using the viscoplastic self-consistent method(Lebensohn and Tomeacute 1993) which was introduced in Section 32for evaluating slip systems in high pressure deformationexperiments

We will explain the general procedure for a 2D model of a sub-ducting slab into the D00 zone (Wenk et al 2011) Fig 24 (top) is asnapshot of a section of the upper mantle with downwelling coldslabs (blue) und upwelling hot plumes (red) Below (Fig 24 bot-tom) is an enlarged section of D00 extending 300 km above thecore-mantle boundary It indicates the path of some streamlinesWe are following the lowest tracer 189 Post-perovskite and fer-ropericlase are likely the main components in the cooler parts ofthe enigmatic D00 zone and texture calculations were done withsuch a 2-phase system In addition significant amounts of cubicCaSiO3 perovskite may be present but this was not considered inthis model because of relatively low anisotropy

Plasticity calculations were performed by assuming differentcombinations of dominant slip systems for pPv since there is someambiguity (Section 32 and Table 2) (100) (010) (001) (egMerkel et al 2004 2007 Miyagi et al 2010 2011 Wu et al2017 Goryaeva et al 2015 2016) They are shown in Fig 25 fordominant (001)[100] slip for pPv and dominant 110h1 1 0islip for periclase (MgO) (eg Merkel et al 2002 Miyajima et al2009) at three step increments There is moderate CPO at 1200steps but it becomes very strong at 3600 steps For periclase thereis a significant rotation of the pattern due to simple shear similarto what was observed in halite with the same crystal structure(Wenk et al 2009) The simple shear rotation is less pronouncedfor orthorhombic pPv than for cubic periclase

Below the pole figures are corresponding maps of P-velocitiesagain expressing significant rotations for periclase Post-perovskite shows very low P-velocities parallel to the core-mantle boundary For two-phase materials the combination mayadd or reduce overall anisotropy It should be mentioned that plas-ticity models assume deformation by dislocation slip At deepmantle conditions other mechanisms are likely active that do notcontribute crystal rotations such as dislocation climb grain

Fig 24 2D convection model illustrating subduction of a cold slab (blue) into the lowe(reproduced from Wenk et al 2011)

boundary sliding and to some extent dynamic recrystallizationWe will return to some of these issues in Section 45 For this cal-culation it was assumed that only half of the strain is accommo-dated by dislocation glide

Following this procedure for many streamlines we can mapanisotropic velocity patterns over the whole region of the geody-namic model Fig 26 shows five simulations one for ferropericlaseand perovskite and three for post-perovskite assuming differentdominant slip systems Only the pattern for dominant (001) dislo-cation glide of post-perovskite compares well with seismic obser-vations of fast SH waves in regions of faster than averageisotropic Vs (eg Fig 3) The anti-correlation of anisotropy in Sand P is consistent with a seismic study of the average profile withdepth of VTI parameters constrained by normal mode data(Beghein et al 2006) Perovskite was also considered but did notmatch the seismic observations One additional argument in favorof (001) slip is the strong splitting and prediction of a tilted fastaxis This is also more compatible in both direction and strengthwith the observations of splitting in Sdiff at the edge of the AfricanLLSVP (Cottaar and Romanowicz 2013)

This is an interesting example linking microscopic and macro-scopic observations Deformation mechanisms at the crystal scale(dislocations) derived from laboratory experiments predict defor-mation mechanisms and are then applied to Earth processes overlarge volumes and long time-scales Comparing the geodynamicresults with seismic observations in this case seems to confirmthe assumptions about microscopic processes ie the type of dislo-cations that are active However the interpretation relies heavilyon the very tentative seismic observation of anti-correlation of Sand P anisotropy in the deep mantle

45 Flow calculation based on a global tomographic model

This type of flow model is based on the joint inversion of globalS-wave travel times the global gravity field dynamic surfacetopography tectonic plate motions and the excess ellipticity ofthe core-mantle boundary (Walker et al 2011) A theory of viscousflow in a compressible self-gravitating spherical mantle is used tocalculate the mantle convective flow predicted on the basis of thetomographically-inferred 3D density anomalies (Mitrovica andForte 2004) Fig 27 shows a map of the horizontal flow vectors(arrows) and radial components of flow velocity (color blue nega-tive red positive) illustrating upwelling in the Pacific and in SouthAfrica for one model From the 3D mantle flow field polycrystalplasticity calculations similar to themodel discussed in Section 43are used to calculate orientation patterns and corresponding aniso-tropic elastic properties

In tomographic models of radial anisotropy in P (Boschi andDziewonski 2000) and instantaneous flow calculations globalmaps of VTI inferred from different pPv models are compared with

rmost mantle The insert illustrates some tracers and temperatures in the D00 zone

Fig 25 (001) Pole figures and P-wave velocities for three positions along tracer 189 marked on Fig Equal area projection Core-mantle boundary is horizontal

76 B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90

global seismic VTI models of D00 (Walker et al 2011) They suggesta preference for slip of dislocations on (010) or (100) and 110rather than on (001) However this preference is based on the cal-culation of correlations that are dominated by regions within theLLSVPs where in fact pPv might not be present since the LLSVPsare very likely hotter than average regions and the pPv-bridgmanite transition may occur at pressures corresponding tothe core (Fig 9b) The correlation is dominated by the centers ofthe Pacific and African LLSVP where actually one might not expect

Fig 26 D00 zone with plots of squared ratios of horizontally and vertically polarizedS waves (left side) and horizontal and vertical P-waves for different phases (ppvpost-perovskite pv perovskite and MgO) and different dominant slip systems(Wenk et al 2011)

pPv to be present (Fig 9b) Clearly further constraints on P aniso-tropy in the deep mantle are necessary to better discriminateamong possible pPv slip systems

Whereas Walker et al (2011) restricted their analysis to the VTIportion of their predicted anisotropic structure in a follow-upstudy Nowacki et al (2013) extended this approach to allow amost general form of anisotropy albeit focused on three regionsof paleo-subduction where differential S-ScS shear wave splittingmeasurements indicate the presence of azimuthal anisotropy in

Fig 27 Tomographic inversion model for mantle flow Map showing the radial(color red positive blue negative) and horizontal flow (arrows) 150 km above theCMB (from Walker et al 2011)

B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90 77

D00 Testing as previously the predictions of anisotropy from thesame flow models as in Walker et al (2011) they confirmed thatthe (010) slip system of pPv provided the best fit to the seismicdata Still only the fast axis directions were tested disregardingthe amplitude of splitting arguing that the latter may be unrealis-tically strong in plasticity calculations while imposing any scalingwould be arbitrary

We note that Ford and Long (2015) have independently testedthe seismic anisotropy predictions of the Walker et al (2011) flowmodels on a set of measurements of shear wave splitting at theeastern edge of the African LLSVP They concluded that none ofthe flow models and pPv slip system combinations provided satis-factory predictions of their dataset although when they relax con-straints on the fast axis orientations the (010) slip model isfavored

46 Compositional heterogeneities

Neither the 2D and 3D convection models nor the instantaneousflow model constrained by tomography include the presence ofthermo-chemical piles as have been hypothesized to explainLLSVPs The presence of such piles could significantly modify theflow patterns and focus deformation at the border of the pileswhich seems to be observed in some local shear wave splittingstudies (eg Fig 4) Also it appears that the lowermost mantlemay be compositionally considerably heterogeneous (eg White2015) Subduction of lithospheric slabs is a major contribution toheterogeneity including in the D00 zone (van den Berg et al2010 cf Fig 11a and b) Additional phases are likely presentamong them cubic CaSiO3 perovskite silica and perhaps metalliciron (eg Shi et al 2013) (see Fig 11) Upwelling plumes displaychemical heterogeneity and characteristic isotope signatures weredocumented at hotspots such as Hawaii (Weis et al 2011 NobreSilva et al 2013 Li Y et al 2014) but this does not explain theprevalent seismic anisotropy in the D00 zone expressed in S-wavesplitting patterns with SHgtSV (eg Table 1 Fig 3) and for thiscrystal alignment during subduction is the most obvious explana-tion at present (eg Cottaar et al 2014)

47 Viscosity changes

There are some complications that have not been taken intoaccount in any of these models Changes in viscosity do occureg during phase transformations with strong increases in thetransition zone between the upper and lower mantle (410ndash660 km) The viscosity is assumed to be low in the upper mantle(radial viscosity of reference model 011021 Pa s Becker 2006)increases in the transition zone (11021 Pa s) and then again asminerals transform to denser lower mantle phases (501021Pa s) There is considerable complexity as some slabs descend intothe lower mantle (eg Conrad and Lithgow-Bertelloni 2004)

Recently seismic heterogeneities were attributed to higher vis-cosities in the mid-mantle region (1000 km) leading to a stagna-tion of subducting slabs (Rudolph et al 2015) and this could bedue to composition (eg Bolfan-Casanova et al 2003 suggestedthat the solubility of water decreases) iron fractionation and ironspin transitions (eg Lin et al 2012 Vilella et al 2015) or changesin mechanical properties with pressure of ferropericlase (egMarquardt and Miyagi 2015) and post-perovskite (Catalli et al2009) First principle calculations of Kraych et al (2016) suggesta strong strength increase for bridgmanite with pressure(Fig 21a) and a dramatic decrease for post-perovskite (Goryaevaet al 2016 Fig 21b) The geodynamic models described here donot take changes in viscosity into account nor do they consider ani-sotropic viscosity (eg Christensen 1987)

48 Active deformation mechanisms

The models described in this section attribute anisotropy toplastic deformation of crystals by dislocation glide that inducesrotations and resulting preferred orientation In Section 32 we dis-cussed deformation mechanisms and clearly at lower mantle con-ditions other mechanisms are likely active The deformationmechanism map (Fig 13) suggests a creep regime with a combina-tion of dislocation glide and diffusional dislocation climb (egAmmann et al 2010) Also grain boundary mechanisms may beactive at low stress (eg Chen and Argon 1979) with grain bound-ary sliding grain-size reduction but there are no experimental datafor lower mantle conditions (eg Sun et al 2016 describe disclina-tions in olivine) Recent bonding calculations suggest that disloca-tion climb may dominate in olivine (Boioli et al 2015) andparticularly in bridgmanite (Boioli et al 2017) Since only glidegenerates CPO this may explain why most of the lower mantleappears isotropic To account for these other mechanisms in somegeodynamic convection models only half of the strain was attribu-ted to glide but this limit is arbitrary

Many deformation mechanism maps have been introduced forgeological systems with emphasis on the upper mantle and theinfluences of temperature pressure stress and strain rate (egHansen et al 2011 2012 Kohlstedt and Goetze 1974 Linckenset al 2011) Extrapolating results to the lower mantle is morespeculative but with new models such as Boioli et al (2017)Goryaeva et al (2016) and Kraych et al (2016) this domain maycome within reach

Another mechanism that is likely active in the deep mantle isdynamic recrystallization It has been approached with thermody-namic theory of grain growth under stress (eg Kamb 1961Paterson 1973 Green 1980 Shimizu 1999 2008 Rozel et al2011) While recrystallization can result in grain growth it moreoften produces grain size reduction which has an effect on the rhe-ology (eg De Bresser et al 2001) But evidence from materialsscience suggests that in deformed aggregates recrystallization isoften controlled by crystal defects Grains with high dislocationdensities are less stable and nucleation may occur On the otherhand a grain with low dislocation density may grow and replacea highly strained grain by grain boundary migration (egHaessner 1978) These concepts can be introduced in plasticitymodels and were able to explain orientation patterns observed inexperimentally deformed quartzite halite and ice (Wenk et al1997) and olivine (Wenk and Tomeacute 1999 Kaminski and Ribe2001) but there are too many unknown parameters to predictrecrystallization mechanisms in lower mantle rocks Oftendynamic recrystallization randomizes orientation patterns

49 Complications in polyphase systems

Perhaps the most important complication for anisotropic geo-dynamics is that the lower mantle is a system with two majorphases of different strength The interaction of these phases isnot taken into account in most polycrystal plasticity models Suchsystems are common yet there is not much work neither in mate-rial science nor geological environments and recommendationsformulated at an interdisciplinary polyphase polycrystal plasticityworkshop still apply (Breacutechet et al 1994)

Most rocks in the Earthrsquos crust and mantle are polymineralicyet most experimental and theoretical investigations were doneon monomineralic systems and for example in quartz-mica mix-tures CPO of quartz is greatly reduced compared with a purequartz aggregate (Canova et al 1992 Tullis and Wenk 1994)Under metamorphic conditions complex reactions may occur atgrain boundaries and change the fabric (eg Abart et al 2004Gaidies et al 2017)

78 B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90

In most recrystallized gneisses feldspar and quartz show barelyany preferred orientation (eg Kern et al 2008 Ullemeyer et al2006) This becomes particularly pronounced if rocks have under-gone large secondary deformation resulting in mylonites (egHandy 1994 Kern and Wenk 1990 Herwegh et al 2011Linckens et al 2011 Bercovici and Ricard 2016) In mylonites ofgranitic composition the much stronger and dominant feldsparphase barely deforms and grains tumble in the much weaker andrecrystallizing quartz phase (Fig 28) A similar microstructuremay be expected in highly deformed parts of the lower mantlewith strong bridgmanite in a matrix of weak ferropericlase(Fig 21a) and could explain the lack of significant anisotropy

For the analog system neighborite-halite Kaercher et al (2016)have documented that for single phase systems strong CPO devel-ops but for mixtures CPO is greatly reduced caused by locallyheterogeneous deformation This is also confirmed by DAC experi-ments for perovskite-ferropericlase mixtures (eg Miyagi andWenk 2016 Girard et al 2016)

For the 2-phase problem with local heterogeneities there is nostraightforward polycrystal plasticity model Canova et al (1992)have developed an n-site viscoplastic formulation and applied itto muscovite quartz mixtures There have been attempts withfinite element approaches (eg Mika and Dawson 1999) and Four-ier transform methods (eg Lebensohn 2001) but they are notapplicable to large geophysical systems at least for now and par-

Fig 28 (a) Thin section image of granite mylonite from the Santa Rosa mylonitezone in Southern California with rigid strong plagioclase crystals floating in finegrained recrystallized quartz creating a viscous matrix This represents probably asimilar microstructure as bridgmanite and periclase in the lower mantle (b) Imageof deformed quartzite with feldspar inclusions from the Bergell Alps This pervasiveductile deformation may be similar to sheared post-perovskite in the lowermostmantle Width of images is 10 mm crossed polarizers

ticularly do not account for grain boundary sliding which may bevery significant

For the D00 zone this is likely different because post-perovskiteis of similar strength or weaker than ferropericlase (Fig 21b) andthus deforms with a significant contribution of dislocation glideThe microstructure of highly strained D00 material may be moreanalogous to deformed quartzite with some feldspar inclusionsand extremely strong preferred orientation (Fig 28b)

5 Seismic anisotropy in the inner core

We conclude this review with a brief discussion about seismicanisotropy in the solid inner core While the presence of a densepossibly fluid core had been suggested long ago based on the highaverage density of the Earth as well as measurements of tides itspresence was confirmed by seismology in the early 20th century(Oldham 1906 Gutenberg 1913) An iron-nickel compositionwas assigned in analogy to iron meteorites In 1936 Inge Lehmanndiscovered the presence of an inner core of different elastic proper-ties within the fluid outer core (Lehmann 1936) Several decadeslater the solidity of the inner core was demonstrated byDziewonski and Gilbert (1971) based on the measurements ofeigenfrequencies of inner core-sensitive free oscillations Birch(1952) showed that the density of an iron-nickel alloy is too highcompared to seismological estimates and proposed the presenceof 10 of lighter elements Since then the structure and compo-sition of the core was refined based on seismic gravitational andmagnetic evidence (eg Hirose et al 2013)

The presence of cylindrical anisotropy in the inner core withthe fast axis aligned with the Earthrsquos rotation axis was first pro-posed thirty years ago to explain two types of independent seismicobservations (1) travel time anomalies of P waves that traversethe inner core (denoted PKIKP or PKP(DF)) on polar paths (ie ina direction quasi parallel to the Earthrsquos rotation axis) arriving upto 5 s earlier than those travelling on equatorial paths (Morelliet al 1986) and (2) anomalous splitting of inner core sensitive freeoscillations (Woodhouse et al 1986) Neither of these observationscould be explained by long-wavelength heterogeneous structure inthe earthrsquos mantle It was suggested that this anisotropy couldlikely be due to the alignment of intrinsically anisotropic iron crys-tals and in the following decade several models for the physicalcause of such alignment were proposed (Jeanloz and Wenk1988 Romanowicz et al 1996 Bergman 1997 Karato 1999Wenk et al 2000b Buffett and Wenk 2001 Yoshida et al 1996see review by Sumita and Bergman 2015)

In the decades since its discovery many seismic studies haveconfirmed these early observations from ever increasing datasetsleading to a current landscape of the distribution of inner core ani-sotropy that is surprisingly complex for such a small volume of theEarth (eg Tkalcic 2015) The top 100 km of the 1220 km-thickinner core have been found to be isotropic while deeper there isevidence for a hemispherical pattern of anisotropy (Tanaka andHamaguchi 1997 Creager 1999 Niu and Wen 2002 Garcia2002 Waszek et al 2011 Irving and Deuss 2011 Lythgoe et al2014) with weaker anisotropy in the eastern hemisphere than inthe western hemisphere There is also evidence for depth depen-dence with increased strength of anisotropy towards the center(Creager 1992 Vinnik et al 1994) and more recently the sugges-tion of a different orientation of anisotropy in the central part ofthe inner core (Ishii and Dziewonski 2002 Beghein andTrampert 2003) dubbed lsquolsquoInner Most Inner Corerdquo (IMIC Ishii andDziewonski 2002) The IMIC as reexamined in more recent stud-ies would have a radius of about 550 km (eg Cormier andStroujkova 2005 Cao and Romanowicz 2007 Lythgoe et al2014 Wang et al 2015 Romanowicz et al 2016) The signature

B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90 79

of a hemispherical anisotropic structure has also been found fromthe modeling of coupling of pairs of modes sensitive to such struc-ture (Deuss et al 2010) In addition regional variations in thedirection of the fast axis and strength of anisotropy have been doc-umented (eg Breacuteger et al 1999 Sun and Song 2008ab Irving2016) To explain this complexity Tkalcic (2010) suggested thatthe inner core may be made of a patchwork of anisotropic domainsof different orientations Attenuation of PKIKP waves also presentsanisotropic variations with higher attenuation correlated withearly arrivals along quasi-polar paths (Souriau and Romanowicz1996 1997 Oreshin and Vinnik 2004) We refer the reader tomore complete reviews of seismological studies of inner core ani-sotropy (Deuss 2014 Souriau 2015 Tkalcic 2015) Here webriefly describe some of the seismological challenges that are stillpreventing us from a full understanding of these intriguingobservations

One of the main challenges in fully resolving the pattern ofinner core anisotropy is the poor directional sampling availabledue to the limited distribution of sources and receivers in polarregions (eg Tkalcic 2015) Thus paths sampling the inner coreat a given location from different directions which is necessaryto confirm the presence of anisotropy are frequently lacking mak-ing it difficult to image inner core anisotropy in three dimensionswithout imposing strong a priori-constraints (eg Sun and Song2008a Lythgoe et al 2014) The strongest anisotropy in PKIKPdata is found primarily along paths from events in South SandwichIslands (SSI) to Alaska which dominate the set of observations inthe strongly anisotropic western hemisphere that contribute tothe n angle range between 10-30o where n is the angle of the ray-path in the inner core with the Earthrsquos axis of rotation At shorterdistances (lt155) the PKP(DF) phase can be referred to PKP(BC) which is a core phase that does not traverse the inner core(Fig 29) This makes it possible to eliminate contributions fromuncertainties in the source parameters as well as a significant partof the effects of 3D mantle structure given that PKP(BC) and PKP

Fig 29 Raypaths of main body wave phases used in the study of inner-corestructure and anisotropy at an epicentral distance of 155o At this distance all threecore phases PKIKP (also called PKP(DF)) PKP(BC) and PKP(AB) are observed Thephase PKJKP (a shear wave in the inner core) is very difficult to observe and isplotted here only for reference

(DF) have very similar paths throughout the mantle diverging onlyin the vicinity of the inner core

In fact the SSI dataset shows a wide range of travel timeanomalies ranging from 0 to gt5 s when referred to the PKP(BC)phase suggesting a strong local anomaly (eg Tkalcic et al2002) When plotted as a function of the angle n the global PKP(BC)-PKP(DF) travel time dataset (which covers epicentral dis-tances between 150o and 160) forms an L-shaped curve which isnot well explained by best fitting simple models of inner core ani-sotropy with fast axis aligned with the Earthrsquos rotation axis(Fig 30) for which one would expect a parabolic shape accordingto the equation

dt frac14 athorn bcos2nthorn ccos4n

where a b c are related to integrals of elastic anisotropic parame-ters along the path in the inner core

At larger distances the reference outer core phase is PKP(AB)which spends significant time in the highly heterogeneous D00

region at the base of the mantle Therefore absolute travel timeanomalies of PKP(DF) are preferred although in that case contri-butions from mantle 3D structure and uncertainties in sourceparameters can bias the data (eg Breacuteger et al 2000) Most studieswill therefore only consider events from the high quality relocatedEHB catalog (Engdahl et al 1998) which presently exists onlythrough 2010 Still analysis of these PKP(DF) data indicate thatin the western hemisphere a similar trend is observed in the abso-lute PKP(DF) travel time residuals as in the PKP(DF)-PKP(AB) resid-uals as a function of angle n (Fig 30b) Most recent estimates of thecorresponding anisotropy are on the order of 3ndash4 in the IMICwhich is considerable and difficult to reconcile with current pre-dictions from mineral physics (see Section 6) let alone the esti-mate of 3ndash88 of Lythgoe et al (2014)

To explain this trend and other aspects of complexity in traveltime measurements of core sensitive phases that cannot beexplained by mantle structure Romanowicz et al (2003) proposedalternative models that would involve structure in the outer corewith either faster than average velocities in the inner core tangentcylinder or in polar caps at the top of the outer core that couldrepresent an increased concentration of light elements For exam-ple Fig 31 shows the pattern obtained when plotting absolutetravel time anomalies for DFBC and AB plotted at the entry pointof the corresponding raypath into the outer core on the Alaskaside for south-Sandwich to Alaska paths as well as paths fromAlaska to Antarctica When plotted in this manner the travel-time anomalies form a coherent pattern suggesting a localizedanomaly that may originate near the core-mantle boundary onthe Alaska side compatible with both a polar cap in the outer coreor heterogeneity within at least part of the tangent cylinder Mostanomalously split inner core sensitive normal modes could beexplained by either of these models except for mode 3S2 whichexhibits particularly strong splitting (Romanowicz and Breacuteger2000) These results have been reexamined critically by Ishii andDziewonski (2005)

Putting structure in the outer core remains controversial (egSouriau et al 2003) as significant density anomalies in the vigor-ously convecting outer core appear to be ruled out (eg Stevenson1987) However recent work suggesting the possibility of stagnantlayers at the top of the outer core from magneto-hydrodynamicsconsiderations (eg Buffett 2014) indicates that at least the polarcap hypothesis should perhaps remain on the table as alternativeto a strongly anisotropic region in the inner core On the otherhand Tkalcic (2010) found that differential travel time anomaliesof similar amplitude are observed on PcP-P data in the vicinity ofSSI Because such data do not sample the inner core at all Tkalcic(2010) proposed that a significant part of the SSI anomaly could

Fig 30 Travel time anomalies of core phases as a function of angle n of the ray path in the inner core with respect to the Earthrsquos rotation axis from the combined Berkeleydata collection (Tkalcic et al 2002) and from Leykam et al (2010) Left (DFndashBC) ndash Right absolute DF a) and d) all data b) and e) for events in the south-Sandwich Islands c)and f) for events in Alaska

80 B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90

be located in the deep mantle although no such structure has beenidentified yet tomographically Therefore explaining the broadspread of PKP(DF) travel time anomalies on SSI paths to Alaskaremains an open question which needs to be answered beforerobust bounds on the strength of anisotropy in the inner corersquoswestern hemisphere can be provided to mineral physicists Accu-mulation of data from the current deployment of USArray in Alaskamay shed more light on this question

This leads us to the second and possibly related challenge thathas come to light recently (Lincot et al 2015 2016 Romanowiczet al 2016) which is how to reconcile the 3ndash8 seismic anisotropyinferred in the inner corersquos western hemisphere with currentknowledge from mineral physics

6 Mineral physics of the inner core

61 Phase relations

From the mineral physics point of view a first order questionhas been the phase in which iron is present in the inner coreThe high pressure e phase of iron was first confirmed by X-raydiffraction by Mao et al (1967) and a hexagonal close-packed(hcp) structure was identified Since then many high pressureexperiments have been conducted Most important are those per-tinent to conditions of the inner core (Fig 32) They includedynamic shock compression with relatively large error margins(eg Alfegrave et al 2002 Anzellini et al 2013 Brown 2001 Ping

Fig 31 Absolute travel time anomalies for DF (circles and triangles) BC (crosses)and AB (squares) for events at latitudes lower than 50S or higher than 50Nplotted as a function of the location of the entry point of the ray path into the outercore Triangles are for events at latitude gt50N observed at stations at latitudeslt50S Expanded from Romanowicz et al (2003) to include data from Leykamet al (2010) as also shown in Fig 34bndashf This collection of travel time anomaliesforms a coherent pattern with a sharp gradient delineating a localized boundarybetween very fast paths to the northwest and normal paths to the southeastsuggesting a lsquolsquopolar caprdquo pattern that may or may not originate in the inner coreNote that the color code is centered at dt = 35 s

Fig 32 Pressurendashtemperature phase diagram for iron at high pressure illustratingdiamond anvil and shock experiments as well as ab initio simulations The linescorrespond to melting curves (courtesy of BK Godwal)

B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90 81

et al 2013) and DAC experiments at high pressure and tempera-ture up to 380 GPa and 6000 K (eg Tateno et al 2010) Basedon theoretical calculations some authors have suggested thatbody-centered cubic (bcc) iron could be stable just below the melt-ing point at core pressures (eg Vocadlo et al 2003 Belonoshkoet al 2003 2006 Dubrovinsky et al 2007 Bouchet et al 2013)but most recent studies indicate that bcc is unstable at these con-ditions (eg Godwal et al 2015)

An important aspect is that the inner core may not be chemi-cally and structurally homogeneous It is likely that nickel a com-ponent in iron meteorites is also present in the core (Sakai et al2011 Tateno et al 2012) Furthermore to account for the lowerdensity implied by seismic data suggests that lighter elementsmay be present and a good candidate is silicon The Fe-Si systemhas been studied at intermediate pressure-temperatures (egSakai et al 2011 Fischer et al 2013 Fig 33) and inner core con-ditions (Tateno et al 2015) At high pressure and high tempera-ture FeSi crystallizes in the cubic B2 structure (CsCl structure)which is an ordered bcc structure Fe3Si forms a DO3 structure withdoubling of the B2 unit cell and ordering At lower pressures FeSiforms the B20 structure which is partially disordered bcc with alack of inversion symmetry (eg Jeong and Pickett 2004) Elasticproperties of FeSi have been investigated by Petrova et al (2010)Badro et al (2014) explored a range of possible elements in thecore (O S Si Ni) and concluded that oxygen is required in the outercore

62 Causes of anisotropy in the inner core

Potential mechanisms for alignment of crystals in the inner coreare dislocation-plasticity (eg Jeanloz andWenk 1988 Wenk et al2000a Lincot et al 2015 2016) growth from a melt (eg Bergman1997 Deguen 2012) magnetic Maxwell stresses (eg Karato1999 Buffett and Wenk 2001)

Radial DAC experiments (eg Wenk et al 2000a Merkel et al2004 2013 Miyagi et al 2008) documented texture developmentin e iron at high pressure and inferred (0001) and subordinatef11 20g slip combined with mechanical twinning as potentialmechanisms However these experiments were not at inner coreconditions

Elastic properties at core conditions rely on first principle calcu-lations and various groups have been involved (eg Vocadlo et al2008 2009 Mattesini et al 2010) It is interesting to find thatresults are quite contradictory as expressed in P-wave velocityprofiles for hcp single crystals with the c-axis at n = 0 (Fig 34b)While Vocadlo et al (2009) predict maximum velocities perpendic-ular to the c-axis Mattesini et al (2010) suggest maximum veloc-ities parallel to the c-axis (the elastic tensor of hexagonal crystals isaxially symmetric about the c-axis) Estimates of inner core seismicanisotropy are very high ((Vp-fast Vp-slow)Vp-iso = 3ndash8 Fig 34a)compared with the rather small P-wave anisotropy obtained fromfirst principles calculations for single crystals (eg 49 for Vocadloet al 2009 at 308 GPa and 5000 K or 57 for Mattesini et al 2010at 346 GPa and 6000 K) and the best fit with seismic data would bea hexagonal single crystal aligned with the c-axis more or less par-allel to the N-S axis A huge single crystal seems unlikely giventhat the largest documented crystals on Earth are about 20 m insize and with pressurendashtemperature gradients it is likely thathuge crystals at high temperature would undergo transformationsand recrystallization over geologic times

A recent study (Lincot et al 2016) constructed a multi-scalemodel combining self-consistent polycrystal plasticity inner-core formation models and Monte Carlo simulations of elasticparameters to predict travel times of inner core PKP waves andconfront them with observations These authors found that theycould explain as much as 3 seismic anisotropy with an hcp-ironstructure with fast c axis and with anomalous single crystal aniso-tropies near the melting point of up to 20 (Martorell et al 2013)with dominant pyramidal hc + ai slip and crystal alignment pro-vided by a low degree boundary condition for crystallization atthe ICB While this model might account for the faster PKP traveltimes on polar compared to equatorial paths it does not reproducethe L-shaped travel time anomaly curve as a function of angle n(Fig 30)

Fig 33 Phase diagrams of the Fe-Si system (Fischer et al 2013) (a) Pressurendashtemperature phase diagram illustrating stability fields of the various phases for Fe-9Si (b)Temperature-composition diagram at 145 GPa illustrating the transition from hcp to B2

Fig 34 (a) Comparison of relative velocity variations (in) as a function of angle n of the ray path in the inner core with respect to the Earthrsquos rotation axis for severalseismological models Black OIC model of Wang et al (2003) Grey OIC model of Beghein and Trampert (2003) Blue best fitting IMIC model using Wang et alrsquos model forOIC anisotropy corrections Green best fitting IMIC model using Beghein and Trampertrsquos (2003) OIC model for anisotropy corrections in the OIC In the latter two cases theIMIC radius is held at 600 km The IMIC model obtained is only slightly sensitive to the radius in the range 500ndash600 km Dashed lines indicate the range of uncertainty on theIMIC model (b) Calculated normalized P-wave velocities of hexagonal single crystals based on first principle elastic properties at various temperatures and pressures An isstrength of anisotropy The polar angle n is zero parallel to the hexagonal c-axis Mat Mattesini et al 2010 Voc Vocadlo et al (2009) Based on Romanowicz et al (2016)

82 B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90

7 Conclusions and future directions

71 Anisotropy in the deep mantle

In the last ten years global seismic tomography has providedincreasingly refined images of seismic heterogeneity in the deepEarth There is now agreement on the long wavelength structuredominated by the presence of two low shear velocity provinces(LLSVPs) under Africa and the central Pacific which may requirecompositional heterogeneity at least at their base There is alsoevidence for smaller scale structures suggestive of subductingslabs and upwelling plumes in the lower mantle While the bulkof the lower mantle appears largely isotropic the long wavelengthpattern of VTI anisotropy detected in D00 from shear wave tomo-graphic studies seems to track that of isotropic velocity with SHfaster than SV outside of the LLSVPs and SV faster than SH withinthem However the agreement among different models is limited

to the very longest wavelengths (lsquolsquodegree 200) and there are stilldebates about trade-offs between isotropic and anisotropicstructure

On the other hand recent local studies of shear wave splittingare consistently showing the presence of strong seismic anisotropy(both radial and azimuthal) at the edges of the LLSVPs primarily onthe fast side Because anisotropy in post-perovskite (pPv) isthought to be much stronger than in perovskite and pPv is likelymore widely present outside of the LLSVP (ie colder regions man-ifested by faster than average shear velocity) than inside theLLSVPs (which are likely warmer) these observations suggest thatCPO of pPv may be the cause indicating the presence of strongdeformation due to constrained flow at the base of the mantlewith a change of direction towards the vertical at the border ofthe LLSVP and more vertically oriented flow within it While veryattractive because it can also explain opposite polarity behavior inreflections of P and S waves on the discontinuity at the top of D00

B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90 83

(Thomas et al 2011 Cobden et al 2015) the interpretation interms of pPv must be considered with caution given the uncertain-ties on whether pPv is actually present at deep mantle depths

A priority for future seismic studies is to continue investigatingthe patterns of anisotropy on the borders of the LLSVPs as well as inthe vicinity of upwelling plumes where high concentrations ofstrain are expected This would be greatly helped by installationsof large aperture broadband arrays on the ocean floor collectinghigh quality horizontal component data for at least 1 year to covergaps in the available sampling of D00 in these regions We also lackrobust constraints on deep mantle P anisotropy which would helpdifferentiate between dominant (001) and (010) slip systems inpost-perovskite

Also mineral physics has added a lot of new information mostsignificantly the discovery of post-perovskite (Oganov and Ono2004) and derivation of deformation mechanisms both by experi-ments and theoretical models But as the anisotropic seismic struc-ture of the Earth has become more complex over the last ten yearsso has the interpretation with mineral physics concepts opening awide range of opportunities for new investigations Perhaps mostsignificant have been the recent advances in modeling crystaldeformation based on bonding characteristics at a wide range ofconditions that are relevant for the mantle but cannot beapproached with experiments like slow strain rates It will beimportant to apply theory to experimental conditions and thismight explain why DAC experiments at high pressure suggest(001) slip for MgSiO3 post-perovskite (Miyagi et al 2010 Wuet al 2017) while bonding models predict (010) slip at deep man-tle conditions (Goryaeva et al 2016)

High pressure experiments will remain crucial With advancesin multi-anvil technology it will become possible to reach lowermantle conditions (Yamazaki et al 2014) with larger samplesand better defined deformation geometry than DAC which isrestricted to the 50 lm range) with large gradients in pressuredeformation rates and temperature In addition D-DIA experi-ments can provide tomographic information about microstructuralevolution eg during phase transitions and recrystallization (Wanget al 2011) Also DAC technology is adding new possibilities suchas resistive heating for high temperature experiments multigraintexture analysis for coarser aggregates (eg Barton and Bernier2012 Langrand et al 2017) and the possibility of using DAC withLaue microdiffraction (Tamura 2014) to perform orientation andmicrostructural mapping in situ at high pressure

In the future also a larger range of compositions needs to beexplored experimentally for example iron-magnesium contentmultiphase systems (pPv ferropericlase and CaSiO3 perovskite)and the significance of perovskitepost-perovskite transformations

Geodynamic models need refinements New 3D models withtracers (eg Cottaar et al 2014 Li M et al 2014) still do notaccount for the very significant viscosity changes implied by min-eral physics And following texture evolution along streamlinesprovides results at different times for the advancing tracers whilerelating anisotropy results to the Earth assumes that the stream-line does not change which is clearly not the case

The issue of deformation mechanisms was addressed in Sec-tion 48 All models for lower mantle anisotropy assume disloca-tion glide of post-perovskite and ferropericlase as the cause ofcrystal alignment and use a self-consistent viscoplastic plasticitymodel Some arbitrary strain fraction corrections are introducedto account for mechanisms such as climb grain boundary migra-tion grain boundary sliding that do not contribute to texture Inthe future the significance of these mechanisms should be studiedmore systematically both with experiments and models There arestrong indications that the activity of different mechanisms is thecause for lack of significant anisotropy in large parts of the lowermantle

72 Inner core anisotropy

While the complexities of the lower mantle are developing intoa realistic and solvable puzzle inner core anisotropy is becomingmore enigmatic As we learn more about the large seismic aniso-tropy it is not clear what the origin of this signal is and how muchoriginates in the inner core There is room for many possible inter-pretations including a layered inner core with a bcc iron structurein the innermost inner core and an outer shell with an hcp struc-ture (Wang et al 2015) While such a structure is not impossibleit is quite unlikely (eg Romanowicz et al 2016) and not presentlyresolvable from seismological observations The high axial veloci-ties compared with equatorial velocities are difficult to explainand particularly the striking L-shape of the PKP travel time residualas a function of angle of the raypath in the inner core with respectto the rotation axis It is not impossible that heterogeneous struc-tures in the outer liquid core particularly columnar convectionwith a characteristic seismic pattern (eg Jones 2011 Soderlundet al 2012) influence the apparent seismic signature of the innercore A priority for future seismic studies in our view is to achieveconsensus on the origin of the observed L-shape mentioned aboveThe dense temporary broadband arrays recently installed in Alaska(as part of the Earthscope program) and in Antarctica should helpin that endeavor

On the mineral physics side there is general agreement thathexagonal close-packed iron is the most likely component butthe actual composition is still debated and an iron-silicon alloymay exist There is uncertainty and disagreement about elasticproperties of pure iron at inner core conditions derived with firstprinciples calculations (eg Vocadlo et al 2009 versus Mattesiniet al 2010) and no information about elastic properties of iron-silicon alloys While there are many experiments documentingphase relations both of Fe and Fe-Si at high pressure and temper-ature (eg Tateno et al 2010 2015) there is still considerableuncertainty about the melting temperature

These studies highlight the chemical and structural complexi-ties of the core with likely heterogeneities in the inner core vari-able elastic properties and anisotropy A multi-disciplinaryapproach including seismologists geodynamicists mineral physi-cists and material scientists is required to make progress Such col-laborations have been initiated and show great promise for thenear future

Acknowledgements

We are grateful to Mark Jellinek and Tim Horscroft for invitingus to prepare this review It was an opportunity for us to explorethe extensive literature on the subject and also to discover that alot of work remains to be done Particularly interesting was inter-action with colleagues and students at the 2016 CIDER Workshopin Santa Barbara HRW is appreciative of discussions with RainerAbart Sanne Cottaar Patrick Cordier Thorne Lay Sebastien MerkelLowell Miyagi and Kaiqing Yuan CIDER is funded through NSF(FESD grant EAR 1135452) We acknowledge support from NSF(EAR 1343908 1417229 CSEDI-106751) DOE (DE-FG02-05ER15637) CDAC We acknowledge constructive reviews by MarkJellinek and Maureen Long

References

Abart R Kunze K Milke R Sperb R Heinrich W et al 2004 Silicon and oxygenself diffusion in enstatite polycrystals the Milke (2001) rim growthexperiments revisited Contrib Mineral Petrol 147 633ndash646 httpdxdoiorg101007s00410-004-0596-9

Alfegrave D Price GD Gillan MJ 2002 Iron under Earthrsquos core conditions Liquid-state thermodynamics and high pressure melting curve from ab initio

Fig 25 (001) Pole figures and P-wave velocities for three positions along tracer 189 marked on Fig Equal area projection Core-mantle boundary is horizontal

76 B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90

global seismic VTI models of D00 (Walker et al 2011) They suggesta preference for slip of dislocations on (010) or (100) and 110rather than on (001) However this preference is based on the cal-culation of correlations that are dominated by regions within theLLSVPs where in fact pPv might not be present since the LLSVPsare very likely hotter than average regions and the pPv-bridgmanite transition may occur at pressures corresponding tothe core (Fig 9b) The correlation is dominated by the centers ofthe Pacific and African LLSVP where actually one might not expect

Fig 26 D00 zone with plots of squared ratios of horizontally and vertically polarizedS waves (left side) and horizontal and vertical P-waves for different phases (ppvpost-perovskite pv perovskite and MgO) and different dominant slip systems(Wenk et al 2011)

pPv to be present (Fig 9b) Clearly further constraints on P aniso-tropy in the deep mantle are necessary to better discriminateamong possible pPv slip systems

Whereas Walker et al (2011) restricted their analysis to the VTIportion of their predicted anisotropic structure in a follow-upstudy Nowacki et al (2013) extended this approach to allow amost general form of anisotropy albeit focused on three regionsof paleo-subduction where differential S-ScS shear wave splittingmeasurements indicate the presence of azimuthal anisotropy in

Fig 27 Tomographic inversion model for mantle flow Map showing the radial(color red positive blue negative) and horizontal flow (arrows) 150 km above theCMB (from Walker et al 2011)

B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90 77

D00 Testing as previously the predictions of anisotropy from thesame flow models as in Walker et al (2011) they confirmed thatthe (010) slip system of pPv provided the best fit to the seismicdata Still only the fast axis directions were tested disregardingthe amplitude of splitting arguing that the latter may be unrealis-tically strong in plasticity calculations while imposing any scalingwould be arbitrary

We note that Ford and Long (2015) have independently testedthe seismic anisotropy predictions of the Walker et al (2011) flowmodels on a set of measurements of shear wave splitting at theeastern edge of the African LLSVP They concluded that none ofthe flow models and pPv slip system combinations provided satis-factory predictions of their dataset although when they relax con-straints on the fast axis orientations the (010) slip model isfavored

46 Compositional heterogeneities

Neither the 2D and 3D convection models nor the instantaneousflow model constrained by tomography include the presence ofthermo-chemical piles as have been hypothesized to explainLLSVPs The presence of such piles could significantly modify theflow patterns and focus deformation at the border of the pileswhich seems to be observed in some local shear wave splittingstudies (eg Fig 4) Also it appears that the lowermost mantlemay be compositionally considerably heterogeneous (eg White2015) Subduction of lithospheric slabs is a major contribution toheterogeneity including in the D00 zone (van den Berg et al2010 cf Fig 11a and b) Additional phases are likely presentamong them cubic CaSiO3 perovskite silica and perhaps metalliciron (eg Shi et al 2013) (see Fig 11) Upwelling plumes displaychemical heterogeneity and characteristic isotope signatures weredocumented at hotspots such as Hawaii (Weis et al 2011 NobreSilva et al 2013 Li Y et al 2014) but this does not explain theprevalent seismic anisotropy in the D00 zone expressed in S-wavesplitting patterns with SHgtSV (eg Table 1 Fig 3) and for thiscrystal alignment during subduction is the most obvious explana-tion at present (eg Cottaar et al 2014)

47 Viscosity changes

There are some complications that have not been taken intoaccount in any of these models Changes in viscosity do occureg during phase transformations with strong increases in thetransition zone between the upper and lower mantle (410ndash660 km) The viscosity is assumed to be low in the upper mantle(radial viscosity of reference model 011021 Pa s Becker 2006)increases in the transition zone (11021 Pa s) and then again asminerals transform to denser lower mantle phases (501021Pa s) There is considerable complexity as some slabs descend intothe lower mantle (eg Conrad and Lithgow-Bertelloni 2004)

Recently seismic heterogeneities were attributed to higher vis-cosities in the mid-mantle region (1000 km) leading to a stagna-tion of subducting slabs (Rudolph et al 2015) and this could bedue to composition (eg Bolfan-Casanova et al 2003 suggestedthat the solubility of water decreases) iron fractionation and ironspin transitions (eg Lin et al 2012 Vilella et al 2015) or changesin mechanical properties with pressure of ferropericlase (egMarquardt and Miyagi 2015) and post-perovskite (Catalli et al2009) First principle calculations of Kraych et al (2016) suggesta strong strength increase for bridgmanite with pressure(Fig 21a) and a dramatic decrease for post-perovskite (Goryaevaet al 2016 Fig 21b) The geodynamic models described here donot take changes in viscosity into account nor do they consider ani-sotropic viscosity (eg Christensen 1987)

48 Active deformation mechanisms

The models described in this section attribute anisotropy toplastic deformation of crystals by dislocation glide that inducesrotations and resulting preferred orientation In Section 32 we dis-cussed deformation mechanisms and clearly at lower mantle con-ditions other mechanisms are likely active The deformationmechanism map (Fig 13) suggests a creep regime with a combina-tion of dislocation glide and diffusional dislocation climb (egAmmann et al 2010) Also grain boundary mechanisms may beactive at low stress (eg Chen and Argon 1979) with grain bound-ary sliding grain-size reduction but there are no experimental datafor lower mantle conditions (eg Sun et al 2016 describe disclina-tions in olivine) Recent bonding calculations suggest that disloca-tion climb may dominate in olivine (Boioli et al 2015) andparticularly in bridgmanite (Boioli et al 2017) Since only glidegenerates CPO this may explain why most of the lower mantleappears isotropic To account for these other mechanisms in somegeodynamic convection models only half of the strain was attribu-ted to glide but this limit is arbitrary

Many deformation mechanism maps have been introduced forgeological systems with emphasis on the upper mantle and theinfluences of temperature pressure stress and strain rate (egHansen et al 2011 2012 Kohlstedt and Goetze 1974 Linckenset al 2011) Extrapolating results to the lower mantle is morespeculative but with new models such as Boioli et al (2017)Goryaeva et al (2016) and Kraych et al (2016) this domain maycome within reach

Another mechanism that is likely active in the deep mantle isdynamic recrystallization It has been approached with thermody-namic theory of grain growth under stress (eg Kamb 1961Paterson 1973 Green 1980 Shimizu 1999 2008 Rozel et al2011) While recrystallization can result in grain growth it moreoften produces grain size reduction which has an effect on the rhe-ology (eg De Bresser et al 2001) But evidence from materialsscience suggests that in deformed aggregates recrystallization isoften controlled by crystal defects Grains with high dislocationdensities are less stable and nucleation may occur On the otherhand a grain with low dislocation density may grow and replacea highly strained grain by grain boundary migration (egHaessner 1978) These concepts can be introduced in plasticitymodels and were able to explain orientation patterns observed inexperimentally deformed quartzite halite and ice (Wenk et al1997) and olivine (Wenk and Tomeacute 1999 Kaminski and Ribe2001) but there are too many unknown parameters to predictrecrystallization mechanisms in lower mantle rocks Oftendynamic recrystallization randomizes orientation patterns

49 Complications in polyphase systems

Perhaps the most important complication for anisotropic geo-dynamics is that the lower mantle is a system with two majorphases of different strength The interaction of these phases isnot taken into account in most polycrystal plasticity models Suchsystems are common yet there is not much work neither in mate-rial science nor geological environments and recommendationsformulated at an interdisciplinary polyphase polycrystal plasticityworkshop still apply (Breacutechet et al 1994)

Most rocks in the Earthrsquos crust and mantle are polymineralicyet most experimental and theoretical investigations were doneon monomineralic systems and for example in quartz-mica mix-tures CPO of quartz is greatly reduced compared with a purequartz aggregate (Canova et al 1992 Tullis and Wenk 1994)Under metamorphic conditions complex reactions may occur atgrain boundaries and change the fabric (eg Abart et al 2004Gaidies et al 2017)

78 B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90

In most recrystallized gneisses feldspar and quartz show barelyany preferred orientation (eg Kern et al 2008 Ullemeyer et al2006) This becomes particularly pronounced if rocks have under-gone large secondary deformation resulting in mylonites (egHandy 1994 Kern and Wenk 1990 Herwegh et al 2011Linckens et al 2011 Bercovici and Ricard 2016) In mylonites ofgranitic composition the much stronger and dominant feldsparphase barely deforms and grains tumble in the much weaker andrecrystallizing quartz phase (Fig 28) A similar microstructuremay be expected in highly deformed parts of the lower mantlewith strong bridgmanite in a matrix of weak ferropericlase(Fig 21a) and could explain the lack of significant anisotropy

For the analog system neighborite-halite Kaercher et al (2016)have documented that for single phase systems strong CPO devel-ops but for mixtures CPO is greatly reduced caused by locallyheterogeneous deformation This is also confirmed by DAC experi-ments for perovskite-ferropericlase mixtures (eg Miyagi andWenk 2016 Girard et al 2016)

For the 2-phase problem with local heterogeneities there is nostraightforward polycrystal plasticity model Canova et al (1992)have developed an n-site viscoplastic formulation and applied itto muscovite quartz mixtures There have been attempts withfinite element approaches (eg Mika and Dawson 1999) and Four-ier transform methods (eg Lebensohn 2001) but they are notapplicable to large geophysical systems at least for now and par-

Fig 28 (a) Thin section image of granite mylonite from the Santa Rosa mylonitezone in Southern California with rigid strong plagioclase crystals floating in finegrained recrystallized quartz creating a viscous matrix This represents probably asimilar microstructure as bridgmanite and periclase in the lower mantle (b) Imageof deformed quartzite with feldspar inclusions from the Bergell Alps This pervasiveductile deformation may be similar to sheared post-perovskite in the lowermostmantle Width of images is 10 mm crossed polarizers

ticularly do not account for grain boundary sliding which may bevery significant

For the D00 zone this is likely different because post-perovskiteis of similar strength or weaker than ferropericlase (Fig 21b) andthus deforms with a significant contribution of dislocation glideThe microstructure of highly strained D00 material may be moreanalogous to deformed quartzite with some feldspar inclusionsand extremely strong preferred orientation (Fig 28b)

5 Seismic anisotropy in the inner core

We conclude this review with a brief discussion about seismicanisotropy in the solid inner core While the presence of a densepossibly fluid core had been suggested long ago based on the highaverage density of the Earth as well as measurements of tides itspresence was confirmed by seismology in the early 20th century(Oldham 1906 Gutenberg 1913) An iron-nickel compositionwas assigned in analogy to iron meteorites In 1936 Inge Lehmanndiscovered the presence of an inner core of different elastic proper-ties within the fluid outer core (Lehmann 1936) Several decadeslater the solidity of the inner core was demonstrated byDziewonski and Gilbert (1971) based on the measurements ofeigenfrequencies of inner core-sensitive free oscillations Birch(1952) showed that the density of an iron-nickel alloy is too highcompared to seismological estimates and proposed the presenceof 10 of lighter elements Since then the structure and compo-sition of the core was refined based on seismic gravitational andmagnetic evidence (eg Hirose et al 2013)

The presence of cylindrical anisotropy in the inner core withthe fast axis aligned with the Earthrsquos rotation axis was first pro-posed thirty years ago to explain two types of independent seismicobservations (1) travel time anomalies of P waves that traversethe inner core (denoted PKIKP or PKP(DF)) on polar paths (ie ina direction quasi parallel to the Earthrsquos rotation axis) arriving upto 5 s earlier than those travelling on equatorial paths (Morelliet al 1986) and (2) anomalous splitting of inner core sensitive freeoscillations (Woodhouse et al 1986) Neither of these observationscould be explained by long-wavelength heterogeneous structure inthe earthrsquos mantle It was suggested that this anisotropy couldlikely be due to the alignment of intrinsically anisotropic iron crys-tals and in the following decade several models for the physicalcause of such alignment were proposed (Jeanloz and Wenk1988 Romanowicz et al 1996 Bergman 1997 Karato 1999Wenk et al 2000b Buffett and Wenk 2001 Yoshida et al 1996see review by Sumita and Bergman 2015)

In the decades since its discovery many seismic studies haveconfirmed these early observations from ever increasing datasetsleading to a current landscape of the distribution of inner core ani-sotropy that is surprisingly complex for such a small volume of theEarth (eg Tkalcic 2015) The top 100 km of the 1220 km-thickinner core have been found to be isotropic while deeper there isevidence for a hemispherical pattern of anisotropy (Tanaka andHamaguchi 1997 Creager 1999 Niu and Wen 2002 Garcia2002 Waszek et al 2011 Irving and Deuss 2011 Lythgoe et al2014) with weaker anisotropy in the eastern hemisphere than inthe western hemisphere There is also evidence for depth depen-dence with increased strength of anisotropy towards the center(Creager 1992 Vinnik et al 1994) and more recently the sugges-tion of a different orientation of anisotropy in the central part ofthe inner core (Ishii and Dziewonski 2002 Beghein andTrampert 2003) dubbed lsquolsquoInner Most Inner Corerdquo (IMIC Ishii andDziewonski 2002) The IMIC as reexamined in more recent stud-ies would have a radius of about 550 km (eg Cormier andStroujkova 2005 Cao and Romanowicz 2007 Lythgoe et al2014 Wang et al 2015 Romanowicz et al 2016) The signature

B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90 79

of a hemispherical anisotropic structure has also been found fromthe modeling of coupling of pairs of modes sensitive to such struc-ture (Deuss et al 2010) In addition regional variations in thedirection of the fast axis and strength of anisotropy have been doc-umented (eg Breacuteger et al 1999 Sun and Song 2008ab Irving2016) To explain this complexity Tkalcic (2010) suggested thatthe inner core may be made of a patchwork of anisotropic domainsof different orientations Attenuation of PKIKP waves also presentsanisotropic variations with higher attenuation correlated withearly arrivals along quasi-polar paths (Souriau and Romanowicz1996 1997 Oreshin and Vinnik 2004) We refer the reader tomore complete reviews of seismological studies of inner core ani-sotropy (Deuss 2014 Souriau 2015 Tkalcic 2015) Here webriefly describe some of the seismological challenges that are stillpreventing us from a full understanding of these intriguingobservations

One of the main challenges in fully resolving the pattern ofinner core anisotropy is the poor directional sampling availabledue to the limited distribution of sources and receivers in polarregions (eg Tkalcic 2015) Thus paths sampling the inner coreat a given location from different directions which is necessaryto confirm the presence of anisotropy are frequently lacking mak-ing it difficult to image inner core anisotropy in three dimensionswithout imposing strong a priori-constraints (eg Sun and Song2008a Lythgoe et al 2014) The strongest anisotropy in PKIKPdata is found primarily along paths from events in South SandwichIslands (SSI) to Alaska which dominate the set of observations inthe strongly anisotropic western hemisphere that contribute tothe n angle range between 10-30o where n is the angle of the ray-path in the inner core with the Earthrsquos axis of rotation At shorterdistances (lt155) the PKP(DF) phase can be referred to PKP(BC) which is a core phase that does not traverse the inner core(Fig 29) This makes it possible to eliminate contributions fromuncertainties in the source parameters as well as a significant partof the effects of 3D mantle structure given that PKP(BC) and PKP

Fig 29 Raypaths of main body wave phases used in the study of inner-corestructure and anisotropy at an epicentral distance of 155o At this distance all threecore phases PKIKP (also called PKP(DF)) PKP(BC) and PKP(AB) are observed Thephase PKJKP (a shear wave in the inner core) is very difficult to observe and isplotted here only for reference

(DF) have very similar paths throughout the mantle diverging onlyin the vicinity of the inner core

In fact the SSI dataset shows a wide range of travel timeanomalies ranging from 0 to gt5 s when referred to the PKP(BC)phase suggesting a strong local anomaly (eg Tkalcic et al2002) When plotted as a function of the angle n the global PKP(BC)-PKP(DF) travel time dataset (which covers epicentral dis-tances between 150o and 160) forms an L-shaped curve which isnot well explained by best fitting simple models of inner core ani-sotropy with fast axis aligned with the Earthrsquos rotation axis(Fig 30) for which one would expect a parabolic shape accordingto the equation

dt frac14 athorn bcos2nthorn ccos4n

where a b c are related to integrals of elastic anisotropic parame-ters along the path in the inner core

At larger distances the reference outer core phase is PKP(AB)which spends significant time in the highly heterogeneous D00

region at the base of the mantle Therefore absolute travel timeanomalies of PKP(DF) are preferred although in that case contri-butions from mantle 3D structure and uncertainties in sourceparameters can bias the data (eg Breacuteger et al 2000) Most studieswill therefore only consider events from the high quality relocatedEHB catalog (Engdahl et al 1998) which presently exists onlythrough 2010 Still analysis of these PKP(DF) data indicate thatin the western hemisphere a similar trend is observed in the abso-lute PKP(DF) travel time residuals as in the PKP(DF)-PKP(AB) resid-uals as a function of angle n (Fig 30b) Most recent estimates of thecorresponding anisotropy are on the order of 3ndash4 in the IMICwhich is considerable and difficult to reconcile with current pre-dictions from mineral physics (see Section 6) let alone the esti-mate of 3ndash88 of Lythgoe et al (2014)

To explain this trend and other aspects of complexity in traveltime measurements of core sensitive phases that cannot beexplained by mantle structure Romanowicz et al (2003) proposedalternative models that would involve structure in the outer corewith either faster than average velocities in the inner core tangentcylinder or in polar caps at the top of the outer core that couldrepresent an increased concentration of light elements For exam-ple Fig 31 shows the pattern obtained when plotting absolutetravel time anomalies for DFBC and AB plotted at the entry pointof the corresponding raypath into the outer core on the Alaskaside for south-Sandwich to Alaska paths as well as paths fromAlaska to Antarctica When plotted in this manner the travel-time anomalies form a coherent pattern suggesting a localizedanomaly that may originate near the core-mantle boundary onthe Alaska side compatible with both a polar cap in the outer coreor heterogeneity within at least part of the tangent cylinder Mostanomalously split inner core sensitive normal modes could beexplained by either of these models except for mode 3S2 whichexhibits particularly strong splitting (Romanowicz and Breacuteger2000) These results have been reexamined critically by Ishii andDziewonski (2005)

Putting structure in the outer core remains controversial (egSouriau et al 2003) as significant density anomalies in the vigor-ously convecting outer core appear to be ruled out (eg Stevenson1987) However recent work suggesting the possibility of stagnantlayers at the top of the outer core from magneto-hydrodynamicsconsiderations (eg Buffett 2014) indicates that at least the polarcap hypothesis should perhaps remain on the table as alternativeto a strongly anisotropic region in the inner core On the otherhand Tkalcic (2010) found that differential travel time anomaliesof similar amplitude are observed on PcP-P data in the vicinity ofSSI Because such data do not sample the inner core at all Tkalcic(2010) proposed that a significant part of the SSI anomaly could

Fig 30 Travel time anomalies of core phases as a function of angle n of the ray path in the inner core with respect to the Earthrsquos rotation axis from the combined Berkeleydata collection (Tkalcic et al 2002) and from Leykam et al (2010) Left (DFndashBC) ndash Right absolute DF a) and d) all data b) and e) for events in the south-Sandwich Islands c)and f) for events in Alaska

80 B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90

be located in the deep mantle although no such structure has beenidentified yet tomographically Therefore explaining the broadspread of PKP(DF) travel time anomalies on SSI paths to Alaskaremains an open question which needs to be answered beforerobust bounds on the strength of anisotropy in the inner corersquoswestern hemisphere can be provided to mineral physicists Accu-mulation of data from the current deployment of USArray in Alaskamay shed more light on this question

This leads us to the second and possibly related challenge thathas come to light recently (Lincot et al 2015 2016 Romanowiczet al 2016) which is how to reconcile the 3ndash8 seismic anisotropyinferred in the inner corersquos western hemisphere with currentknowledge from mineral physics

6 Mineral physics of the inner core

61 Phase relations

From the mineral physics point of view a first order questionhas been the phase in which iron is present in the inner coreThe high pressure e phase of iron was first confirmed by X-raydiffraction by Mao et al (1967) and a hexagonal close-packed(hcp) structure was identified Since then many high pressureexperiments have been conducted Most important are those per-tinent to conditions of the inner core (Fig 32) They includedynamic shock compression with relatively large error margins(eg Alfegrave et al 2002 Anzellini et al 2013 Brown 2001 Ping

Fig 31 Absolute travel time anomalies for DF (circles and triangles) BC (crosses)and AB (squares) for events at latitudes lower than 50S or higher than 50Nplotted as a function of the location of the entry point of the ray path into the outercore Triangles are for events at latitude gt50N observed at stations at latitudeslt50S Expanded from Romanowicz et al (2003) to include data from Leykamet al (2010) as also shown in Fig 34bndashf This collection of travel time anomaliesforms a coherent pattern with a sharp gradient delineating a localized boundarybetween very fast paths to the northwest and normal paths to the southeastsuggesting a lsquolsquopolar caprdquo pattern that may or may not originate in the inner coreNote that the color code is centered at dt = 35 s

Fig 32 Pressurendashtemperature phase diagram for iron at high pressure illustratingdiamond anvil and shock experiments as well as ab initio simulations The linescorrespond to melting curves (courtesy of BK Godwal)

B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90 81

et al 2013) and DAC experiments at high pressure and tempera-ture up to 380 GPa and 6000 K (eg Tateno et al 2010) Basedon theoretical calculations some authors have suggested thatbody-centered cubic (bcc) iron could be stable just below the melt-ing point at core pressures (eg Vocadlo et al 2003 Belonoshkoet al 2003 2006 Dubrovinsky et al 2007 Bouchet et al 2013)but most recent studies indicate that bcc is unstable at these con-ditions (eg Godwal et al 2015)

An important aspect is that the inner core may not be chemi-cally and structurally homogeneous It is likely that nickel a com-ponent in iron meteorites is also present in the core (Sakai et al2011 Tateno et al 2012) Furthermore to account for the lowerdensity implied by seismic data suggests that lighter elementsmay be present and a good candidate is silicon The Fe-Si systemhas been studied at intermediate pressure-temperatures (egSakai et al 2011 Fischer et al 2013 Fig 33) and inner core con-ditions (Tateno et al 2015) At high pressure and high tempera-ture FeSi crystallizes in the cubic B2 structure (CsCl structure)which is an ordered bcc structure Fe3Si forms a DO3 structure withdoubling of the B2 unit cell and ordering At lower pressures FeSiforms the B20 structure which is partially disordered bcc with alack of inversion symmetry (eg Jeong and Pickett 2004) Elasticproperties of FeSi have been investigated by Petrova et al (2010)Badro et al (2014) explored a range of possible elements in thecore (O S Si Ni) and concluded that oxygen is required in the outercore

62 Causes of anisotropy in the inner core

Potential mechanisms for alignment of crystals in the inner coreare dislocation-plasticity (eg Jeanloz andWenk 1988 Wenk et al2000a Lincot et al 2015 2016) growth from a melt (eg Bergman1997 Deguen 2012) magnetic Maxwell stresses (eg Karato1999 Buffett and Wenk 2001)

Radial DAC experiments (eg Wenk et al 2000a Merkel et al2004 2013 Miyagi et al 2008) documented texture developmentin e iron at high pressure and inferred (0001) and subordinatef11 20g slip combined with mechanical twinning as potentialmechanisms However these experiments were not at inner coreconditions

Elastic properties at core conditions rely on first principle calcu-lations and various groups have been involved (eg Vocadlo et al2008 2009 Mattesini et al 2010) It is interesting to find thatresults are quite contradictory as expressed in P-wave velocityprofiles for hcp single crystals with the c-axis at n = 0 (Fig 34b)While Vocadlo et al (2009) predict maximum velocities perpendic-ular to the c-axis Mattesini et al (2010) suggest maximum veloc-ities parallel to the c-axis (the elastic tensor of hexagonal crystals isaxially symmetric about the c-axis) Estimates of inner core seismicanisotropy are very high ((Vp-fast Vp-slow)Vp-iso = 3ndash8 Fig 34a)compared with the rather small P-wave anisotropy obtained fromfirst principles calculations for single crystals (eg 49 for Vocadloet al 2009 at 308 GPa and 5000 K or 57 for Mattesini et al 2010at 346 GPa and 6000 K) and the best fit with seismic data would bea hexagonal single crystal aligned with the c-axis more or less par-allel to the N-S axis A huge single crystal seems unlikely giventhat the largest documented crystals on Earth are about 20 m insize and with pressurendashtemperature gradients it is likely thathuge crystals at high temperature would undergo transformationsand recrystallization over geologic times

A recent study (Lincot et al 2016) constructed a multi-scalemodel combining self-consistent polycrystal plasticity inner-core formation models and Monte Carlo simulations of elasticparameters to predict travel times of inner core PKP waves andconfront them with observations These authors found that theycould explain as much as 3 seismic anisotropy with an hcp-ironstructure with fast c axis and with anomalous single crystal aniso-tropies near the melting point of up to 20 (Martorell et al 2013)with dominant pyramidal hc + ai slip and crystal alignment pro-vided by a low degree boundary condition for crystallization atthe ICB While this model might account for the faster PKP traveltimes on polar compared to equatorial paths it does not reproducethe L-shaped travel time anomaly curve as a function of angle n(Fig 30)

Fig 33 Phase diagrams of the Fe-Si system (Fischer et al 2013) (a) Pressurendashtemperature phase diagram illustrating stability fields of the various phases for Fe-9Si (b)Temperature-composition diagram at 145 GPa illustrating the transition from hcp to B2

Fig 34 (a) Comparison of relative velocity variations (in) as a function of angle n of the ray path in the inner core with respect to the Earthrsquos rotation axis for severalseismological models Black OIC model of Wang et al (2003) Grey OIC model of Beghein and Trampert (2003) Blue best fitting IMIC model using Wang et alrsquos model forOIC anisotropy corrections Green best fitting IMIC model using Beghein and Trampertrsquos (2003) OIC model for anisotropy corrections in the OIC In the latter two cases theIMIC radius is held at 600 km The IMIC model obtained is only slightly sensitive to the radius in the range 500ndash600 km Dashed lines indicate the range of uncertainty on theIMIC model (b) Calculated normalized P-wave velocities of hexagonal single crystals based on first principle elastic properties at various temperatures and pressures An isstrength of anisotropy The polar angle n is zero parallel to the hexagonal c-axis Mat Mattesini et al 2010 Voc Vocadlo et al (2009) Based on Romanowicz et al (2016)

82 B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90

7 Conclusions and future directions

71 Anisotropy in the deep mantle

In the last ten years global seismic tomography has providedincreasingly refined images of seismic heterogeneity in the deepEarth There is now agreement on the long wavelength structuredominated by the presence of two low shear velocity provinces(LLSVPs) under Africa and the central Pacific which may requirecompositional heterogeneity at least at their base There is alsoevidence for smaller scale structures suggestive of subductingslabs and upwelling plumes in the lower mantle While the bulkof the lower mantle appears largely isotropic the long wavelengthpattern of VTI anisotropy detected in D00 from shear wave tomo-graphic studies seems to track that of isotropic velocity with SHfaster than SV outside of the LLSVPs and SV faster than SH withinthem However the agreement among different models is limited

to the very longest wavelengths (lsquolsquodegree 200) and there are stilldebates about trade-offs between isotropic and anisotropicstructure

On the other hand recent local studies of shear wave splittingare consistently showing the presence of strong seismic anisotropy(both radial and azimuthal) at the edges of the LLSVPs primarily onthe fast side Because anisotropy in post-perovskite (pPv) isthought to be much stronger than in perovskite and pPv is likelymore widely present outside of the LLSVP (ie colder regions man-ifested by faster than average shear velocity) than inside theLLSVPs (which are likely warmer) these observations suggest thatCPO of pPv may be the cause indicating the presence of strongdeformation due to constrained flow at the base of the mantlewith a change of direction towards the vertical at the border ofthe LLSVP and more vertically oriented flow within it While veryattractive because it can also explain opposite polarity behavior inreflections of P and S waves on the discontinuity at the top of D00

B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90 83

(Thomas et al 2011 Cobden et al 2015) the interpretation interms of pPv must be considered with caution given the uncertain-ties on whether pPv is actually present at deep mantle depths

A priority for future seismic studies is to continue investigatingthe patterns of anisotropy on the borders of the LLSVPs as well as inthe vicinity of upwelling plumes where high concentrations ofstrain are expected This would be greatly helped by installationsof large aperture broadband arrays on the ocean floor collectinghigh quality horizontal component data for at least 1 year to covergaps in the available sampling of D00 in these regions We also lackrobust constraints on deep mantle P anisotropy which would helpdifferentiate between dominant (001) and (010) slip systems inpost-perovskite

Also mineral physics has added a lot of new information mostsignificantly the discovery of post-perovskite (Oganov and Ono2004) and derivation of deformation mechanisms both by experi-ments and theoretical models But as the anisotropic seismic struc-ture of the Earth has become more complex over the last ten yearsso has the interpretation with mineral physics concepts opening awide range of opportunities for new investigations Perhaps mostsignificant have been the recent advances in modeling crystaldeformation based on bonding characteristics at a wide range ofconditions that are relevant for the mantle but cannot beapproached with experiments like slow strain rates It will beimportant to apply theory to experimental conditions and thismight explain why DAC experiments at high pressure suggest(001) slip for MgSiO3 post-perovskite (Miyagi et al 2010 Wuet al 2017) while bonding models predict (010) slip at deep man-tle conditions (Goryaeva et al 2016)

High pressure experiments will remain crucial With advancesin multi-anvil technology it will become possible to reach lowermantle conditions (Yamazaki et al 2014) with larger samplesand better defined deformation geometry than DAC which isrestricted to the 50 lm range) with large gradients in pressuredeformation rates and temperature In addition D-DIA experi-ments can provide tomographic information about microstructuralevolution eg during phase transitions and recrystallization (Wanget al 2011) Also DAC technology is adding new possibilities suchas resistive heating for high temperature experiments multigraintexture analysis for coarser aggregates (eg Barton and Bernier2012 Langrand et al 2017) and the possibility of using DAC withLaue microdiffraction (Tamura 2014) to perform orientation andmicrostructural mapping in situ at high pressure

In the future also a larger range of compositions needs to beexplored experimentally for example iron-magnesium contentmultiphase systems (pPv ferropericlase and CaSiO3 perovskite)and the significance of perovskitepost-perovskite transformations

Geodynamic models need refinements New 3D models withtracers (eg Cottaar et al 2014 Li M et al 2014) still do notaccount for the very significant viscosity changes implied by min-eral physics And following texture evolution along streamlinesprovides results at different times for the advancing tracers whilerelating anisotropy results to the Earth assumes that the stream-line does not change which is clearly not the case

The issue of deformation mechanisms was addressed in Sec-tion 48 All models for lower mantle anisotropy assume disloca-tion glide of post-perovskite and ferropericlase as the cause ofcrystal alignment and use a self-consistent viscoplastic plasticitymodel Some arbitrary strain fraction corrections are introducedto account for mechanisms such as climb grain boundary migra-tion grain boundary sliding that do not contribute to texture Inthe future the significance of these mechanisms should be studiedmore systematically both with experiments and models There arestrong indications that the activity of different mechanisms is thecause for lack of significant anisotropy in large parts of the lowermantle

72 Inner core anisotropy

While the complexities of the lower mantle are developing intoa realistic and solvable puzzle inner core anisotropy is becomingmore enigmatic As we learn more about the large seismic aniso-tropy it is not clear what the origin of this signal is and how muchoriginates in the inner core There is room for many possible inter-pretations including a layered inner core with a bcc iron structurein the innermost inner core and an outer shell with an hcp struc-ture (Wang et al 2015) While such a structure is not impossibleit is quite unlikely (eg Romanowicz et al 2016) and not presentlyresolvable from seismological observations The high axial veloci-ties compared with equatorial velocities are difficult to explainand particularly the striking L-shape of the PKP travel time residualas a function of angle of the raypath in the inner core with respectto the rotation axis It is not impossible that heterogeneous struc-tures in the outer liquid core particularly columnar convectionwith a characteristic seismic pattern (eg Jones 2011 Soderlundet al 2012) influence the apparent seismic signature of the innercore A priority for future seismic studies in our view is to achieveconsensus on the origin of the observed L-shape mentioned aboveThe dense temporary broadband arrays recently installed in Alaska(as part of the Earthscope program) and in Antarctica should helpin that endeavor

On the mineral physics side there is general agreement thathexagonal close-packed iron is the most likely component butthe actual composition is still debated and an iron-silicon alloymay exist There is uncertainty and disagreement about elasticproperties of pure iron at inner core conditions derived with firstprinciples calculations (eg Vocadlo et al 2009 versus Mattesiniet al 2010) and no information about elastic properties of iron-silicon alloys While there are many experiments documentingphase relations both of Fe and Fe-Si at high pressure and temper-ature (eg Tateno et al 2010 2015) there is still considerableuncertainty about the melting temperature

These studies highlight the chemical and structural complexi-ties of the core with likely heterogeneities in the inner core vari-able elastic properties and anisotropy A multi-disciplinaryapproach including seismologists geodynamicists mineral physi-cists and material scientists is required to make progress Such col-laborations have been initiated and show great promise for thenear future

Acknowledgements

We are grateful to Mark Jellinek and Tim Horscroft for invitingus to prepare this review It was an opportunity for us to explorethe extensive literature on the subject and also to discover that alot of work remains to be done Particularly interesting was inter-action with colleagues and students at the 2016 CIDER Workshopin Santa Barbara HRW is appreciative of discussions with RainerAbart Sanne Cottaar Patrick Cordier Thorne Lay Sebastien MerkelLowell Miyagi and Kaiqing Yuan CIDER is funded through NSF(FESD grant EAR 1135452) We acknowledge support from NSF(EAR 1343908 1417229 CSEDI-106751) DOE (DE-FG02-05ER15637) CDAC We acknowledge constructive reviews by MarkJellinek and Maureen Long

References

Abart R Kunze K Milke R Sperb R Heinrich W et al 2004 Silicon and oxygenself diffusion in enstatite polycrystals the Milke (2001) rim growthexperiments revisited Contrib Mineral Petrol 147 633ndash646 httpdxdoiorg101007s00410-004-0596-9

Alfegrave D Price GD Gillan MJ 2002 Iron under Earthrsquos core conditions Liquid-state thermodynamics and high pressure melting curve from ab initio

B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90 77

D00 Testing as previously the predictions of anisotropy from thesame flow models as in Walker et al (2011) they confirmed thatthe (010) slip system of pPv provided the best fit to the seismicdata Still only the fast axis directions were tested disregardingthe amplitude of splitting arguing that the latter may be unrealis-tically strong in plasticity calculations while imposing any scalingwould be arbitrary

We note that Ford and Long (2015) have independently testedthe seismic anisotropy predictions of the Walker et al (2011) flowmodels on a set of measurements of shear wave splitting at theeastern edge of the African LLSVP They concluded that none ofthe flow models and pPv slip system combinations provided satis-factory predictions of their dataset although when they relax con-straints on the fast axis orientations the (010) slip model isfavored

46 Compositional heterogeneities

Neither the 2D and 3D convection models nor the instantaneousflow model constrained by tomography include the presence ofthermo-chemical piles as have been hypothesized to explainLLSVPs The presence of such piles could significantly modify theflow patterns and focus deformation at the border of the pileswhich seems to be observed in some local shear wave splittingstudies (eg Fig 4) Also it appears that the lowermost mantlemay be compositionally considerably heterogeneous (eg White2015) Subduction of lithospheric slabs is a major contribution toheterogeneity including in the D00 zone (van den Berg et al2010 cf Fig 11a and b) Additional phases are likely presentamong them cubic CaSiO3 perovskite silica and perhaps metalliciron (eg Shi et al 2013) (see Fig 11) Upwelling plumes displaychemical heterogeneity and characteristic isotope signatures weredocumented at hotspots such as Hawaii (Weis et al 2011 NobreSilva et al 2013 Li Y et al 2014) but this does not explain theprevalent seismic anisotropy in the D00 zone expressed in S-wavesplitting patterns with SHgtSV (eg Table 1 Fig 3) and for thiscrystal alignment during subduction is the most obvious explana-tion at present (eg Cottaar et al 2014)

47 Viscosity changes

There are some complications that have not been taken intoaccount in any of these models Changes in viscosity do occureg during phase transformations with strong increases in thetransition zone between the upper and lower mantle (410ndash660 km) The viscosity is assumed to be low in the upper mantle(radial viscosity of reference model 011021 Pa s Becker 2006)increases in the transition zone (11021 Pa s) and then again asminerals transform to denser lower mantle phases (501021Pa s) There is considerable complexity as some slabs descend intothe lower mantle (eg Conrad and Lithgow-Bertelloni 2004)

Recently seismic heterogeneities were attributed to higher vis-cosities in the mid-mantle region (1000 km) leading to a stagna-tion of subducting slabs (Rudolph et al 2015) and this could bedue to composition (eg Bolfan-Casanova et al 2003 suggestedthat the solubility of water decreases) iron fractionation and ironspin transitions (eg Lin et al 2012 Vilella et al 2015) or changesin mechanical properties with pressure of ferropericlase (egMarquardt and Miyagi 2015) and post-perovskite (Catalli et al2009) First principle calculations of Kraych et al (2016) suggesta strong strength increase for bridgmanite with pressure(Fig 21a) and a dramatic decrease for post-perovskite (Goryaevaet al 2016 Fig 21b) The geodynamic models described here donot take changes in viscosity into account nor do they consider ani-sotropic viscosity (eg Christensen 1987)

48 Active deformation mechanisms

The models described in this section attribute anisotropy toplastic deformation of crystals by dislocation glide that inducesrotations and resulting preferred orientation In Section 32 we dis-cussed deformation mechanisms and clearly at lower mantle con-ditions other mechanisms are likely active The deformationmechanism map (Fig 13) suggests a creep regime with a combina-tion of dislocation glide and diffusional dislocation climb (egAmmann et al 2010) Also grain boundary mechanisms may beactive at low stress (eg Chen and Argon 1979) with grain bound-ary sliding grain-size reduction but there are no experimental datafor lower mantle conditions (eg Sun et al 2016 describe disclina-tions in olivine) Recent bonding calculations suggest that disloca-tion climb may dominate in olivine (Boioli et al 2015) andparticularly in bridgmanite (Boioli et al 2017) Since only glidegenerates CPO this may explain why most of the lower mantleappears isotropic To account for these other mechanisms in somegeodynamic convection models only half of the strain was attribu-ted to glide but this limit is arbitrary

Many deformation mechanism maps have been introduced forgeological systems with emphasis on the upper mantle and theinfluences of temperature pressure stress and strain rate (egHansen et al 2011 2012 Kohlstedt and Goetze 1974 Linckenset al 2011) Extrapolating results to the lower mantle is morespeculative but with new models such as Boioli et al (2017)Goryaeva et al (2016) and Kraych et al (2016) this domain maycome within reach

Another mechanism that is likely active in the deep mantle isdynamic recrystallization It has been approached with thermody-namic theory of grain growth under stress (eg Kamb 1961Paterson 1973 Green 1980 Shimizu 1999 2008 Rozel et al2011) While recrystallization can result in grain growth it moreoften produces grain size reduction which has an effect on the rhe-ology (eg De Bresser et al 2001) But evidence from materialsscience suggests that in deformed aggregates recrystallization isoften controlled by crystal defects Grains with high dislocationdensities are less stable and nucleation may occur On the otherhand a grain with low dislocation density may grow and replacea highly strained grain by grain boundary migration (egHaessner 1978) These concepts can be introduced in plasticitymodels and were able to explain orientation patterns observed inexperimentally deformed quartzite halite and ice (Wenk et al1997) and olivine (Wenk and Tomeacute 1999 Kaminski and Ribe2001) but there are too many unknown parameters to predictrecrystallization mechanisms in lower mantle rocks Oftendynamic recrystallization randomizes orientation patterns

49 Complications in polyphase systems

Perhaps the most important complication for anisotropic geo-dynamics is that the lower mantle is a system with two majorphases of different strength The interaction of these phases isnot taken into account in most polycrystal plasticity models Suchsystems are common yet there is not much work neither in mate-rial science nor geological environments and recommendationsformulated at an interdisciplinary polyphase polycrystal plasticityworkshop still apply (Breacutechet et al 1994)

Most rocks in the Earthrsquos crust and mantle are polymineralicyet most experimental and theoretical investigations were doneon monomineralic systems and for example in quartz-mica mix-tures CPO of quartz is greatly reduced compared with a purequartz aggregate (Canova et al 1992 Tullis and Wenk 1994)Under metamorphic conditions complex reactions may occur atgrain boundaries and change the fabric (eg Abart et al 2004Gaidies et al 2017)

78 B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90

In most recrystallized gneisses feldspar and quartz show barelyany preferred orientation (eg Kern et al 2008 Ullemeyer et al2006) This becomes particularly pronounced if rocks have under-gone large secondary deformation resulting in mylonites (egHandy 1994 Kern and Wenk 1990 Herwegh et al 2011Linckens et al 2011 Bercovici and Ricard 2016) In mylonites ofgranitic composition the much stronger and dominant feldsparphase barely deforms and grains tumble in the much weaker andrecrystallizing quartz phase (Fig 28) A similar microstructuremay be expected in highly deformed parts of the lower mantlewith strong bridgmanite in a matrix of weak ferropericlase(Fig 21a) and could explain the lack of significant anisotropy

For the analog system neighborite-halite Kaercher et al (2016)have documented that for single phase systems strong CPO devel-ops but for mixtures CPO is greatly reduced caused by locallyheterogeneous deformation This is also confirmed by DAC experi-ments for perovskite-ferropericlase mixtures (eg Miyagi andWenk 2016 Girard et al 2016)

For the 2-phase problem with local heterogeneities there is nostraightforward polycrystal plasticity model Canova et al (1992)have developed an n-site viscoplastic formulation and applied itto muscovite quartz mixtures There have been attempts withfinite element approaches (eg Mika and Dawson 1999) and Four-ier transform methods (eg Lebensohn 2001) but they are notapplicable to large geophysical systems at least for now and par-

Fig 28 (a) Thin section image of granite mylonite from the Santa Rosa mylonitezone in Southern California with rigid strong plagioclase crystals floating in finegrained recrystallized quartz creating a viscous matrix This represents probably asimilar microstructure as bridgmanite and periclase in the lower mantle (b) Imageof deformed quartzite with feldspar inclusions from the Bergell Alps This pervasiveductile deformation may be similar to sheared post-perovskite in the lowermostmantle Width of images is 10 mm crossed polarizers

ticularly do not account for grain boundary sliding which may bevery significant

For the D00 zone this is likely different because post-perovskiteis of similar strength or weaker than ferropericlase (Fig 21b) andthus deforms with a significant contribution of dislocation glideThe microstructure of highly strained D00 material may be moreanalogous to deformed quartzite with some feldspar inclusionsand extremely strong preferred orientation (Fig 28b)

5 Seismic anisotropy in the inner core

We conclude this review with a brief discussion about seismicanisotropy in the solid inner core While the presence of a densepossibly fluid core had been suggested long ago based on the highaverage density of the Earth as well as measurements of tides itspresence was confirmed by seismology in the early 20th century(Oldham 1906 Gutenberg 1913) An iron-nickel compositionwas assigned in analogy to iron meteorites In 1936 Inge Lehmanndiscovered the presence of an inner core of different elastic proper-ties within the fluid outer core (Lehmann 1936) Several decadeslater the solidity of the inner core was demonstrated byDziewonski and Gilbert (1971) based on the measurements ofeigenfrequencies of inner core-sensitive free oscillations Birch(1952) showed that the density of an iron-nickel alloy is too highcompared to seismological estimates and proposed the presenceof 10 of lighter elements Since then the structure and compo-sition of the core was refined based on seismic gravitational andmagnetic evidence (eg Hirose et al 2013)

The presence of cylindrical anisotropy in the inner core withthe fast axis aligned with the Earthrsquos rotation axis was first pro-posed thirty years ago to explain two types of independent seismicobservations (1) travel time anomalies of P waves that traversethe inner core (denoted PKIKP or PKP(DF)) on polar paths (ie ina direction quasi parallel to the Earthrsquos rotation axis) arriving upto 5 s earlier than those travelling on equatorial paths (Morelliet al 1986) and (2) anomalous splitting of inner core sensitive freeoscillations (Woodhouse et al 1986) Neither of these observationscould be explained by long-wavelength heterogeneous structure inthe earthrsquos mantle It was suggested that this anisotropy couldlikely be due to the alignment of intrinsically anisotropic iron crys-tals and in the following decade several models for the physicalcause of such alignment were proposed (Jeanloz and Wenk1988 Romanowicz et al 1996 Bergman 1997 Karato 1999Wenk et al 2000b Buffett and Wenk 2001 Yoshida et al 1996see review by Sumita and Bergman 2015)

In the decades since its discovery many seismic studies haveconfirmed these early observations from ever increasing datasetsleading to a current landscape of the distribution of inner core ani-sotropy that is surprisingly complex for such a small volume of theEarth (eg Tkalcic 2015) The top 100 km of the 1220 km-thickinner core have been found to be isotropic while deeper there isevidence for a hemispherical pattern of anisotropy (Tanaka andHamaguchi 1997 Creager 1999 Niu and Wen 2002 Garcia2002 Waszek et al 2011 Irving and Deuss 2011 Lythgoe et al2014) with weaker anisotropy in the eastern hemisphere than inthe western hemisphere There is also evidence for depth depen-dence with increased strength of anisotropy towards the center(Creager 1992 Vinnik et al 1994) and more recently the sugges-tion of a different orientation of anisotropy in the central part ofthe inner core (Ishii and Dziewonski 2002 Beghein andTrampert 2003) dubbed lsquolsquoInner Most Inner Corerdquo (IMIC Ishii andDziewonski 2002) The IMIC as reexamined in more recent stud-ies would have a radius of about 550 km (eg Cormier andStroujkova 2005 Cao and Romanowicz 2007 Lythgoe et al2014 Wang et al 2015 Romanowicz et al 2016) The signature

B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90 79

of a hemispherical anisotropic structure has also been found fromthe modeling of coupling of pairs of modes sensitive to such struc-ture (Deuss et al 2010) In addition regional variations in thedirection of the fast axis and strength of anisotropy have been doc-umented (eg Breacuteger et al 1999 Sun and Song 2008ab Irving2016) To explain this complexity Tkalcic (2010) suggested thatthe inner core may be made of a patchwork of anisotropic domainsof different orientations Attenuation of PKIKP waves also presentsanisotropic variations with higher attenuation correlated withearly arrivals along quasi-polar paths (Souriau and Romanowicz1996 1997 Oreshin and Vinnik 2004) We refer the reader tomore complete reviews of seismological studies of inner core ani-sotropy (Deuss 2014 Souriau 2015 Tkalcic 2015) Here webriefly describe some of the seismological challenges that are stillpreventing us from a full understanding of these intriguingobservations

One of the main challenges in fully resolving the pattern ofinner core anisotropy is the poor directional sampling availabledue to the limited distribution of sources and receivers in polarregions (eg Tkalcic 2015) Thus paths sampling the inner coreat a given location from different directions which is necessaryto confirm the presence of anisotropy are frequently lacking mak-ing it difficult to image inner core anisotropy in three dimensionswithout imposing strong a priori-constraints (eg Sun and Song2008a Lythgoe et al 2014) The strongest anisotropy in PKIKPdata is found primarily along paths from events in South SandwichIslands (SSI) to Alaska which dominate the set of observations inthe strongly anisotropic western hemisphere that contribute tothe n angle range between 10-30o where n is the angle of the ray-path in the inner core with the Earthrsquos axis of rotation At shorterdistances (lt155) the PKP(DF) phase can be referred to PKP(BC) which is a core phase that does not traverse the inner core(Fig 29) This makes it possible to eliminate contributions fromuncertainties in the source parameters as well as a significant partof the effects of 3D mantle structure given that PKP(BC) and PKP

Fig 29 Raypaths of main body wave phases used in the study of inner-corestructure and anisotropy at an epicentral distance of 155o At this distance all threecore phases PKIKP (also called PKP(DF)) PKP(BC) and PKP(AB) are observed Thephase PKJKP (a shear wave in the inner core) is very difficult to observe and isplotted here only for reference

(DF) have very similar paths throughout the mantle diverging onlyin the vicinity of the inner core

In fact the SSI dataset shows a wide range of travel timeanomalies ranging from 0 to gt5 s when referred to the PKP(BC)phase suggesting a strong local anomaly (eg Tkalcic et al2002) When plotted as a function of the angle n the global PKP(BC)-PKP(DF) travel time dataset (which covers epicentral dis-tances between 150o and 160) forms an L-shaped curve which isnot well explained by best fitting simple models of inner core ani-sotropy with fast axis aligned with the Earthrsquos rotation axis(Fig 30) for which one would expect a parabolic shape accordingto the equation

dt frac14 athorn bcos2nthorn ccos4n

where a b c are related to integrals of elastic anisotropic parame-ters along the path in the inner core

At larger distances the reference outer core phase is PKP(AB)which spends significant time in the highly heterogeneous D00

region at the base of the mantle Therefore absolute travel timeanomalies of PKP(DF) are preferred although in that case contri-butions from mantle 3D structure and uncertainties in sourceparameters can bias the data (eg Breacuteger et al 2000) Most studieswill therefore only consider events from the high quality relocatedEHB catalog (Engdahl et al 1998) which presently exists onlythrough 2010 Still analysis of these PKP(DF) data indicate thatin the western hemisphere a similar trend is observed in the abso-lute PKP(DF) travel time residuals as in the PKP(DF)-PKP(AB) resid-uals as a function of angle n (Fig 30b) Most recent estimates of thecorresponding anisotropy are on the order of 3ndash4 in the IMICwhich is considerable and difficult to reconcile with current pre-dictions from mineral physics (see Section 6) let alone the esti-mate of 3ndash88 of Lythgoe et al (2014)

To explain this trend and other aspects of complexity in traveltime measurements of core sensitive phases that cannot beexplained by mantle structure Romanowicz et al (2003) proposedalternative models that would involve structure in the outer corewith either faster than average velocities in the inner core tangentcylinder or in polar caps at the top of the outer core that couldrepresent an increased concentration of light elements For exam-ple Fig 31 shows the pattern obtained when plotting absolutetravel time anomalies for DFBC and AB plotted at the entry pointof the corresponding raypath into the outer core on the Alaskaside for south-Sandwich to Alaska paths as well as paths fromAlaska to Antarctica When plotted in this manner the travel-time anomalies form a coherent pattern suggesting a localizedanomaly that may originate near the core-mantle boundary onthe Alaska side compatible with both a polar cap in the outer coreor heterogeneity within at least part of the tangent cylinder Mostanomalously split inner core sensitive normal modes could beexplained by either of these models except for mode 3S2 whichexhibits particularly strong splitting (Romanowicz and Breacuteger2000) These results have been reexamined critically by Ishii andDziewonski (2005)

Putting structure in the outer core remains controversial (egSouriau et al 2003) as significant density anomalies in the vigor-ously convecting outer core appear to be ruled out (eg Stevenson1987) However recent work suggesting the possibility of stagnantlayers at the top of the outer core from magneto-hydrodynamicsconsiderations (eg Buffett 2014) indicates that at least the polarcap hypothesis should perhaps remain on the table as alternativeto a strongly anisotropic region in the inner core On the otherhand Tkalcic (2010) found that differential travel time anomaliesof similar amplitude are observed on PcP-P data in the vicinity ofSSI Because such data do not sample the inner core at all Tkalcic(2010) proposed that a significant part of the SSI anomaly could

Fig 30 Travel time anomalies of core phases as a function of angle n of the ray path in the inner core with respect to the Earthrsquos rotation axis from the combined Berkeleydata collection (Tkalcic et al 2002) and from Leykam et al (2010) Left (DFndashBC) ndash Right absolute DF a) and d) all data b) and e) for events in the south-Sandwich Islands c)and f) for events in Alaska

80 B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90

be located in the deep mantle although no such structure has beenidentified yet tomographically Therefore explaining the broadspread of PKP(DF) travel time anomalies on SSI paths to Alaskaremains an open question which needs to be answered beforerobust bounds on the strength of anisotropy in the inner corersquoswestern hemisphere can be provided to mineral physicists Accu-mulation of data from the current deployment of USArray in Alaskamay shed more light on this question

This leads us to the second and possibly related challenge thathas come to light recently (Lincot et al 2015 2016 Romanowiczet al 2016) which is how to reconcile the 3ndash8 seismic anisotropyinferred in the inner corersquos western hemisphere with currentknowledge from mineral physics

6 Mineral physics of the inner core

61 Phase relations

From the mineral physics point of view a first order questionhas been the phase in which iron is present in the inner coreThe high pressure e phase of iron was first confirmed by X-raydiffraction by Mao et al (1967) and a hexagonal close-packed(hcp) structure was identified Since then many high pressureexperiments have been conducted Most important are those per-tinent to conditions of the inner core (Fig 32) They includedynamic shock compression with relatively large error margins(eg Alfegrave et al 2002 Anzellini et al 2013 Brown 2001 Ping

Fig 31 Absolute travel time anomalies for DF (circles and triangles) BC (crosses)and AB (squares) for events at latitudes lower than 50S or higher than 50Nplotted as a function of the location of the entry point of the ray path into the outercore Triangles are for events at latitude gt50N observed at stations at latitudeslt50S Expanded from Romanowicz et al (2003) to include data from Leykamet al (2010) as also shown in Fig 34bndashf This collection of travel time anomaliesforms a coherent pattern with a sharp gradient delineating a localized boundarybetween very fast paths to the northwest and normal paths to the southeastsuggesting a lsquolsquopolar caprdquo pattern that may or may not originate in the inner coreNote that the color code is centered at dt = 35 s

Fig 32 Pressurendashtemperature phase diagram for iron at high pressure illustratingdiamond anvil and shock experiments as well as ab initio simulations The linescorrespond to melting curves (courtesy of BK Godwal)

B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90 81

et al 2013) and DAC experiments at high pressure and tempera-ture up to 380 GPa and 6000 K (eg Tateno et al 2010) Basedon theoretical calculations some authors have suggested thatbody-centered cubic (bcc) iron could be stable just below the melt-ing point at core pressures (eg Vocadlo et al 2003 Belonoshkoet al 2003 2006 Dubrovinsky et al 2007 Bouchet et al 2013)but most recent studies indicate that bcc is unstable at these con-ditions (eg Godwal et al 2015)

An important aspect is that the inner core may not be chemi-cally and structurally homogeneous It is likely that nickel a com-ponent in iron meteorites is also present in the core (Sakai et al2011 Tateno et al 2012) Furthermore to account for the lowerdensity implied by seismic data suggests that lighter elementsmay be present and a good candidate is silicon The Fe-Si systemhas been studied at intermediate pressure-temperatures (egSakai et al 2011 Fischer et al 2013 Fig 33) and inner core con-ditions (Tateno et al 2015) At high pressure and high tempera-ture FeSi crystallizes in the cubic B2 structure (CsCl structure)which is an ordered bcc structure Fe3Si forms a DO3 structure withdoubling of the B2 unit cell and ordering At lower pressures FeSiforms the B20 structure which is partially disordered bcc with alack of inversion symmetry (eg Jeong and Pickett 2004) Elasticproperties of FeSi have been investigated by Petrova et al (2010)Badro et al (2014) explored a range of possible elements in thecore (O S Si Ni) and concluded that oxygen is required in the outercore

62 Causes of anisotropy in the inner core

Potential mechanisms for alignment of crystals in the inner coreare dislocation-plasticity (eg Jeanloz andWenk 1988 Wenk et al2000a Lincot et al 2015 2016) growth from a melt (eg Bergman1997 Deguen 2012) magnetic Maxwell stresses (eg Karato1999 Buffett and Wenk 2001)

Radial DAC experiments (eg Wenk et al 2000a Merkel et al2004 2013 Miyagi et al 2008) documented texture developmentin e iron at high pressure and inferred (0001) and subordinatef11 20g slip combined with mechanical twinning as potentialmechanisms However these experiments were not at inner coreconditions

Elastic properties at core conditions rely on first principle calcu-lations and various groups have been involved (eg Vocadlo et al2008 2009 Mattesini et al 2010) It is interesting to find thatresults are quite contradictory as expressed in P-wave velocityprofiles for hcp single crystals with the c-axis at n = 0 (Fig 34b)While Vocadlo et al (2009) predict maximum velocities perpendic-ular to the c-axis Mattesini et al (2010) suggest maximum veloc-ities parallel to the c-axis (the elastic tensor of hexagonal crystals isaxially symmetric about the c-axis) Estimates of inner core seismicanisotropy are very high ((Vp-fast Vp-slow)Vp-iso = 3ndash8 Fig 34a)compared with the rather small P-wave anisotropy obtained fromfirst principles calculations for single crystals (eg 49 for Vocadloet al 2009 at 308 GPa and 5000 K or 57 for Mattesini et al 2010at 346 GPa and 6000 K) and the best fit with seismic data would bea hexagonal single crystal aligned with the c-axis more or less par-allel to the N-S axis A huge single crystal seems unlikely giventhat the largest documented crystals on Earth are about 20 m insize and with pressurendashtemperature gradients it is likely thathuge crystals at high temperature would undergo transformationsand recrystallization over geologic times

A recent study (Lincot et al 2016) constructed a multi-scalemodel combining self-consistent polycrystal plasticity inner-core formation models and Monte Carlo simulations of elasticparameters to predict travel times of inner core PKP waves andconfront them with observations These authors found that theycould explain as much as 3 seismic anisotropy with an hcp-ironstructure with fast c axis and with anomalous single crystal aniso-tropies near the melting point of up to 20 (Martorell et al 2013)with dominant pyramidal hc + ai slip and crystal alignment pro-vided by a low degree boundary condition for crystallization atthe ICB While this model might account for the faster PKP traveltimes on polar compared to equatorial paths it does not reproducethe L-shaped travel time anomaly curve as a function of angle n(Fig 30)

Fig 33 Phase diagrams of the Fe-Si system (Fischer et al 2013) (a) Pressurendashtemperature phase diagram illustrating stability fields of the various phases for Fe-9Si (b)Temperature-composition diagram at 145 GPa illustrating the transition from hcp to B2

Fig 34 (a) Comparison of relative velocity variations (in) as a function of angle n of the ray path in the inner core with respect to the Earthrsquos rotation axis for severalseismological models Black OIC model of Wang et al (2003) Grey OIC model of Beghein and Trampert (2003) Blue best fitting IMIC model using Wang et alrsquos model forOIC anisotropy corrections Green best fitting IMIC model using Beghein and Trampertrsquos (2003) OIC model for anisotropy corrections in the OIC In the latter two cases theIMIC radius is held at 600 km The IMIC model obtained is only slightly sensitive to the radius in the range 500ndash600 km Dashed lines indicate the range of uncertainty on theIMIC model (b) Calculated normalized P-wave velocities of hexagonal single crystals based on first principle elastic properties at various temperatures and pressures An isstrength of anisotropy The polar angle n is zero parallel to the hexagonal c-axis Mat Mattesini et al 2010 Voc Vocadlo et al (2009) Based on Romanowicz et al (2016)

82 B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90

7 Conclusions and future directions

71 Anisotropy in the deep mantle

In the last ten years global seismic tomography has providedincreasingly refined images of seismic heterogeneity in the deepEarth There is now agreement on the long wavelength structuredominated by the presence of two low shear velocity provinces(LLSVPs) under Africa and the central Pacific which may requirecompositional heterogeneity at least at their base There is alsoevidence for smaller scale structures suggestive of subductingslabs and upwelling plumes in the lower mantle While the bulkof the lower mantle appears largely isotropic the long wavelengthpattern of VTI anisotropy detected in D00 from shear wave tomo-graphic studies seems to track that of isotropic velocity with SHfaster than SV outside of the LLSVPs and SV faster than SH withinthem However the agreement among different models is limited

to the very longest wavelengths (lsquolsquodegree 200) and there are stilldebates about trade-offs between isotropic and anisotropicstructure

On the other hand recent local studies of shear wave splittingare consistently showing the presence of strong seismic anisotropy(both radial and azimuthal) at the edges of the LLSVPs primarily onthe fast side Because anisotropy in post-perovskite (pPv) isthought to be much stronger than in perovskite and pPv is likelymore widely present outside of the LLSVP (ie colder regions man-ifested by faster than average shear velocity) than inside theLLSVPs (which are likely warmer) these observations suggest thatCPO of pPv may be the cause indicating the presence of strongdeformation due to constrained flow at the base of the mantlewith a change of direction towards the vertical at the border ofthe LLSVP and more vertically oriented flow within it While veryattractive because it can also explain opposite polarity behavior inreflections of P and S waves on the discontinuity at the top of D00

B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90 83

(Thomas et al 2011 Cobden et al 2015) the interpretation interms of pPv must be considered with caution given the uncertain-ties on whether pPv is actually present at deep mantle depths

A priority for future seismic studies is to continue investigatingthe patterns of anisotropy on the borders of the LLSVPs as well as inthe vicinity of upwelling plumes where high concentrations ofstrain are expected This would be greatly helped by installationsof large aperture broadband arrays on the ocean floor collectinghigh quality horizontal component data for at least 1 year to covergaps in the available sampling of D00 in these regions We also lackrobust constraints on deep mantle P anisotropy which would helpdifferentiate between dominant (001) and (010) slip systems inpost-perovskite

Also mineral physics has added a lot of new information mostsignificantly the discovery of post-perovskite (Oganov and Ono2004) and derivation of deformation mechanisms both by experi-ments and theoretical models But as the anisotropic seismic struc-ture of the Earth has become more complex over the last ten yearsso has the interpretation with mineral physics concepts opening awide range of opportunities for new investigations Perhaps mostsignificant have been the recent advances in modeling crystaldeformation based on bonding characteristics at a wide range ofconditions that are relevant for the mantle but cannot beapproached with experiments like slow strain rates It will beimportant to apply theory to experimental conditions and thismight explain why DAC experiments at high pressure suggest(001) slip for MgSiO3 post-perovskite (Miyagi et al 2010 Wuet al 2017) while bonding models predict (010) slip at deep man-tle conditions (Goryaeva et al 2016)

High pressure experiments will remain crucial With advancesin multi-anvil technology it will become possible to reach lowermantle conditions (Yamazaki et al 2014) with larger samplesand better defined deformation geometry than DAC which isrestricted to the 50 lm range) with large gradients in pressuredeformation rates and temperature In addition D-DIA experi-ments can provide tomographic information about microstructuralevolution eg during phase transitions and recrystallization (Wanget al 2011) Also DAC technology is adding new possibilities suchas resistive heating for high temperature experiments multigraintexture analysis for coarser aggregates (eg Barton and Bernier2012 Langrand et al 2017) and the possibility of using DAC withLaue microdiffraction (Tamura 2014) to perform orientation andmicrostructural mapping in situ at high pressure

In the future also a larger range of compositions needs to beexplored experimentally for example iron-magnesium contentmultiphase systems (pPv ferropericlase and CaSiO3 perovskite)and the significance of perovskitepost-perovskite transformations

Geodynamic models need refinements New 3D models withtracers (eg Cottaar et al 2014 Li M et al 2014) still do notaccount for the very significant viscosity changes implied by min-eral physics And following texture evolution along streamlinesprovides results at different times for the advancing tracers whilerelating anisotropy results to the Earth assumes that the stream-line does not change which is clearly not the case

The issue of deformation mechanisms was addressed in Sec-tion 48 All models for lower mantle anisotropy assume disloca-tion glide of post-perovskite and ferropericlase as the cause ofcrystal alignment and use a self-consistent viscoplastic plasticitymodel Some arbitrary strain fraction corrections are introducedto account for mechanisms such as climb grain boundary migra-tion grain boundary sliding that do not contribute to texture Inthe future the significance of these mechanisms should be studiedmore systematically both with experiments and models There arestrong indications that the activity of different mechanisms is thecause for lack of significant anisotropy in large parts of the lowermantle

72 Inner core anisotropy

While the complexities of the lower mantle are developing intoa realistic and solvable puzzle inner core anisotropy is becomingmore enigmatic As we learn more about the large seismic aniso-tropy it is not clear what the origin of this signal is and how muchoriginates in the inner core There is room for many possible inter-pretations including a layered inner core with a bcc iron structurein the innermost inner core and an outer shell with an hcp struc-ture (Wang et al 2015) While such a structure is not impossibleit is quite unlikely (eg Romanowicz et al 2016) and not presentlyresolvable from seismological observations The high axial veloci-ties compared with equatorial velocities are difficult to explainand particularly the striking L-shape of the PKP travel time residualas a function of angle of the raypath in the inner core with respectto the rotation axis It is not impossible that heterogeneous struc-tures in the outer liquid core particularly columnar convectionwith a characteristic seismic pattern (eg Jones 2011 Soderlundet al 2012) influence the apparent seismic signature of the innercore A priority for future seismic studies in our view is to achieveconsensus on the origin of the observed L-shape mentioned aboveThe dense temporary broadband arrays recently installed in Alaska(as part of the Earthscope program) and in Antarctica should helpin that endeavor

On the mineral physics side there is general agreement thathexagonal close-packed iron is the most likely component butthe actual composition is still debated and an iron-silicon alloymay exist There is uncertainty and disagreement about elasticproperties of pure iron at inner core conditions derived with firstprinciples calculations (eg Vocadlo et al 2009 versus Mattesiniet al 2010) and no information about elastic properties of iron-silicon alloys While there are many experiments documentingphase relations both of Fe and Fe-Si at high pressure and temper-ature (eg Tateno et al 2010 2015) there is still considerableuncertainty about the melting temperature

These studies highlight the chemical and structural complexi-ties of the core with likely heterogeneities in the inner core vari-able elastic properties and anisotropy A multi-disciplinaryapproach including seismologists geodynamicists mineral physi-cists and material scientists is required to make progress Such col-laborations have been initiated and show great promise for thenear future

Acknowledgements

We are grateful to Mark Jellinek and Tim Horscroft for invitingus to prepare this review It was an opportunity for us to explorethe extensive literature on the subject and also to discover that alot of work remains to be done Particularly interesting was inter-action with colleagues and students at the 2016 CIDER Workshopin Santa Barbara HRW is appreciative of discussions with RainerAbart Sanne Cottaar Patrick Cordier Thorne Lay Sebastien MerkelLowell Miyagi and Kaiqing Yuan CIDER is funded through NSF(FESD grant EAR 1135452) We acknowledge support from NSF(EAR 1343908 1417229 CSEDI-106751) DOE (DE-FG02-05ER15637) CDAC We acknowledge constructive reviews by MarkJellinek and Maureen Long

References

Abart R Kunze K Milke R Sperb R Heinrich W et al 2004 Silicon and oxygenself diffusion in enstatite polycrystals the Milke (2001) rim growthexperiments revisited Contrib Mineral Petrol 147 633ndash646 httpdxdoiorg101007s00410-004-0596-9

Alfegrave D Price GD Gillan MJ 2002 Iron under Earthrsquos core conditions Liquid-state thermodynamics and high pressure melting curve from ab initio

78 B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90

In most recrystallized gneisses feldspar and quartz show barelyany preferred orientation (eg Kern et al 2008 Ullemeyer et al2006) This becomes particularly pronounced if rocks have under-gone large secondary deformation resulting in mylonites (egHandy 1994 Kern and Wenk 1990 Herwegh et al 2011Linckens et al 2011 Bercovici and Ricard 2016) In mylonites ofgranitic composition the much stronger and dominant feldsparphase barely deforms and grains tumble in the much weaker andrecrystallizing quartz phase (Fig 28) A similar microstructuremay be expected in highly deformed parts of the lower mantlewith strong bridgmanite in a matrix of weak ferropericlase(Fig 21a) and could explain the lack of significant anisotropy

For the analog system neighborite-halite Kaercher et al (2016)have documented that for single phase systems strong CPO devel-ops but for mixtures CPO is greatly reduced caused by locallyheterogeneous deformation This is also confirmed by DAC experi-ments for perovskite-ferropericlase mixtures (eg Miyagi andWenk 2016 Girard et al 2016)

For the 2-phase problem with local heterogeneities there is nostraightforward polycrystal plasticity model Canova et al (1992)have developed an n-site viscoplastic formulation and applied itto muscovite quartz mixtures There have been attempts withfinite element approaches (eg Mika and Dawson 1999) and Four-ier transform methods (eg Lebensohn 2001) but they are notapplicable to large geophysical systems at least for now and par-

Fig 28 (a) Thin section image of granite mylonite from the Santa Rosa mylonitezone in Southern California with rigid strong plagioclase crystals floating in finegrained recrystallized quartz creating a viscous matrix This represents probably asimilar microstructure as bridgmanite and periclase in the lower mantle (b) Imageof deformed quartzite with feldspar inclusions from the Bergell Alps This pervasiveductile deformation may be similar to sheared post-perovskite in the lowermostmantle Width of images is 10 mm crossed polarizers

ticularly do not account for grain boundary sliding which may bevery significant

For the D00 zone this is likely different because post-perovskiteis of similar strength or weaker than ferropericlase (Fig 21b) andthus deforms with a significant contribution of dislocation glideThe microstructure of highly strained D00 material may be moreanalogous to deformed quartzite with some feldspar inclusionsand extremely strong preferred orientation (Fig 28b)

5 Seismic anisotropy in the inner core

We conclude this review with a brief discussion about seismicanisotropy in the solid inner core While the presence of a densepossibly fluid core had been suggested long ago based on the highaverage density of the Earth as well as measurements of tides itspresence was confirmed by seismology in the early 20th century(Oldham 1906 Gutenberg 1913) An iron-nickel compositionwas assigned in analogy to iron meteorites In 1936 Inge Lehmanndiscovered the presence of an inner core of different elastic proper-ties within the fluid outer core (Lehmann 1936) Several decadeslater the solidity of the inner core was demonstrated byDziewonski and Gilbert (1971) based on the measurements ofeigenfrequencies of inner core-sensitive free oscillations Birch(1952) showed that the density of an iron-nickel alloy is too highcompared to seismological estimates and proposed the presenceof 10 of lighter elements Since then the structure and compo-sition of the core was refined based on seismic gravitational andmagnetic evidence (eg Hirose et al 2013)

The presence of cylindrical anisotropy in the inner core withthe fast axis aligned with the Earthrsquos rotation axis was first pro-posed thirty years ago to explain two types of independent seismicobservations (1) travel time anomalies of P waves that traversethe inner core (denoted PKIKP or PKP(DF)) on polar paths (ie ina direction quasi parallel to the Earthrsquos rotation axis) arriving upto 5 s earlier than those travelling on equatorial paths (Morelliet al 1986) and (2) anomalous splitting of inner core sensitive freeoscillations (Woodhouse et al 1986) Neither of these observationscould be explained by long-wavelength heterogeneous structure inthe earthrsquos mantle It was suggested that this anisotropy couldlikely be due to the alignment of intrinsically anisotropic iron crys-tals and in the following decade several models for the physicalcause of such alignment were proposed (Jeanloz and Wenk1988 Romanowicz et al 1996 Bergman 1997 Karato 1999Wenk et al 2000b Buffett and Wenk 2001 Yoshida et al 1996see review by Sumita and Bergman 2015)

In the decades since its discovery many seismic studies haveconfirmed these early observations from ever increasing datasetsleading to a current landscape of the distribution of inner core ani-sotropy that is surprisingly complex for such a small volume of theEarth (eg Tkalcic 2015) The top 100 km of the 1220 km-thickinner core have been found to be isotropic while deeper there isevidence for a hemispherical pattern of anisotropy (Tanaka andHamaguchi 1997 Creager 1999 Niu and Wen 2002 Garcia2002 Waszek et al 2011 Irving and Deuss 2011 Lythgoe et al2014) with weaker anisotropy in the eastern hemisphere than inthe western hemisphere There is also evidence for depth depen-dence with increased strength of anisotropy towards the center(Creager 1992 Vinnik et al 1994) and more recently the sugges-tion of a different orientation of anisotropy in the central part ofthe inner core (Ishii and Dziewonski 2002 Beghein andTrampert 2003) dubbed lsquolsquoInner Most Inner Corerdquo (IMIC Ishii andDziewonski 2002) The IMIC as reexamined in more recent stud-ies would have a radius of about 550 km (eg Cormier andStroujkova 2005 Cao and Romanowicz 2007 Lythgoe et al2014 Wang et al 2015 Romanowicz et al 2016) The signature

B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90 79

of a hemispherical anisotropic structure has also been found fromthe modeling of coupling of pairs of modes sensitive to such struc-ture (Deuss et al 2010) In addition regional variations in thedirection of the fast axis and strength of anisotropy have been doc-umented (eg Breacuteger et al 1999 Sun and Song 2008ab Irving2016) To explain this complexity Tkalcic (2010) suggested thatthe inner core may be made of a patchwork of anisotropic domainsof different orientations Attenuation of PKIKP waves also presentsanisotropic variations with higher attenuation correlated withearly arrivals along quasi-polar paths (Souriau and Romanowicz1996 1997 Oreshin and Vinnik 2004) We refer the reader tomore complete reviews of seismological studies of inner core ani-sotropy (Deuss 2014 Souriau 2015 Tkalcic 2015) Here webriefly describe some of the seismological challenges that are stillpreventing us from a full understanding of these intriguingobservations

One of the main challenges in fully resolving the pattern ofinner core anisotropy is the poor directional sampling availabledue to the limited distribution of sources and receivers in polarregions (eg Tkalcic 2015) Thus paths sampling the inner coreat a given location from different directions which is necessaryto confirm the presence of anisotropy are frequently lacking mak-ing it difficult to image inner core anisotropy in three dimensionswithout imposing strong a priori-constraints (eg Sun and Song2008a Lythgoe et al 2014) The strongest anisotropy in PKIKPdata is found primarily along paths from events in South SandwichIslands (SSI) to Alaska which dominate the set of observations inthe strongly anisotropic western hemisphere that contribute tothe n angle range between 10-30o where n is the angle of the ray-path in the inner core with the Earthrsquos axis of rotation At shorterdistances (lt155) the PKP(DF) phase can be referred to PKP(BC) which is a core phase that does not traverse the inner core(Fig 29) This makes it possible to eliminate contributions fromuncertainties in the source parameters as well as a significant partof the effects of 3D mantle structure given that PKP(BC) and PKP

Fig 29 Raypaths of main body wave phases used in the study of inner-corestructure and anisotropy at an epicentral distance of 155o At this distance all threecore phases PKIKP (also called PKP(DF)) PKP(BC) and PKP(AB) are observed Thephase PKJKP (a shear wave in the inner core) is very difficult to observe and isplotted here only for reference

(DF) have very similar paths throughout the mantle diverging onlyin the vicinity of the inner core

In fact the SSI dataset shows a wide range of travel timeanomalies ranging from 0 to gt5 s when referred to the PKP(BC)phase suggesting a strong local anomaly (eg Tkalcic et al2002) When plotted as a function of the angle n the global PKP(BC)-PKP(DF) travel time dataset (which covers epicentral dis-tances between 150o and 160) forms an L-shaped curve which isnot well explained by best fitting simple models of inner core ani-sotropy with fast axis aligned with the Earthrsquos rotation axis(Fig 30) for which one would expect a parabolic shape accordingto the equation

dt frac14 athorn bcos2nthorn ccos4n

where a b c are related to integrals of elastic anisotropic parame-ters along the path in the inner core

At larger distances the reference outer core phase is PKP(AB)which spends significant time in the highly heterogeneous D00

region at the base of the mantle Therefore absolute travel timeanomalies of PKP(DF) are preferred although in that case contri-butions from mantle 3D structure and uncertainties in sourceparameters can bias the data (eg Breacuteger et al 2000) Most studieswill therefore only consider events from the high quality relocatedEHB catalog (Engdahl et al 1998) which presently exists onlythrough 2010 Still analysis of these PKP(DF) data indicate thatin the western hemisphere a similar trend is observed in the abso-lute PKP(DF) travel time residuals as in the PKP(DF)-PKP(AB) resid-uals as a function of angle n (Fig 30b) Most recent estimates of thecorresponding anisotropy are on the order of 3ndash4 in the IMICwhich is considerable and difficult to reconcile with current pre-dictions from mineral physics (see Section 6) let alone the esti-mate of 3ndash88 of Lythgoe et al (2014)

To explain this trend and other aspects of complexity in traveltime measurements of core sensitive phases that cannot beexplained by mantle structure Romanowicz et al (2003) proposedalternative models that would involve structure in the outer corewith either faster than average velocities in the inner core tangentcylinder or in polar caps at the top of the outer core that couldrepresent an increased concentration of light elements For exam-ple Fig 31 shows the pattern obtained when plotting absolutetravel time anomalies for DFBC and AB plotted at the entry pointof the corresponding raypath into the outer core on the Alaskaside for south-Sandwich to Alaska paths as well as paths fromAlaska to Antarctica When plotted in this manner the travel-time anomalies form a coherent pattern suggesting a localizedanomaly that may originate near the core-mantle boundary onthe Alaska side compatible with both a polar cap in the outer coreor heterogeneity within at least part of the tangent cylinder Mostanomalously split inner core sensitive normal modes could beexplained by either of these models except for mode 3S2 whichexhibits particularly strong splitting (Romanowicz and Breacuteger2000) These results have been reexamined critically by Ishii andDziewonski (2005)

Putting structure in the outer core remains controversial (egSouriau et al 2003) as significant density anomalies in the vigor-ously convecting outer core appear to be ruled out (eg Stevenson1987) However recent work suggesting the possibility of stagnantlayers at the top of the outer core from magneto-hydrodynamicsconsiderations (eg Buffett 2014) indicates that at least the polarcap hypothesis should perhaps remain on the table as alternativeto a strongly anisotropic region in the inner core On the otherhand Tkalcic (2010) found that differential travel time anomaliesof similar amplitude are observed on PcP-P data in the vicinity ofSSI Because such data do not sample the inner core at all Tkalcic(2010) proposed that a significant part of the SSI anomaly could

Fig 30 Travel time anomalies of core phases as a function of angle n of the ray path in the inner core with respect to the Earthrsquos rotation axis from the combined Berkeleydata collection (Tkalcic et al 2002) and from Leykam et al (2010) Left (DFndashBC) ndash Right absolute DF a) and d) all data b) and e) for events in the south-Sandwich Islands c)and f) for events in Alaska

80 B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90

be located in the deep mantle although no such structure has beenidentified yet tomographically Therefore explaining the broadspread of PKP(DF) travel time anomalies on SSI paths to Alaskaremains an open question which needs to be answered beforerobust bounds on the strength of anisotropy in the inner corersquoswestern hemisphere can be provided to mineral physicists Accu-mulation of data from the current deployment of USArray in Alaskamay shed more light on this question

This leads us to the second and possibly related challenge thathas come to light recently (Lincot et al 2015 2016 Romanowiczet al 2016) which is how to reconcile the 3ndash8 seismic anisotropyinferred in the inner corersquos western hemisphere with currentknowledge from mineral physics

6 Mineral physics of the inner core

61 Phase relations

From the mineral physics point of view a first order questionhas been the phase in which iron is present in the inner coreThe high pressure e phase of iron was first confirmed by X-raydiffraction by Mao et al (1967) and a hexagonal close-packed(hcp) structure was identified Since then many high pressureexperiments have been conducted Most important are those per-tinent to conditions of the inner core (Fig 32) They includedynamic shock compression with relatively large error margins(eg Alfegrave et al 2002 Anzellini et al 2013 Brown 2001 Ping

Fig 31 Absolute travel time anomalies for DF (circles and triangles) BC (crosses)and AB (squares) for events at latitudes lower than 50S or higher than 50Nplotted as a function of the location of the entry point of the ray path into the outercore Triangles are for events at latitude gt50N observed at stations at latitudeslt50S Expanded from Romanowicz et al (2003) to include data from Leykamet al (2010) as also shown in Fig 34bndashf This collection of travel time anomaliesforms a coherent pattern with a sharp gradient delineating a localized boundarybetween very fast paths to the northwest and normal paths to the southeastsuggesting a lsquolsquopolar caprdquo pattern that may or may not originate in the inner coreNote that the color code is centered at dt = 35 s

Fig 32 Pressurendashtemperature phase diagram for iron at high pressure illustratingdiamond anvil and shock experiments as well as ab initio simulations The linescorrespond to melting curves (courtesy of BK Godwal)

B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90 81

et al 2013) and DAC experiments at high pressure and tempera-ture up to 380 GPa and 6000 K (eg Tateno et al 2010) Basedon theoretical calculations some authors have suggested thatbody-centered cubic (bcc) iron could be stable just below the melt-ing point at core pressures (eg Vocadlo et al 2003 Belonoshkoet al 2003 2006 Dubrovinsky et al 2007 Bouchet et al 2013)but most recent studies indicate that bcc is unstable at these con-ditions (eg Godwal et al 2015)

An important aspect is that the inner core may not be chemi-cally and structurally homogeneous It is likely that nickel a com-ponent in iron meteorites is also present in the core (Sakai et al2011 Tateno et al 2012) Furthermore to account for the lowerdensity implied by seismic data suggests that lighter elementsmay be present and a good candidate is silicon The Fe-Si systemhas been studied at intermediate pressure-temperatures (egSakai et al 2011 Fischer et al 2013 Fig 33) and inner core con-ditions (Tateno et al 2015) At high pressure and high tempera-ture FeSi crystallizes in the cubic B2 structure (CsCl structure)which is an ordered bcc structure Fe3Si forms a DO3 structure withdoubling of the B2 unit cell and ordering At lower pressures FeSiforms the B20 structure which is partially disordered bcc with alack of inversion symmetry (eg Jeong and Pickett 2004) Elasticproperties of FeSi have been investigated by Petrova et al (2010)Badro et al (2014) explored a range of possible elements in thecore (O S Si Ni) and concluded that oxygen is required in the outercore

62 Causes of anisotropy in the inner core

Potential mechanisms for alignment of crystals in the inner coreare dislocation-plasticity (eg Jeanloz andWenk 1988 Wenk et al2000a Lincot et al 2015 2016) growth from a melt (eg Bergman1997 Deguen 2012) magnetic Maxwell stresses (eg Karato1999 Buffett and Wenk 2001)

Radial DAC experiments (eg Wenk et al 2000a Merkel et al2004 2013 Miyagi et al 2008) documented texture developmentin e iron at high pressure and inferred (0001) and subordinatef11 20g slip combined with mechanical twinning as potentialmechanisms However these experiments were not at inner coreconditions

Elastic properties at core conditions rely on first principle calcu-lations and various groups have been involved (eg Vocadlo et al2008 2009 Mattesini et al 2010) It is interesting to find thatresults are quite contradictory as expressed in P-wave velocityprofiles for hcp single crystals with the c-axis at n = 0 (Fig 34b)While Vocadlo et al (2009) predict maximum velocities perpendic-ular to the c-axis Mattesini et al (2010) suggest maximum veloc-ities parallel to the c-axis (the elastic tensor of hexagonal crystals isaxially symmetric about the c-axis) Estimates of inner core seismicanisotropy are very high ((Vp-fast Vp-slow)Vp-iso = 3ndash8 Fig 34a)compared with the rather small P-wave anisotropy obtained fromfirst principles calculations for single crystals (eg 49 for Vocadloet al 2009 at 308 GPa and 5000 K or 57 for Mattesini et al 2010at 346 GPa and 6000 K) and the best fit with seismic data would bea hexagonal single crystal aligned with the c-axis more or less par-allel to the N-S axis A huge single crystal seems unlikely giventhat the largest documented crystals on Earth are about 20 m insize and with pressurendashtemperature gradients it is likely thathuge crystals at high temperature would undergo transformationsand recrystallization over geologic times

A recent study (Lincot et al 2016) constructed a multi-scalemodel combining self-consistent polycrystal plasticity inner-core formation models and Monte Carlo simulations of elasticparameters to predict travel times of inner core PKP waves andconfront them with observations These authors found that theycould explain as much as 3 seismic anisotropy with an hcp-ironstructure with fast c axis and with anomalous single crystal aniso-tropies near the melting point of up to 20 (Martorell et al 2013)with dominant pyramidal hc + ai slip and crystal alignment pro-vided by a low degree boundary condition for crystallization atthe ICB While this model might account for the faster PKP traveltimes on polar compared to equatorial paths it does not reproducethe L-shaped travel time anomaly curve as a function of angle n(Fig 30)

Fig 33 Phase diagrams of the Fe-Si system (Fischer et al 2013) (a) Pressurendashtemperature phase diagram illustrating stability fields of the various phases for Fe-9Si (b)Temperature-composition diagram at 145 GPa illustrating the transition from hcp to B2

Fig 34 (a) Comparison of relative velocity variations (in) as a function of angle n of the ray path in the inner core with respect to the Earthrsquos rotation axis for severalseismological models Black OIC model of Wang et al (2003) Grey OIC model of Beghein and Trampert (2003) Blue best fitting IMIC model using Wang et alrsquos model forOIC anisotropy corrections Green best fitting IMIC model using Beghein and Trampertrsquos (2003) OIC model for anisotropy corrections in the OIC In the latter two cases theIMIC radius is held at 600 km The IMIC model obtained is only slightly sensitive to the radius in the range 500ndash600 km Dashed lines indicate the range of uncertainty on theIMIC model (b) Calculated normalized P-wave velocities of hexagonal single crystals based on first principle elastic properties at various temperatures and pressures An isstrength of anisotropy The polar angle n is zero parallel to the hexagonal c-axis Mat Mattesini et al 2010 Voc Vocadlo et al (2009) Based on Romanowicz et al (2016)

82 B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90

7 Conclusions and future directions

71 Anisotropy in the deep mantle

In the last ten years global seismic tomography has providedincreasingly refined images of seismic heterogeneity in the deepEarth There is now agreement on the long wavelength structuredominated by the presence of two low shear velocity provinces(LLSVPs) under Africa and the central Pacific which may requirecompositional heterogeneity at least at their base There is alsoevidence for smaller scale structures suggestive of subductingslabs and upwelling plumes in the lower mantle While the bulkof the lower mantle appears largely isotropic the long wavelengthpattern of VTI anisotropy detected in D00 from shear wave tomo-graphic studies seems to track that of isotropic velocity with SHfaster than SV outside of the LLSVPs and SV faster than SH withinthem However the agreement among different models is limited

to the very longest wavelengths (lsquolsquodegree 200) and there are stilldebates about trade-offs between isotropic and anisotropicstructure

On the other hand recent local studies of shear wave splittingare consistently showing the presence of strong seismic anisotropy(both radial and azimuthal) at the edges of the LLSVPs primarily onthe fast side Because anisotropy in post-perovskite (pPv) isthought to be much stronger than in perovskite and pPv is likelymore widely present outside of the LLSVP (ie colder regions man-ifested by faster than average shear velocity) than inside theLLSVPs (which are likely warmer) these observations suggest thatCPO of pPv may be the cause indicating the presence of strongdeformation due to constrained flow at the base of the mantlewith a change of direction towards the vertical at the border ofthe LLSVP and more vertically oriented flow within it While veryattractive because it can also explain opposite polarity behavior inreflections of P and S waves on the discontinuity at the top of D00

B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90 83

(Thomas et al 2011 Cobden et al 2015) the interpretation interms of pPv must be considered with caution given the uncertain-ties on whether pPv is actually present at deep mantle depths

A priority for future seismic studies is to continue investigatingthe patterns of anisotropy on the borders of the LLSVPs as well as inthe vicinity of upwelling plumes where high concentrations ofstrain are expected This would be greatly helped by installationsof large aperture broadband arrays on the ocean floor collectinghigh quality horizontal component data for at least 1 year to covergaps in the available sampling of D00 in these regions We also lackrobust constraints on deep mantle P anisotropy which would helpdifferentiate between dominant (001) and (010) slip systems inpost-perovskite

Also mineral physics has added a lot of new information mostsignificantly the discovery of post-perovskite (Oganov and Ono2004) and derivation of deformation mechanisms both by experi-ments and theoretical models But as the anisotropic seismic struc-ture of the Earth has become more complex over the last ten yearsso has the interpretation with mineral physics concepts opening awide range of opportunities for new investigations Perhaps mostsignificant have been the recent advances in modeling crystaldeformation based on bonding characteristics at a wide range ofconditions that are relevant for the mantle but cannot beapproached with experiments like slow strain rates It will beimportant to apply theory to experimental conditions and thismight explain why DAC experiments at high pressure suggest(001) slip for MgSiO3 post-perovskite (Miyagi et al 2010 Wuet al 2017) while bonding models predict (010) slip at deep man-tle conditions (Goryaeva et al 2016)

High pressure experiments will remain crucial With advancesin multi-anvil technology it will become possible to reach lowermantle conditions (Yamazaki et al 2014) with larger samplesand better defined deformation geometry than DAC which isrestricted to the 50 lm range) with large gradients in pressuredeformation rates and temperature In addition D-DIA experi-ments can provide tomographic information about microstructuralevolution eg during phase transitions and recrystallization (Wanget al 2011) Also DAC technology is adding new possibilities suchas resistive heating for high temperature experiments multigraintexture analysis for coarser aggregates (eg Barton and Bernier2012 Langrand et al 2017) and the possibility of using DAC withLaue microdiffraction (Tamura 2014) to perform orientation andmicrostructural mapping in situ at high pressure

In the future also a larger range of compositions needs to beexplored experimentally for example iron-magnesium contentmultiphase systems (pPv ferropericlase and CaSiO3 perovskite)and the significance of perovskitepost-perovskite transformations

Geodynamic models need refinements New 3D models withtracers (eg Cottaar et al 2014 Li M et al 2014) still do notaccount for the very significant viscosity changes implied by min-eral physics And following texture evolution along streamlinesprovides results at different times for the advancing tracers whilerelating anisotropy results to the Earth assumes that the stream-line does not change which is clearly not the case

The issue of deformation mechanisms was addressed in Sec-tion 48 All models for lower mantle anisotropy assume disloca-tion glide of post-perovskite and ferropericlase as the cause ofcrystal alignment and use a self-consistent viscoplastic plasticitymodel Some arbitrary strain fraction corrections are introducedto account for mechanisms such as climb grain boundary migra-tion grain boundary sliding that do not contribute to texture Inthe future the significance of these mechanisms should be studiedmore systematically both with experiments and models There arestrong indications that the activity of different mechanisms is thecause for lack of significant anisotropy in large parts of the lowermantle

72 Inner core anisotropy

While the complexities of the lower mantle are developing intoa realistic and solvable puzzle inner core anisotropy is becomingmore enigmatic As we learn more about the large seismic aniso-tropy it is not clear what the origin of this signal is and how muchoriginates in the inner core There is room for many possible inter-pretations including a layered inner core with a bcc iron structurein the innermost inner core and an outer shell with an hcp struc-ture (Wang et al 2015) While such a structure is not impossibleit is quite unlikely (eg Romanowicz et al 2016) and not presentlyresolvable from seismological observations The high axial veloci-ties compared with equatorial velocities are difficult to explainand particularly the striking L-shape of the PKP travel time residualas a function of angle of the raypath in the inner core with respectto the rotation axis It is not impossible that heterogeneous struc-tures in the outer liquid core particularly columnar convectionwith a characteristic seismic pattern (eg Jones 2011 Soderlundet al 2012) influence the apparent seismic signature of the innercore A priority for future seismic studies in our view is to achieveconsensus on the origin of the observed L-shape mentioned aboveThe dense temporary broadband arrays recently installed in Alaska(as part of the Earthscope program) and in Antarctica should helpin that endeavor

On the mineral physics side there is general agreement thathexagonal close-packed iron is the most likely component butthe actual composition is still debated and an iron-silicon alloymay exist There is uncertainty and disagreement about elasticproperties of pure iron at inner core conditions derived with firstprinciples calculations (eg Vocadlo et al 2009 versus Mattesiniet al 2010) and no information about elastic properties of iron-silicon alloys While there are many experiments documentingphase relations both of Fe and Fe-Si at high pressure and temper-ature (eg Tateno et al 2010 2015) there is still considerableuncertainty about the melting temperature

These studies highlight the chemical and structural complexi-ties of the core with likely heterogeneities in the inner core vari-able elastic properties and anisotropy A multi-disciplinaryapproach including seismologists geodynamicists mineral physi-cists and material scientists is required to make progress Such col-laborations have been initiated and show great promise for thenear future

Acknowledgements

We are grateful to Mark Jellinek and Tim Horscroft for invitingus to prepare this review It was an opportunity for us to explorethe extensive literature on the subject and also to discover that alot of work remains to be done Particularly interesting was inter-action with colleagues and students at the 2016 CIDER Workshopin Santa Barbara HRW is appreciative of discussions with RainerAbart Sanne Cottaar Patrick Cordier Thorne Lay Sebastien MerkelLowell Miyagi and Kaiqing Yuan CIDER is funded through NSF(FESD grant EAR 1135452) We acknowledge support from NSF(EAR 1343908 1417229 CSEDI-106751) DOE (DE-FG02-05ER15637) CDAC We acknowledge constructive reviews by MarkJellinek and Maureen Long

References

Abart R Kunze K Milke R Sperb R Heinrich W et al 2004 Silicon and oxygenself diffusion in enstatite polycrystals the Milke (2001) rim growthexperiments revisited Contrib Mineral Petrol 147 633ndash646 httpdxdoiorg101007s00410-004-0596-9

Alfegrave D Price GD Gillan MJ 2002 Iron under Earthrsquos core conditions Liquid-state thermodynamics and high pressure melting curve from ab initio

B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90 79

of a hemispherical anisotropic structure has also been found fromthe modeling of coupling of pairs of modes sensitive to such struc-ture (Deuss et al 2010) In addition regional variations in thedirection of the fast axis and strength of anisotropy have been doc-umented (eg Breacuteger et al 1999 Sun and Song 2008ab Irving2016) To explain this complexity Tkalcic (2010) suggested thatthe inner core may be made of a patchwork of anisotropic domainsof different orientations Attenuation of PKIKP waves also presentsanisotropic variations with higher attenuation correlated withearly arrivals along quasi-polar paths (Souriau and Romanowicz1996 1997 Oreshin and Vinnik 2004) We refer the reader tomore complete reviews of seismological studies of inner core ani-sotropy (Deuss 2014 Souriau 2015 Tkalcic 2015) Here webriefly describe some of the seismological challenges that are stillpreventing us from a full understanding of these intriguingobservations

One of the main challenges in fully resolving the pattern ofinner core anisotropy is the poor directional sampling availabledue to the limited distribution of sources and receivers in polarregions (eg Tkalcic 2015) Thus paths sampling the inner coreat a given location from different directions which is necessaryto confirm the presence of anisotropy are frequently lacking mak-ing it difficult to image inner core anisotropy in three dimensionswithout imposing strong a priori-constraints (eg Sun and Song2008a Lythgoe et al 2014) The strongest anisotropy in PKIKPdata is found primarily along paths from events in South SandwichIslands (SSI) to Alaska which dominate the set of observations inthe strongly anisotropic western hemisphere that contribute tothe n angle range between 10-30o where n is the angle of the ray-path in the inner core with the Earthrsquos axis of rotation At shorterdistances (lt155) the PKP(DF) phase can be referred to PKP(BC) which is a core phase that does not traverse the inner core(Fig 29) This makes it possible to eliminate contributions fromuncertainties in the source parameters as well as a significant partof the effects of 3D mantle structure given that PKP(BC) and PKP

Fig 29 Raypaths of main body wave phases used in the study of inner-corestructure and anisotropy at an epicentral distance of 155o At this distance all threecore phases PKIKP (also called PKP(DF)) PKP(BC) and PKP(AB) are observed Thephase PKJKP (a shear wave in the inner core) is very difficult to observe and isplotted here only for reference

(DF) have very similar paths throughout the mantle diverging onlyin the vicinity of the inner core

In fact the SSI dataset shows a wide range of travel timeanomalies ranging from 0 to gt5 s when referred to the PKP(BC)phase suggesting a strong local anomaly (eg Tkalcic et al2002) When plotted as a function of the angle n the global PKP(BC)-PKP(DF) travel time dataset (which covers epicentral dis-tances between 150o and 160) forms an L-shaped curve which isnot well explained by best fitting simple models of inner core ani-sotropy with fast axis aligned with the Earthrsquos rotation axis(Fig 30) for which one would expect a parabolic shape accordingto the equation

dt frac14 athorn bcos2nthorn ccos4n

where a b c are related to integrals of elastic anisotropic parame-ters along the path in the inner core

At larger distances the reference outer core phase is PKP(AB)which spends significant time in the highly heterogeneous D00

region at the base of the mantle Therefore absolute travel timeanomalies of PKP(DF) are preferred although in that case contri-butions from mantle 3D structure and uncertainties in sourceparameters can bias the data (eg Breacuteger et al 2000) Most studieswill therefore only consider events from the high quality relocatedEHB catalog (Engdahl et al 1998) which presently exists onlythrough 2010 Still analysis of these PKP(DF) data indicate thatin the western hemisphere a similar trend is observed in the abso-lute PKP(DF) travel time residuals as in the PKP(DF)-PKP(AB) resid-uals as a function of angle n (Fig 30b) Most recent estimates of thecorresponding anisotropy are on the order of 3ndash4 in the IMICwhich is considerable and difficult to reconcile with current pre-dictions from mineral physics (see Section 6) let alone the esti-mate of 3ndash88 of Lythgoe et al (2014)

To explain this trend and other aspects of complexity in traveltime measurements of core sensitive phases that cannot beexplained by mantle structure Romanowicz et al (2003) proposedalternative models that would involve structure in the outer corewith either faster than average velocities in the inner core tangentcylinder or in polar caps at the top of the outer core that couldrepresent an increased concentration of light elements For exam-ple Fig 31 shows the pattern obtained when plotting absolutetravel time anomalies for DFBC and AB plotted at the entry pointof the corresponding raypath into the outer core on the Alaskaside for south-Sandwich to Alaska paths as well as paths fromAlaska to Antarctica When plotted in this manner the travel-time anomalies form a coherent pattern suggesting a localizedanomaly that may originate near the core-mantle boundary onthe Alaska side compatible with both a polar cap in the outer coreor heterogeneity within at least part of the tangent cylinder Mostanomalously split inner core sensitive normal modes could beexplained by either of these models except for mode 3S2 whichexhibits particularly strong splitting (Romanowicz and Breacuteger2000) These results have been reexamined critically by Ishii andDziewonski (2005)

Putting structure in the outer core remains controversial (egSouriau et al 2003) as significant density anomalies in the vigor-ously convecting outer core appear to be ruled out (eg Stevenson1987) However recent work suggesting the possibility of stagnantlayers at the top of the outer core from magneto-hydrodynamicsconsiderations (eg Buffett 2014) indicates that at least the polarcap hypothesis should perhaps remain on the table as alternativeto a strongly anisotropic region in the inner core On the otherhand Tkalcic (2010) found that differential travel time anomaliesof similar amplitude are observed on PcP-P data in the vicinity ofSSI Because such data do not sample the inner core at all Tkalcic(2010) proposed that a significant part of the SSI anomaly could

Fig 30 Travel time anomalies of core phases as a function of angle n of the ray path in the inner core with respect to the Earthrsquos rotation axis from the combined Berkeleydata collection (Tkalcic et al 2002) and from Leykam et al (2010) Left (DFndashBC) ndash Right absolute DF a) and d) all data b) and e) for events in the south-Sandwich Islands c)and f) for events in Alaska

80 B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90

be located in the deep mantle although no such structure has beenidentified yet tomographically Therefore explaining the broadspread of PKP(DF) travel time anomalies on SSI paths to Alaskaremains an open question which needs to be answered beforerobust bounds on the strength of anisotropy in the inner corersquoswestern hemisphere can be provided to mineral physicists Accu-mulation of data from the current deployment of USArray in Alaskamay shed more light on this question

This leads us to the second and possibly related challenge thathas come to light recently (Lincot et al 2015 2016 Romanowiczet al 2016) which is how to reconcile the 3ndash8 seismic anisotropyinferred in the inner corersquos western hemisphere with currentknowledge from mineral physics

6 Mineral physics of the inner core

61 Phase relations

From the mineral physics point of view a first order questionhas been the phase in which iron is present in the inner coreThe high pressure e phase of iron was first confirmed by X-raydiffraction by Mao et al (1967) and a hexagonal close-packed(hcp) structure was identified Since then many high pressureexperiments have been conducted Most important are those per-tinent to conditions of the inner core (Fig 32) They includedynamic shock compression with relatively large error margins(eg Alfegrave et al 2002 Anzellini et al 2013 Brown 2001 Ping

Fig 31 Absolute travel time anomalies for DF (circles and triangles) BC (crosses)and AB (squares) for events at latitudes lower than 50S or higher than 50Nplotted as a function of the location of the entry point of the ray path into the outercore Triangles are for events at latitude gt50N observed at stations at latitudeslt50S Expanded from Romanowicz et al (2003) to include data from Leykamet al (2010) as also shown in Fig 34bndashf This collection of travel time anomaliesforms a coherent pattern with a sharp gradient delineating a localized boundarybetween very fast paths to the northwest and normal paths to the southeastsuggesting a lsquolsquopolar caprdquo pattern that may or may not originate in the inner coreNote that the color code is centered at dt = 35 s

Fig 32 Pressurendashtemperature phase diagram for iron at high pressure illustratingdiamond anvil and shock experiments as well as ab initio simulations The linescorrespond to melting curves (courtesy of BK Godwal)

B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90 81

et al 2013) and DAC experiments at high pressure and tempera-ture up to 380 GPa and 6000 K (eg Tateno et al 2010) Basedon theoretical calculations some authors have suggested thatbody-centered cubic (bcc) iron could be stable just below the melt-ing point at core pressures (eg Vocadlo et al 2003 Belonoshkoet al 2003 2006 Dubrovinsky et al 2007 Bouchet et al 2013)but most recent studies indicate that bcc is unstable at these con-ditions (eg Godwal et al 2015)

An important aspect is that the inner core may not be chemi-cally and structurally homogeneous It is likely that nickel a com-ponent in iron meteorites is also present in the core (Sakai et al2011 Tateno et al 2012) Furthermore to account for the lowerdensity implied by seismic data suggests that lighter elementsmay be present and a good candidate is silicon The Fe-Si systemhas been studied at intermediate pressure-temperatures (egSakai et al 2011 Fischer et al 2013 Fig 33) and inner core con-ditions (Tateno et al 2015) At high pressure and high tempera-ture FeSi crystallizes in the cubic B2 structure (CsCl structure)which is an ordered bcc structure Fe3Si forms a DO3 structure withdoubling of the B2 unit cell and ordering At lower pressures FeSiforms the B20 structure which is partially disordered bcc with alack of inversion symmetry (eg Jeong and Pickett 2004) Elasticproperties of FeSi have been investigated by Petrova et al (2010)Badro et al (2014) explored a range of possible elements in thecore (O S Si Ni) and concluded that oxygen is required in the outercore

62 Causes of anisotropy in the inner core

Potential mechanisms for alignment of crystals in the inner coreare dislocation-plasticity (eg Jeanloz andWenk 1988 Wenk et al2000a Lincot et al 2015 2016) growth from a melt (eg Bergman1997 Deguen 2012) magnetic Maxwell stresses (eg Karato1999 Buffett and Wenk 2001)

Radial DAC experiments (eg Wenk et al 2000a Merkel et al2004 2013 Miyagi et al 2008) documented texture developmentin e iron at high pressure and inferred (0001) and subordinatef11 20g slip combined with mechanical twinning as potentialmechanisms However these experiments were not at inner coreconditions

Elastic properties at core conditions rely on first principle calcu-lations and various groups have been involved (eg Vocadlo et al2008 2009 Mattesini et al 2010) It is interesting to find thatresults are quite contradictory as expressed in P-wave velocityprofiles for hcp single crystals with the c-axis at n = 0 (Fig 34b)While Vocadlo et al (2009) predict maximum velocities perpendic-ular to the c-axis Mattesini et al (2010) suggest maximum veloc-ities parallel to the c-axis (the elastic tensor of hexagonal crystals isaxially symmetric about the c-axis) Estimates of inner core seismicanisotropy are very high ((Vp-fast Vp-slow)Vp-iso = 3ndash8 Fig 34a)compared with the rather small P-wave anisotropy obtained fromfirst principles calculations for single crystals (eg 49 for Vocadloet al 2009 at 308 GPa and 5000 K or 57 for Mattesini et al 2010at 346 GPa and 6000 K) and the best fit with seismic data would bea hexagonal single crystal aligned with the c-axis more or less par-allel to the N-S axis A huge single crystal seems unlikely giventhat the largest documented crystals on Earth are about 20 m insize and with pressurendashtemperature gradients it is likely thathuge crystals at high temperature would undergo transformationsand recrystallization over geologic times

A recent study (Lincot et al 2016) constructed a multi-scalemodel combining self-consistent polycrystal plasticity inner-core formation models and Monte Carlo simulations of elasticparameters to predict travel times of inner core PKP waves andconfront them with observations These authors found that theycould explain as much as 3 seismic anisotropy with an hcp-ironstructure with fast c axis and with anomalous single crystal aniso-tropies near the melting point of up to 20 (Martorell et al 2013)with dominant pyramidal hc + ai slip and crystal alignment pro-vided by a low degree boundary condition for crystallization atthe ICB While this model might account for the faster PKP traveltimes on polar compared to equatorial paths it does not reproducethe L-shaped travel time anomaly curve as a function of angle n(Fig 30)

Fig 33 Phase diagrams of the Fe-Si system (Fischer et al 2013) (a) Pressurendashtemperature phase diagram illustrating stability fields of the various phases for Fe-9Si (b)Temperature-composition diagram at 145 GPa illustrating the transition from hcp to B2

Fig 34 (a) Comparison of relative velocity variations (in) as a function of angle n of the ray path in the inner core with respect to the Earthrsquos rotation axis for severalseismological models Black OIC model of Wang et al (2003) Grey OIC model of Beghein and Trampert (2003) Blue best fitting IMIC model using Wang et alrsquos model forOIC anisotropy corrections Green best fitting IMIC model using Beghein and Trampertrsquos (2003) OIC model for anisotropy corrections in the OIC In the latter two cases theIMIC radius is held at 600 km The IMIC model obtained is only slightly sensitive to the radius in the range 500ndash600 km Dashed lines indicate the range of uncertainty on theIMIC model (b) Calculated normalized P-wave velocities of hexagonal single crystals based on first principle elastic properties at various temperatures and pressures An isstrength of anisotropy The polar angle n is zero parallel to the hexagonal c-axis Mat Mattesini et al 2010 Voc Vocadlo et al (2009) Based on Romanowicz et al (2016)

82 B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90

7 Conclusions and future directions

71 Anisotropy in the deep mantle

In the last ten years global seismic tomography has providedincreasingly refined images of seismic heterogeneity in the deepEarth There is now agreement on the long wavelength structuredominated by the presence of two low shear velocity provinces(LLSVPs) under Africa and the central Pacific which may requirecompositional heterogeneity at least at their base There is alsoevidence for smaller scale structures suggestive of subductingslabs and upwelling plumes in the lower mantle While the bulkof the lower mantle appears largely isotropic the long wavelengthpattern of VTI anisotropy detected in D00 from shear wave tomo-graphic studies seems to track that of isotropic velocity with SHfaster than SV outside of the LLSVPs and SV faster than SH withinthem However the agreement among different models is limited

to the very longest wavelengths (lsquolsquodegree 200) and there are stilldebates about trade-offs between isotropic and anisotropicstructure

On the other hand recent local studies of shear wave splittingare consistently showing the presence of strong seismic anisotropy(both radial and azimuthal) at the edges of the LLSVPs primarily onthe fast side Because anisotropy in post-perovskite (pPv) isthought to be much stronger than in perovskite and pPv is likelymore widely present outside of the LLSVP (ie colder regions man-ifested by faster than average shear velocity) than inside theLLSVPs (which are likely warmer) these observations suggest thatCPO of pPv may be the cause indicating the presence of strongdeformation due to constrained flow at the base of the mantlewith a change of direction towards the vertical at the border ofthe LLSVP and more vertically oriented flow within it While veryattractive because it can also explain opposite polarity behavior inreflections of P and S waves on the discontinuity at the top of D00

B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90 83

(Thomas et al 2011 Cobden et al 2015) the interpretation interms of pPv must be considered with caution given the uncertain-ties on whether pPv is actually present at deep mantle depths

A priority for future seismic studies is to continue investigatingthe patterns of anisotropy on the borders of the LLSVPs as well as inthe vicinity of upwelling plumes where high concentrations ofstrain are expected This would be greatly helped by installationsof large aperture broadband arrays on the ocean floor collectinghigh quality horizontal component data for at least 1 year to covergaps in the available sampling of D00 in these regions We also lackrobust constraints on deep mantle P anisotropy which would helpdifferentiate between dominant (001) and (010) slip systems inpost-perovskite

Also mineral physics has added a lot of new information mostsignificantly the discovery of post-perovskite (Oganov and Ono2004) and derivation of deformation mechanisms both by experi-ments and theoretical models But as the anisotropic seismic struc-ture of the Earth has become more complex over the last ten yearsso has the interpretation with mineral physics concepts opening awide range of opportunities for new investigations Perhaps mostsignificant have been the recent advances in modeling crystaldeformation based on bonding characteristics at a wide range ofconditions that are relevant for the mantle but cannot beapproached with experiments like slow strain rates It will beimportant to apply theory to experimental conditions and thismight explain why DAC experiments at high pressure suggest(001) slip for MgSiO3 post-perovskite (Miyagi et al 2010 Wuet al 2017) while bonding models predict (010) slip at deep man-tle conditions (Goryaeva et al 2016)

High pressure experiments will remain crucial With advancesin multi-anvil technology it will become possible to reach lowermantle conditions (Yamazaki et al 2014) with larger samplesand better defined deformation geometry than DAC which isrestricted to the 50 lm range) with large gradients in pressuredeformation rates and temperature In addition D-DIA experi-ments can provide tomographic information about microstructuralevolution eg during phase transitions and recrystallization (Wanget al 2011) Also DAC technology is adding new possibilities suchas resistive heating for high temperature experiments multigraintexture analysis for coarser aggregates (eg Barton and Bernier2012 Langrand et al 2017) and the possibility of using DAC withLaue microdiffraction (Tamura 2014) to perform orientation andmicrostructural mapping in situ at high pressure

In the future also a larger range of compositions needs to beexplored experimentally for example iron-magnesium contentmultiphase systems (pPv ferropericlase and CaSiO3 perovskite)and the significance of perovskitepost-perovskite transformations

Geodynamic models need refinements New 3D models withtracers (eg Cottaar et al 2014 Li M et al 2014) still do notaccount for the very significant viscosity changes implied by min-eral physics And following texture evolution along streamlinesprovides results at different times for the advancing tracers whilerelating anisotropy results to the Earth assumes that the stream-line does not change which is clearly not the case

The issue of deformation mechanisms was addressed in Sec-tion 48 All models for lower mantle anisotropy assume disloca-tion glide of post-perovskite and ferropericlase as the cause ofcrystal alignment and use a self-consistent viscoplastic plasticitymodel Some arbitrary strain fraction corrections are introducedto account for mechanisms such as climb grain boundary migra-tion grain boundary sliding that do not contribute to texture Inthe future the significance of these mechanisms should be studiedmore systematically both with experiments and models There arestrong indications that the activity of different mechanisms is thecause for lack of significant anisotropy in large parts of the lowermantle

72 Inner core anisotropy

While the complexities of the lower mantle are developing intoa realistic and solvable puzzle inner core anisotropy is becomingmore enigmatic As we learn more about the large seismic aniso-tropy it is not clear what the origin of this signal is and how muchoriginates in the inner core There is room for many possible inter-pretations including a layered inner core with a bcc iron structurein the innermost inner core and an outer shell with an hcp struc-ture (Wang et al 2015) While such a structure is not impossibleit is quite unlikely (eg Romanowicz et al 2016) and not presentlyresolvable from seismological observations The high axial veloci-ties compared with equatorial velocities are difficult to explainand particularly the striking L-shape of the PKP travel time residualas a function of angle of the raypath in the inner core with respectto the rotation axis It is not impossible that heterogeneous struc-tures in the outer liquid core particularly columnar convectionwith a characteristic seismic pattern (eg Jones 2011 Soderlundet al 2012) influence the apparent seismic signature of the innercore A priority for future seismic studies in our view is to achieveconsensus on the origin of the observed L-shape mentioned aboveThe dense temporary broadband arrays recently installed in Alaska(as part of the Earthscope program) and in Antarctica should helpin that endeavor

On the mineral physics side there is general agreement thathexagonal close-packed iron is the most likely component butthe actual composition is still debated and an iron-silicon alloymay exist There is uncertainty and disagreement about elasticproperties of pure iron at inner core conditions derived with firstprinciples calculations (eg Vocadlo et al 2009 versus Mattesiniet al 2010) and no information about elastic properties of iron-silicon alloys While there are many experiments documentingphase relations both of Fe and Fe-Si at high pressure and temper-ature (eg Tateno et al 2010 2015) there is still considerableuncertainty about the melting temperature

These studies highlight the chemical and structural complexi-ties of the core with likely heterogeneities in the inner core vari-able elastic properties and anisotropy A multi-disciplinaryapproach including seismologists geodynamicists mineral physi-cists and material scientists is required to make progress Such col-laborations have been initiated and show great promise for thenear future

Acknowledgements

We are grateful to Mark Jellinek and Tim Horscroft for invitingus to prepare this review It was an opportunity for us to explorethe extensive literature on the subject and also to discover that alot of work remains to be done Particularly interesting was inter-action with colleagues and students at the 2016 CIDER Workshopin Santa Barbara HRW is appreciative of discussions with RainerAbart Sanne Cottaar Patrick Cordier Thorne Lay Sebastien MerkelLowell Miyagi and Kaiqing Yuan CIDER is funded through NSF(FESD grant EAR 1135452) We acknowledge support from NSF(EAR 1343908 1417229 CSEDI-106751) DOE (DE-FG02-05ER15637) CDAC We acknowledge constructive reviews by MarkJellinek and Maureen Long

References

Abart R Kunze K Milke R Sperb R Heinrich W et al 2004 Silicon and oxygenself diffusion in enstatite polycrystals the Milke (2001) rim growthexperiments revisited Contrib Mineral Petrol 147 633ndash646 httpdxdoiorg101007s00410-004-0596-9

Alfegrave D Price GD Gillan MJ 2002 Iron under Earthrsquos core conditions Liquid-state thermodynamics and high pressure melting curve from ab initio

Fig 30 Travel time anomalies of core phases as a function of angle n of the ray path in the inner core with respect to the Earthrsquos rotation axis from the combined Berkeleydata collection (Tkalcic et al 2002) and from Leykam et al (2010) Left (DFndashBC) ndash Right absolute DF a) and d) all data b) and e) for events in the south-Sandwich Islands c)and f) for events in Alaska

80 B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90

be located in the deep mantle although no such structure has beenidentified yet tomographically Therefore explaining the broadspread of PKP(DF) travel time anomalies on SSI paths to Alaskaremains an open question which needs to be answered beforerobust bounds on the strength of anisotropy in the inner corersquoswestern hemisphere can be provided to mineral physicists Accu-mulation of data from the current deployment of USArray in Alaskamay shed more light on this question

This leads us to the second and possibly related challenge thathas come to light recently (Lincot et al 2015 2016 Romanowiczet al 2016) which is how to reconcile the 3ndash8 seismic anisotropyinferred in the inner corersquos western hemisphere with currentknowledge from mineral physics

6 Mineral physics of the inner core

61 Phase relations

From the mineral physics point of view a first order questionhas been the phase in which iron is present in the inner coreThe high pressure e phase of iron was first confirmed by X-raydiffraction by Mao et al (1967) and a hexagonal close-packed(hcp) structure was identified Since then many high pressureexperiments have been conducted Most important are those per-tinent to conditions of the inner core (Fig 32) They includedynamic shock compression with relatively large error margins(eg Alfegrave et al 2002 Anzellini et al 2013 Brown 2001 Ping

Fig 31 Absolute travel time anomalies for DF (circles and triangles) BC (crosses)and AB (squares) for events at latitudes lower than 50S or higher than 50Nplotted as a function of the location of the entry point of the ray path into the outercore Triangles are for events at latitude gt50N observed at stations at latitudeslt50S Expanded from Romanowicz et al (2003) to include data from Leykamet al (2010) as also shown in Fig 34bndashf This collection of travel time anomaliesforms a coherent pattern with a sharp gradient delineating a localized boundarybetween very fast paths to the northwest and normal paths to the southeastsuggesting a lsquolsquopolar caprdquo pattern that may or may not originate in the inner coreNote that the color code is centered at dt = 35 s

Fig 32 Pressurendashtemperature phase diagram for iron at high pressure illustratingdiamond anvil and shock experiments as well as ab initio simulations The linescorrespond to melting curves (courtesy of BK Godwal)

B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90 81

et al 2013) and DAC experiments at high pressure and tempera-ture up to 380 GPa and 6000 K (eg Tateno et al 2010) Basedon theoretical calculations some authors have suggested thatbody-centered cubic (bcc) iron could be stable just below the melt-ing point at core pressures (eg Vocadlo et al 2003 Belonoshkoet al 2003 2006 Dubrovinsky et al 2007 Bouchet et al 2013)but most recent studies indicate that bcc is unstable at these con-ditions (eg Godwal et al 2015)

An important aspect is that the inner core may not be chemi-cally and structurally homogeneous It is likely that nickel a com-ponent in iron meteorites is also present in the core (Sakai et al2011 Tateno et al 2012) Furthermore to account for the lowerdensity implied by seismic data suggests that lighter elementsmay be present and a good candidate is silicon The Fe-Si systemhas been studied at intermediate pressure-temperatures (egSakai et al 2011 Fischer et al 2013 Fig 33) and inner core con-ditions (Tateno et al 2015) At high pressure and high tempera-ture FeSi crystallizes in the cubic B2 structure (CsCl structure)which is an ordered bcc structure Fe3Si forms a DO3 structure withdoubling of the B2 unit cell and ordering At lower pressures FeSiforms the B20 structure which is partially disordered bcc with alack of inversion symmetry (eg Jeong and Pickett 2004) Elasticproperties of FeSi have been investigated by Petrova et al (2010)Badro et al (2014) explored a range of possible elements in thecore (O S Si Ni) and concluded that oxygen is required in the outercore

62 Causes of anisotropy in the inner core

Potential mechanisms for alignment of crystals in the inner coreare dislocation-plasticity (eg Jeanloz andWenk 1988 Wenk et al2000a Lincot et al 2015 2016) growth from a melt (eg Bergman1997 Deguen 2012) magnetic Maxwell stresses (eg Karato1999 Buffett and Wenk 2001)

Radial DAC experiments (eg Wenk et al 2000a Merkel et al2004 2013 Miyagi et al 2008) documented texture developmentin e iron at high pressure and inferred (0001) and subordinatef11 20g slip combined with mechanical twinning as potentialmechanisms However these experiments were not at inner coreconditions

Elastic properties at core conditions rely on first principle calcu-lations and various groups have been involved (eg Vocadlo et al2008 2009 Mattesini et al 2010) It is interesting to find thatresults are quite contradictory as expressed in P-wave velocityprofiles for hcp single crystals with the c-axis at n = 0 (Fig 34b)While Vocadlo et al (2009) predict maximum velocities perpendic-ular to the c-axis Mattesini et al (2010) suggest maximum veloc-ities parallel to the c-axis (the elastic tensor of hexagonal crystals isaxially symmetric about the c-axis) Estimates of inner core seismicanisotropy are very high ((Vp-fast Vp-slow)Vp-iso = 3ndash8 Fig 34a)compared with the rather small P-wave anisotropy obtained fromfirst principles calculations for single crystals (eg 49 for Vocadloet al 2009 at 308 GPa and 5000 K or 57 for Mattesini et al 2010at 346 GPa and 6000 K) and the best fit with seismic data would bea hexagonal single crystal aligned with the c-axis more or less par-allel to the N-S axis A huge single crystal seems unlikely giventhat the largest documented crystals on Earth are about 20 m insize and with pressurendashtemperature gradients it is likely thathuge crystals at high temperature would undergo transformationsand recrystallization over geologic times

A recent study (Lincot et al 2016) constructed a multi-scalemodel combining self-consistent polycrystal plasticity inner-core formation models and Monte Carlo simulations of elasticparameters to predict travel times of inner core PKP waves andconfront them with observations These authors found that theycould explain as much as 3 seismic anisotropy with an hcp-ironstructure with fast c axis and with anomalous single crystal aniso-tropies near the melting point of up to 20 (Martorell et al 2013)with dominant pyramidal hc + ai slip and crystal alignment pro-vided by a low degree boundary condition for crystallization atthe ICB While this model might account for the faster PKP traveltimes on polar compared to equatorial paths it does not reproducethe L-shaped travel time anomaly curve as a function of angle n(Fig 30)

Fig 33 Phase diagrams of the Fe-Si system (Fischer et al 2013) (a) Pressurendashtemperature phase diagram illustrating stability fields of the various phases for Fe-9Si (b)Temperature-composition diagram at 145 GPa illustrating the transition from hcp to B2

Fig 34 (a) Comparison of relative velocity variations (in) as a function of angle n of the ray path in the inner core with respect to the Earthrsquos rotation axis for severalseismological models Black OIC model of Wang et al (2003) Grey OIC model of Beghein and Trampert (2003) Blue best fitting IMIC model using Wang et alrsquos model forOIC anisotropy corrections Green best fitting IMIC model using Beghein and Trampertrsquos (2003) OIC model for anisotropy corrections in the OIC In the latter two cases theIMIC radius is held at 600 km The IMIC model obtained is only slightly sensitive to the radius in the range 500ndash600 km Dashed lines indicate the range of uncertainty on theIMIC model (b) Calculated normalized P-wave velocities of hexagonal single crystals based on first principle elastic properties at various temperatures and pressures An isstrength of anisotropy The polar angle n is zero parallel to the hexagonal c-axis Mat Mattesini et al 2010 Voc Vocadlo et al (2009) Based on Romanowicz et al (2016)

82 B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90

7 Conclusions and future directions

71 Anisotropy in the deep mantle

In the last ten years global seismic tomography has providedincreasingly refined images of seismic heterogeneity in the deepEarth There is now agreement on the long wavelength structuredominated by the presence of two low shear velocity provinces(LLSVPs) under Africa and the central Pacific which may requirecompositional heterogeneity at least at their base There is alsoevidence for smaller scale structures suggestive of subductingslabs and upwelling plumes in the lower mantle While the bulkof the lower mantle appears largely isotropic the long wavelengthpattern of VTI anisotropy detected in D00 from shear wave tomo-graphic studies seems to track that of isotropic velocity with SHfaster than SV outside of the LLSVPs and SV faster than SH withinthem However the agreement among different models is limited

to the very longest wavelengths (lsquolsquodegree 200) and there are stilldebates about trade-offs between isotropic and anisotropicstructure

On the other hand recent local studies of shear wave splittingare consistently showing the presence of strong seismic anisotropy(both radial and azimuthal) at the edges of the LLSVPs primarily onthe fast side Because anisotropy in post-perovskite (pPv) isthought to be much stronger than in perovskite and pPv is likelymore widely present outside of the LLSVP (ie colder regions man-ifested by faster than average shear velocity) than inside theLLSVPs (which are likely warmer) these observations suggest thatCPO of pPv may be the cause indicating the presence of strongdeformation due to constrained flow at the base of the mantlewith a change of direction towards the vertical at the border ofthe LLSVP and more vertically oriented flow within it While veryattractive because it can also explain opposite polarity behavior inreflections of P and S waves on the discontinuity at the top of D00

B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90 83

(Thomas et al 2011 Cobden et al 2015) the interpretation interms of pPv must be considered with caution given the uncertain-ties on whether pPv is actually present at deep mantle depths

A priority for future seismic studies is to continue investigatingthe patterns of anisotropy on the borders of the LLSVPs as well as inthe vicinity of upwelling plumes where high concentrations ofstrain are expected This would be greatly helped by installationsof large aperture broadband arrays on the ocean floor collectinghigh quality horizontal component data for at least 1 year to covergaps in the available sampling of D00 in these regions We also lackrobust constraints on deep mantle P anisotropy which would helpdifferentiate between dominant (001) and (010) slip systems inpost-perovskite

Also mineral physics has added a lot of new information mostsignificantly the discovery of post-perovskite (Oganov and Ono2004) and derivation of deformation mechanisms both by experi-ments and theoretical models But as the anisotropic seismic struc-ture of the Earth has become more complex over the last ten yearsso has the interpretation with mineral physics concepts opening awide range of opportunities for new investigations Perhaps mostsignificant have been the recent advances in modeling crystaldeformation based on bonding characteristics at a wide range ofconditions that are relevant for the mantle but cannot beapproached with experiments like slow strain rates It will beimportant to apply theory to experimental conditions and thismight explain why DAC experiments at high pressure suggest(001) slip for MgSiO3 post-perovskite (Miyagi et al 2010 Wuet al 2017) while bonding models predict (010) slip at deep man-tle conditions (Goryaeva et al 2016)

High pressure experiments will remain crucial With advancesin multi-anvil technology it will become possible to reach lowermantle conditions (Yamazaki et al 2014) with larger samplesand better defined deformation geometry than DAC which isrestricted to the 50 lm range) with large gradients in pressuredeformation rates and temperature In addition D-DIA experi-ments can provide tomographic information about microstructuralevolution eg during phase transitions and recrystallization (Wanget al 2011) Also DAC technology is adding new possibilities suchas resistive heating for high temperature experiments multigraintexture analysis for coarser aggregates (eg Barton and Bernier2012 Langrand et al 2017) and the possibility of using DAC withLaue microdiffraction (Tamura 2014) to perform orientation andmicrostructural mapping in situ at high pressure

In the future also a larger range of compositions needs to beexplored experimentally for example iron-magnesium contentmultiphase systems (pPv ferropericlase and CaSiO3 perovskite)and the significance of perovskitepost-perovskite transformations

Geodynamic models need refinements New 3D models withtracers (eg Cottaar et al 2014 Li M et al 2014) still do notaccount for the very significant viscosity changes implied by min-eral physics And following texture evolution along streamlinesprovides results at different times for the advancing tracers whilerelating anisotropy results to the Earth assumes that the stream-line does not change which is clearly not the case

The issue of deformation mechanisms was addressed in Sec-tion 48 All models for lower mantle anisotropy assume disloca-tion glide of post-perovskite and ferropericlase as the cause ofcrystal alignment and use a self-consistent viscoplastic plasticitymodel Some arbitrary strain fraction corrections are introducedto account for mechanisms such as climb grain boundary migra-tion grain boundary sliding that do not contribute to texture Inthe future the significance of these mechanisms should be studiedmore systematically both with experiments and models There arestrong indications that the activity of different mechanisms is thecause for lack of significant anisotropy in large parts of the lowermantle

72 Inner core anisotropy

While the complexities of the lower mantle are developing intoa realistic and solvable puzzle inner core anisotropy is becomingmore enigmatic As we learn more about the large seismic aniso-tropy it is not clear what the origin of this signal is and how muchoriginates in the inner core There is room for many possible inter-pretations including a layered inner core with a bcc iron structurein the innermost inner core and an outer shell with an hcp struc-ture (Wang et al 2015) While such a structure is not impossibleit is quite unlikely (eg Romanowicz et al 2016) and not presentlyresolvable from seismological observations The high axial veloci-ties compared with equatorial velocities are difficult to explainand particularly the striking L-shape of the PKP travel time residualas a function of angle of the raypath in the inner core with respectto the rotation axis It is not impossible that heterogeneous struc-tures in the outer liquid core particularly columnar convectionwith a characteristic seismic pattern (eg Jones 2011 Soderlundet al 2012) influence the apparent seismic signature of the innercore A priority for future seismic studies in our view is to achieveconsensus on the origin of the observed L-shape mentioned aboveThe dense temporary broadband arrays recently installed in Alaska(as part of the Earthscope program) and in Antarctica should helpin that endeavor

On the mineral physics side there is general agreement thathexagonal close-packed iron is the most likely component butthe actual composition is still debated and an iron-silicon alloymay exist There is uncertainty and disagreement about elasticproperties of pure iron at inner core conditions derived with firstprinciples calculations (eg Vocadlo et al 2009 versus Mattesiniet al 2010) and no information about elastic properties of iron-silicon alloys While there are many experiments documentingphase relations both of Fe and Fe-Si at high pressure and temper-ature (eg Tateno et al 2010 2015) there is still considerableuncertainty about the melting temperature

These studies highlight the chemical and structural complexi-ties of the core with likely heterogeneities in the inner core vari-able elastic properties and anisotropy A multi-disciplinaryapproach including seismologists geodynamicists mineral physi-cists and material scientists is required to make progress Such col-laborations have been initiated and show great promise for thenear future

Acknowledgements

We are grateful to Mark Jellinek and Tim Horscroft for invitingus to prepare this review It was an opportunity for us to explorethe extensive literature on the subject and also to discover that alot of work remains to be done Particularly interesting was inter-action with colleagues and students at the 2016 CIDER Workshopin Santa Barbara HRW is appreciative of discussions with RainerAbart Sanne Cottaar Patrick Cordier Thorne Lay Sebastien MerkelLowell Miyagi and Kaiqing Yuan CIDER is funded through NSF(FESD grant EAR 1135452) We acknowledge support from NSF(EAR 1343908 1417229 CSEDI-106751) DOE (DE-FG02-05ER15637) CDAC We acknowledge constructive reviews by MarkJellinek and Maureen Long

References

Abart R Kunze K Milke R Sperb R Heinrich W et al 2004 Silicon and oxygenself diffusion in enstatite polycrystals the Milke (2001) rim growthexperiments revisited Contrib Mineral Petrol 147 633ndash646 httpdxdoiorg101007s00410-004-0596-9

Alfegrave D Price GD Gillan MJ 2002 Iron under Earthrsquos core conditions Liquid-state thermodynamics and high pressure melting curve from ab initio

Fig 31 Absolute travel time anomalies for DF (circles and triangles) BC (crosses)and AB (squares) for events at latitudes lower than 50S or higher than 50Nplotted as a function of the location of the entry point of the ray path into the outercore Triangles are for events at latitude gt50N observed at stations at latitudeslt50S Expanded from Romanowicz et al (2003) to include data from Leykamet al (2010) as also shown in Fig 34bndashf This collection of travel time anomaliesforms a coherent pattern with a sharp gradient delineating a localized boundarybetween very fast paths to the northwest and normal paths to the southeastsuggesting a lsquolsquopolar caprdquo pattern that may or may not originate in the inner coreNote that the color code is centered at dt = 35 s

Fig 32 Pressurendashtemperature phase diagram for iron at high pressure illustratingdiamond anvil and shock experiments as well as ab initio simulations The linescorrespond to melting curves (courtesy of BK Godwal)

B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90 81

et al 2013) and DAC experiments at high pressure and tempera-ture up to 380 GPa and 6000 K (eg Tateno et al 2010) Basedon theoretical calculations some authors have suggested thatbody-centered cubic (bcc) iron could be stable just below the melt-ing point at core pressures (eg Vocadlo et al 2003 Belonoshkoet al 2003 2006 Dubrovinsky et al 2007 Bouchet et al 2013)but most recent studies indicate that bcc is unstable at these con-ditions (eg Godwal et al 2015)

An important aspect is that the inner core may not be chemi-cally and structurally homogeneous It is likely that nickel a com-ponent in iron meteorites is also present in the core (Sakai et al2011 Tateno et al 2012) Furthermore to account for the lowerdensity implied by seismic data suggests that lighter elementsmay be present and a good candidate is silicon The Fe-Si systemhas been studied at intermediate pressure-temperatures (egSakai et al 2011 Fischer et al 2013 Fig 33) and inner core con-ditions (Tateno et al 2015) At high pressure and high tempera-ture FeSi crystallizes in the cubic B2 structure (CsCl structure)which is an ordered bcc structure Fe3Si forms a DO3 structure withdoubling of the B2 unit cell and ordering At lower pressures FeSiforms the B20 structure which is partially disordered bcc with alack of inversion symmetry (eg Jeong and Pickett 2004) Elasticproperties of FeSi have been investigated by Petrova et al (2010)Badro et al (2014) explored a range of possible elements in thecore (O S Si Ni) and concluded that oxygen is required in the outercore

62 Causes of anisotropy in the inner core

Potential mechanisms for alignment of crystals in the inner coreare dislocation-plasticity (eg Jeanloz andWenk 1988 Wenk et al2000a Lincot et al 2015 2016) growth from a melt (eg Bergman1997 Deguen 2012) magnetic Maxwell stresses (eg Karato1999 Buffett and Wenk 2001)

Radial DAC experiments (eg Wenk et al 2000a Merkel et al2004 2013 Miyagi et al 2008) documented texture developmentin e iron at high pressure and inferred (0001) and subordinatef11 20g slip combined with mechanical twinning as potentialmechanisms However these experiments were not at inner coreconditions

Elastic properties at core conditions rely on first principle calcu-lations and various groups have been involved (eg Vocadlo et al2008 2009 Mattesini et al 2010) It is interesting to find thatresults are quite contradictory as expressed in P-wave velocityprofiles for hcp single crystals with the c-axis at n = 0 (Fig 34b)While Vocadlo et al (2009) predict maximum velocities perpendic-ular to the c-axis Mattesini et al (2010) suggest maximum veloc-ities parallel to the c-axis (the elastic tensor of hexagonal crystals isaxially symmetric about the c-axis) Estimates of inner core seismicanisotropy are very high ((Vp-fast Vp-slow)Vp-iso = 3ndash8 Fig 34a)compared with the rather small P-wave anisotropy obtained fromfirst principles calculations for single crystals (eg 49 for Vocadloet al 2009 at 308 GPa and 5000 K or 57 for Mattesini et al 2010at 346 GPa and 6000 K) and the best fit with seismic data would bea hexagonal single crystal aligned with the c-axis more or less par-allel to the N-S axis A huge single crystal seems unlikely giventhat the largest documented crystals on Earth are about 20 m insize and with pressurendashtemperature gradients it is likely thathuge crystals at high temperature would undergo transformationsand recrystallization over geologic times

A recent study (Lincot et al 2016) constructed a multi-scalemodel combining self-consistent polycrystal plasticity inner-core formation models and Monte Carlo simulations of elasticparameters to predict travel times of inner core PKP waves andconfront them with observations These authors found that theycould explain as much as 3 seismic anisotropy with an hcp-ironstructure with fast c axis and with anomalous single crystal aniso-tropies near the melting point of up to 20 (Martorell et al 2013)with dominant pyramidal hc + ai slip and crystal alignment pro-vided by a low degree boundary condition for crystallization atthe ICB While this model might account for the faster PKP traveltimes on polar compared to equatorial paths it does not reproducethe L-shaped travel time anomaly curve as a function of angle n(Fig 30)

Fig 33 Phase diagrams of the Fe-Si system (Fischer et al 2013) (a) Pressurendashtemperature phase diagram illustrating stability fields of the various phases for Fe-9Si (b)Temperature-composition diagram at 145 GPa illustrating the transition from hcp to B2

Fig 34 (a) Comparison of relative velocity variations (in) as a function of angle n of the ray path in the inner core with respect to the Earthrsquos rotation axis for severalseismological models Black OIC model of Wang et al (2003) Grey OIC model of Beghein and Trampert (2003) Blue best fitting IMIC model using Wang et alrsquos model forOIC anisotropy corrections Green best fitting IMIC model using Beghein and Trampertrsquos (2003) OIC model for anisotropy corrections in the OIC In the latter two cases theIMIC radius is held at 600 km The IMIC model obtained is only slightly sensitive to the radius in the range 500ndash600 km Dashed lines indicate the range of uncertainty on theIMIC model (b) Calculated normalized P-wave velocities of hexagonal single crystals based on first principle elastic properties at various temperatures and pressures An isstrength of anisotropy The polar angle n is zero parallel to the hexagonal c-axis Mat Mattesini et al 2010 Voc Vocadlo et al (2009) Based on Romanowicz et al (2016)

82 B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90

7 Conclusions and future directions

71 Anisotropy in the deep mantle

In the last ten years global seismic tomography has providedincreasingly refined images of seismic heterogeneity in the deepEarth There is now agreement on the long wavelength structuredominated by the presence of two low shear velocity provinces(LLSVPs) under Africa and the central Pacific which may requirecompositional heterogeneity at least at their base There is alsoevidence for smaller scale structures suggestive of subductingslabs and upwelling plumes in the lower mantle While the bulkof the lower mantle appears largely isotropic the long wavelengthpattern of VTI anisotropy detected in D00 from shear wave tomo-graphic studies seems to track that of isotropic velocity with SHfaster than SV outside of the LLSVPs and SV faster than SH withinthem However the agreement among different models is limited

to the very longest wavelengths (lsquolsquodegree 200) and there are stilldebates about trade-offs between isotropic and anisotropicstructure

On the other hand recent local studies of shear wave splittingare consistently showing the presence of strong seismic anisotropy(both radial and azimuthal) at the edges of the LLSVPs primarily onthe fast side Because anisotropy in post-perovskite (pPv) isthought to be much stronger than in perovskite and pPv is likelymore widely present outside of the LLSVP (ie colder regions man-ifested by faster than average shear velocity) than inside theLLSVPs (which are likely warmer) these observations suggest thatCPO of pPv may be the cause indicating the presence of strongdeformation due to constrained flow at the base of the mantlewith a change of direction towards the vertical at the border ofthe LLSVP and more vertically oriented flow within it While veryattractive because it can also explain opposite polarity behavior inreflections of P and S waves on the discontinuity at the top of D00

B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90 83

(Thomas et al 2011 Cobden et al 2015) the interpretation interms of pPv must be considered with caution given the uncertain-ties on whether pPv is actually present at deep mantle depths

A priority for future seismic studies is to continue investigatingthe patterns of anisotropy on the borders of the LLSVPs as well as inthe vicinity of upwelling plumes where high concentrations ofstrain are expected This would be greatly helped by installationsof large aperture broadband arrays on the ocean floor collectinghigh quality horizontal component data for at least 1 year to covergaps in the available sampling of D00 in these regions We also lackrobust constraints on deep mantle P anisotropy which would helpdifferentiate between dominant (001) and (010) slip systems inpost-perovskite

Also mineral physics has added a lot of new information mostsignificantly the discovery of post-perovskite (Oganov and Ono2004) and derivation of deformation mechanisms both by experi-ments and theoretical models But as the anisotropic seismic struc-ture of the Earth has become more complex over the last ten yearsso has the interpretation with mineral physics concepts opening awide range of opportunities for new investigations Perhaps mostsignificant have been the recent advances in modeling crystaldeformation based on bonding characteristics at a wide range ofconditions that are relevant for the mantle but cannot beapproached with experiments like slow strain rates It will beimportant to apply theory to experimental conditions and thismight explain why DAC experiments at high pressure suggest(001) slip for MgSiO3 post-perovskite (Miyagi et al 2010 Wuet al 2017) while bonding models predict (010) slip at deep man-tle conditions (Goryaeva et al 2016)

High pressure experiments will remain crucial With advancesin multi-anvil technology it will become possible to reach lowermantle conditions (Yamazaki et al 2014) with larger samplesand better defined deformation geometry than DAC which isrestricted to the 50 lm range) with large gradients in pressuredeformation rates and temperature In addition D-DIA experi-ments can provide tomographic information about microstructuralevolution eg during phase transitions and recrystallization (Wanget al 2011) Also DAC technology is adding new possibilities suchas resistive heating for high temperature experiments multigraintexture analysis for coarser aggregates (eg Barton and Bernier2012 Langrand et al 2017) and the possibility of using DAC withLaue microdiffraction (Tamura 2014) to perform orientation andmicrostructural mapping in situ at high pressure

In the future also a larger range of compositions needs to beexplored experimentally for example iron-magnesium contentmultiphase systems (pPv ferropericlase and CaSiO3 perovskite)and the significance of perovskitepost-perovskite transformations

Geodynamic models need refinements New 3D models withtracers (eg Cottaar et al 2014 Li M et al 2014) still do notaccount for the very significant viscosity changes implied by min-eral physics And following texture evolution along streamlinesprovides results at different times for the advancing tracers whilerelating anisotropy results to the Earth assumes that the stream-line does not change which is clearly not the case

The issue of deformation mechanisms was addressed in Sec-tion 48 All models for lower mantle anisotropy assume disloca-tion glide of post-perovskite and ferropericlase as the cause ofcrystal alignment and use a self-consistent viscoplastic plasticitymodel Some arbitrary strain fraction corrections are introducedto account for mechanisms such as climb grain boundary migra-tion grain boundary sliding that do not contribute to texture Inthe future the significance of these mechanisms should be studiedmore systematically both with experiments and models There arestrong indications that the activity of different mechanisms is thecause for lack of significant anisotropy in large parts of the lowermantle

72 Inner core anisotropy

While the complexities of the lower mantle are developing intoa realistic and solvable puzzle inner core anisotropy is becomingmore enigmatic As we learn more about the large seismic aniso-tropy it is not clear what the origin of this signal is and how muchoriginates in the inner core There is room for many possible inter-pretations including a layered inner core with a bcc iron structurein the innermost inner core and an outer shell with an hcp struc-ture (Wang et al 2015) While such a structure is not impossibleit is quite unlikely (eg Romanowicz et al 2016) and not presentlyresolvable from seismological observations The high axial veloci-ties compared with equatorial velocities are difficult to explainand particularly the striking L-shape of the PKP travel time residualas a function of angle of the raypath in the inner core with respectto the rotation axis It is not impossible that heterogeneous struc-tures in the outer liquid core particularly columnar convectionwith a characteristic seismic pattern (eg Jones 2011 Soderlundet al 2012) influence the apparent seismic signature of the innercore A priority for future seismic studies in our view is to achieveconsensus on the origin of the observed L-shape mentioned aboveThe dense temporary broadband arrays recently installed in Alaska(as part of the Earthscope program) and in Antarctica should helpin that endeavor

On the mineral physics side there is general agreement thathexagonal close-packed iron is the most likely component butthe actual composition is still debated and an iron-silicon alloymay exist There is uncertainty and disagreement about elasticproperties of pure iron at inner core conditions derived with firstprinciples calculations (eg Vocadlo et al 2009 versus Mattesiniet al 2010) and no information about elastic properties of iron-silicon alloys While there are many experiments documentingphase relations both of Fe and Fe-Si at high pressure and temper-ature (eg Tateno et al 2010 2015) there is still considerableuncertainty about the melting temperature

These studies highlight the chemical and structural complexi-ties of the core with likely heterogeneities in the inner core vari-able elastic properties and anisotropy A multi-disciplinaryapproach including seismologists geodynamicists mineral physi-cists and material scientists is required to make progress Such col-laborations have been initiated and show great promise for thenear future

Acknowledgements

We are grateful to Mark Jellinek and Tim Horscroft for invitingus to prepare this review It was an opportunity for us to explorethe extensive literature on the subject and also to discover that alot of work remains to be done Particularly interesting was inter-action with colleagues and students at the 2016 CIDER Workshopin Santa Barbara HRW is appreciative of discussions with RainerAbart Sanne Cottaar Patrick Cordier Thorne Lay Sebastien MerkelLowell Miyagi and Kaiqing Yuan CIDER is funded through NSF(FESD grant EAR 1135452) We acknowledge support from NSF(EAR 1343908 1417229 CSEDI-106751) DOE (DE-FG02-05ER15637) CDAC We acknowledge constructive reviews by MarkJellinek and Maureen Long

References

Abart R Kunze K Milke R Sperb R Heinrich W et al 2004 Silicon and oxygenself diffusion in enstatite polycrystals the Milke (2001) rim growthexperiments revisited Contrib Mineral Petrol 147 633ndash646 httpdxdoiorg101007s00410-004-0596-9

Alfegrave D Price GD Gillan MJ 2002 Iron under Earthrsquos core conditions Liquid-state thermodynamics and high pressure melting curve from ab initio

Fig 33 Phase diagrams of the Fe-Si system (Fischer et al 2013) (a) Pressurendashtemperature phase diagram illustrating stability fields of the various phases for Fe-9Si (b)Temperature-composition diagram at 145 GPa illustrating the transition from hcp to B2

Fig 34 (a) Comparison of relative velocity variations (in) as a function of angle n of the ray path in the inner core with respect to the Earthrsquos rotation axis for severalseismological models Black OIC model of Wang et al (2003) Grey OIC model of Beghein and Trampert (2003) Blue best fitting IMIC model using Wang et alrsquos model forOIC anisotropy corrections Green best fitting IMIC model using Beghein and Trampertrsquos (2003) OIC model for anisotropy corrections in the OIC In the latter two cases theIMIC radius is held at 600 km The IMIC model obtained is only slightly sensitive to the radius in the range 500ndash600 km Dashed lines indicate the range of uncertainty on theIMIC model (b) Calculated normalized P-wave velocities of hexagonal single crystals based on first principle elastic properties at various temperatures and pressures An isstrength of anisotropy The polar angle n is zero parallel to the hexagonal c-axis Mat Mattesini et al 2010 Voc Vocadlo et al (2009) Based on Romanowicz et al (2016)

82 B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90

7 Conclusions and future directions

71 Anisotropy in the deep mantle

In the last ten years global seismic tomography has providedincreasingly refined images of seismic heterogeneity in the deepEarth There is now agreement on the long wavelength structuredominated by the presence of two low shear velocity provinces(LLSVPs) under Africa and the central Pacific which may requirecompositional heterogeneity at least at their base There is alsoevidence for smaller scale structures suggestive of subductingslabs and upwelling plumes in the lower mantle While the bulkof the lower mantle appears largely isotropic the long wavelengthpattern of VTI anisotropy detected in D00 from shear wave tomo-graphic studies seems to track that of isotropic velocity with SHfaster than SV outside of the LLSVPs and SV faster than SH withinthem However the agreement among different models is limited

to the very longest wavelengths (lsquolsquodegree 200) and there are stilldebates about trade-offs between isotropic and anisotropicstructure

On the other hand recent local studies of shear wave splittingare consistently showing the presence of strong seismic anisotropy(both radial and azimuthal) at the edges of the LLSVPs primarily onthe fast side Because anisotropy in post-perovskite (pPv) isthought to be much stronger than in perovskite and pPv is likelymore widely present outside of the LLSVP (ie colder regions man-ifested by faster than average shear velocity) than inside theLLSVPs (which are likely warmer) these observations suggest thatCPO of pPv may be the cause indicating the presence of strongdeformation due to constrained flow at the base of the mantlewith a change of direction towards the vertical at the border ofthe LLSVP and more vertically oriented flow within it While veryattractive because it can also explain opposite polarity behavior inreflections of P and S waves on the discontinuity at the top of D00

B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90 83

(Thomas et al 2011 Cobden et al 2015) the interpretation interms of pPv must be considered with caution given the uncertain-ties on whether pPv is actually present at deep mantle depths

A priority for future seismic studies is to continue investigatingthe patterns of anisotropy on the borders of the LLSVPs as well as inthe vicinity of upwelling plumes where high concentrations ofstrain are expected This would be greatly helped by installationsof large aperture broadband arrays on the ocean floor collectinghigh quality horizontal component data for at least 1 year to covergaps in the available sampling of D00 in these regions We also lackrobust constraints on deep mantle P anisotropy which would helpdifferentiate between dominant (001) and (010) slip systems inpost-perovskite

Also mineral physics has added a lot of new information mostsignificantly the discovery of post-perovskite (Oganov and Ono2004) and derivation of deformation mechanisms both by experi-ments and theoretical models But as the anisotropic seismic struc-ture of the Earth has become more complex over the last ten yearsso has the interpretation with mineral physics concepts opening awide range of opportunities for new investigations Perhaps mostsignificant have been the recent advances in modeling crystaldeformation based on bonding characteristics at a wide range ofconditions that are relevant for the mantle but cannot beapproached with experiments like slow strain rates It will beimportant to apply theory to experimental conditions and thismight explain why DAC experiments at high pressure suggest(001) slip for MgSiO3 post-perovskite (Miyagi et al 2010 Wuet al 2017) while bonding models predict (010) slip at deep man-tle conditions (Goryaeva et al 2016)

High pressure experiments will remain crucial With advancesin multi-anvil technology it will become possible to reach lowermantle conditions (Yamazaki et al 2014) with larger samplesand better defined deformation geometry than DAC which isrestricted to the 50 lm range) with large gradients in pressuredeformation rates and temperature In addition D-DIA experi-ments can provide tomographic information about microstructuralevolution eg during phase transitions and recrystallization (Wanget al 2011) Also DAC technology is adding new possibilities suchas resistive heating for high temperature experiments multigraintexture analysis for coarser aggregates (eg Barton and Bernier2012 Langrand et al 2017) and the possibility of using DAC withLaue microdiffraction (Tamura 2014) to perform orientation andmicrostructural mapping in situ at high pressure

In the future also a larger range of compositions needs to beexplored experimentally for example iron-magnesium contentmultiphase systems (pPv ferropericlase and CaSiO3 perovskite)and the significance of perovskitepost-perovskite transformations

Geodynamic models need refinements New 3D models withtracers (eg Cottaar et al 2014 Li M et al 2014) still do notaccount for the very significant viscosity changes implied by min-eral physics And following texture evolution along streamlinesprovides results at different times for the advancing tracers whilerelating anisotropy results to the Earth assumes that the stream-line does not change which is clearly not the case

The issue of deformation mechanisms was addressed in Sec-tion 48 All models for lower mantle anisotropy assume disloca-tion glide of post-perovskite and ferropericlase as the cause ofcrystal alignment and use a self-consistent viscoplastic plasticitymodel Some arbitrary strain fraction corrections are introducedto account for mechanisms such as climb grain boundary migra-tion grain boundary sliding that do not contribute to texture Inthe future the significance of these mechanisms should be studiedmore systematically both with experiments and models There arestrong indications that the activity of different mechanisms is thecause for lack of significant anisotropy in large parts of the lowermantle

72 Inner core anisotropy

While the complexities of the lower mantle are developing intoa realistic and solvable puzzle inner core anisotropy is becomingmore enigmatic As we learn more about the large seismic aniso-tropy it is not clear what the origin of this signal is and how muchoriginates in the inner core There is room for many possible inter-pretations including a layered inner core with a bcc iron structurein the innermost inner core and an outer shell with an hcp struc-ture (Wang et al 2015) While such a structure is not impossibleit is quite unlikely (eg Romanowicz et al 2016) and not presentlyresolvable from seismological observations The high axial veloci-ties compared with equatorial velocities are difficult to explainand particularly the striking L-shape of the PKP travel time residualas a function of angle of the raypath in the inner core with respectto the rotation axis It is not impossible that heterogeneous struc-tures in the outer liquid core particularly columnar convectionwith a characteristic seismic pattern (eg Jones 2011 Soderlundet al 2012) influence the apparent seismic signature of the innercore A priority for future seismic studies in our view is to achieveconsensus on the origin of the observed L-shape mentioned aboveThe dense temporary broadband arrays recently installed in Alaska(as part of the Earthscope program) and in Antarctica should helpin that endeavor

On the mineral physics side there is general agreement thathexagonal close-packed iron is the most likely component butthe actual composition is still debated and an iron-silicon alloymay exist There is uncertainty and disagreement about elasticproperties of pure iron at inner core conditions derived with firstprinciples calculations (eg Vocadlo et al 2009 versus Mattesiniet al 2010) and no information about elastic properties of iron-silicon alloys While there are many experiments documentingphase relations both of Fe and Fe-Si at high pressure and temper-ature (eg Tateno et al 2010 2015) there is still considerableuncertainty about the melting temperature

These studies highlight the chemical and structural complexi-ties of the core with likely heterogeneities in the inner core vari-able elastic properties and anisotropy A multi-disciplinaryapproach including seismologists geodynamicists mineral physi-cists and material scientists is required to make progress Such col-laborations have been initiated and show great promise for thenear future

Acknowledgements

We are grateful to Mark Jellinek and Tim Horscroft for invitingus to prepare this review It was an opportunity for us to explorethe extensive literature on the subject and also to discover that alot of work remains to be done Particularly interesting was inter-action with colleagues and students at the 2016 CIDER Workshopin Santa Barbara HRW is appreciative of discussions with RainerAbart Sanne Cottaar Patrick Cordier Thorne Lay Sebastien MerkelLowell Miyagi and Kaiqing Yuan CIDER is funded through NSF(FESD grant EAR 1135452) We acknowledge support from NSF(EAR 1343908 1417229 CSEDI-106751) DOE (DE-FG02-05ER15637) CDAC We acknowledge constructive reviews by MarkJellinek and Maureen Long

References

Abart R Kunze K Milke R Sperb R Heinrich W et al 2004 Silicon and oxygenself diffusion in enstatite polycrystals the Milke (2001) rim growthexperiments revisited Contrib Mineral Petrol 147 633ndash646 httpdxdoiorg101007s00410-004-0596-9

Alfegrave D Price GD Gillan MJ 2002 Iron under Earthrsquos core conditions Liquid-state thermodynamics and high pressure melting curve from ab initio

B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90 83

(Thomas et al 2011 Cobden et al 2015) the interpretation interms of pPv must be considered with caution given the uncertain-ties on whether pPv is actually present at deep mantle depths

A priority for future seismic studies is to continue investigatingthe patterns of anisotropy on the borders of the LLSVPs as well as inthe vicinity of upwelling plumes where high concentrations ofstrain are expected This would be greatly helped by installationsof large aperture broadband arrays on the ocean floor collectinghigh quality horizontal component data for at least 1 year to covergaps in the available sampling of D00 in these regions We also lackrobust constraints on deep mantle P anisotropy which would helpdifferentiate between dominant (001) and (010) slip systems inpost-perovskite

Also mineral physics has added a lot of new information mostsignificantly the discovery of post-perovskite (Oganov and Ono2004) and derivation of deformation mechanisms both by experi-ments and theoretical models But as the anisotropic seismic struc-ture of the Earth has become more complex over the last ten yearsso has the interpretation with mineral physics concepts opening awide range of opportunities for new investigations Perhaps mostsignificant have been the recent advances in modeling crystaldeformation based on bonding characteristics at a wide range ofconditions that are relevant for the mantle but cannot beapproached with experiments like slow strain rates It will beimportant to apply theory to experimental conditions and thismight explain why DAC experiments at high pressure suggest(001) slip for MgSiO3 post-perovskite (Miyagi et al 2010 Wuet al 2017) while bonding models predict (010) slip at deep man-tle conditions (Goryaeva et al 2016)

High pressure experiments will remain crucial With advancesin multi-anvil technology it will become possible to reach lowermantle conditions (Yamazaki et al 2014) with larger samplesand better defined deformation geometry than DAC which isrestricted to the 50 lm range) with large gradients in pressuredeformation rates and temperature In addition D-DIA experi-ments can provide tomographic information about microstructuralevolution eg during phase transitions and recrystallization (Wanget al 2011) Also DAC technology is adding new possibilities suchas resistive heating for high temperature experiments multigraintexture analysis for coarser aggregates (eg Barton and Bernier2012 Langrand et al 2017) and the possibility of using DAC withLaue microdiffraction (Tamura 2014) to perform orientation andmicrostructural mapping in situ at high pressure

In the future also a larger range of compositions needs to beexplored experimentally for example iron-magnesium contentmultiphase systems (pPv ferropericlase and CaSiO3 perovskite)and the significance of perovskitepost-perovskite transformations

Geodynamic models need refinements New 3D models withtracers (eg Cottaar et al 2014 Li M et al 2014) still do notaccount for the very significant viscosity changes implied by min-eral physics And following texture evolution along streamlinesprovides results at different times for the advancing tracers whilerelating anisotropy results to the Earth assumes that the stream-line does not change which is clearly not the case

The issue of deformation mechanisms was addressed in Sec-tion 48 All models for lower mantle anisotropy assume disloca-tion glide of post-perovskite and ferropericlase as the cause ofcrystal alignment and use a self-consistent viscoplastic plasticitymodel Some arbitrary strain fraction corrections are introducedto account for mechanisms such as climb grain boundary migra-tion grain boundary sliding that do not contribute to texture Inthe future the significance of these mechanisms should be studiedmore systematically both with experiments and models There arestrong indications that the activity of different mechanisms is thecause for lack of significant anisotropy in large parts of the lowermantle

72 Inner core anisotropy

While the complexities of the lower mantle are developing intoa realistic and solvable puzzle inner core anisotropy is becomingmore enigmatic As we learn more about the large seismic aniso-tropy it is not clear what the origin of this signal is and how muchoriginates in the inner core There is room for many possible inter-pretations including a layered inner core with a bcc iron structurein the innermost inner core and an outer shell with an hcp struc-ture (Wang et al 2015) While such a structure is not impossibleit is quite unlikely (eg Romanowicz et al 2016) and not presentlyresolvable from seismological observations The high axial veloci-ties compared with equatorial velocities are difficult to explainand particularly the striking L-shape of the PKP travel time residualas a function of angle of the raypath in the inner core with respectto the rotation axis It is not impossible that heterogeneous struc-tures in the outer liquid core particularly columnar convectionwith a characteristic seismic pattern (eg Jones 2011 Soderlundet al 2012) influence the apparent seismic signature of the innercore A priority for future seismic studies in our view is to achieveconsensus on the origin of the observed L-shape mentioned aboveThe dense temporary broadband arrays recently installed in Alaska(as part of the Earthscope program) and in Antarctica should helpin that endeavor

On the mineral physics side there is general agreement thathexagonal close-packed iron is the most likely component butthe actual composition is still debated and an iron-silicon alloymay exist There is uncertainty and disagreement about elasticproperties of pure iron at inner core conditions derived with firstprinciples calculations (eg Vocadlo et al 2009 versus Mattesiniet al 2010) and no information about elastic properties of iron-silicon alloys While there are many experiments documentingphase relations both of Fe and Fe-Si at high pressure and temper-ature (eg Tateno et al 2010 2015) there is still considerableuncertainty about the melting temperature

These studies highlight the chemical and structural complexi-ties of the core with likely heterogeneities in the inner core vari-able elastic properties and anisotropy A multi-disciplinaryapproach including seismologists geodynamicists mineral physi-cists and material scientists is required to make progress Such col-laborations have been initiated and show great promise for thenear future

Acknowledgements

We are grateful to Mark Jellinek and Tim Horscroft for invitingus to prepare this review It was an opportunity for us to explorethe extensive literature on the subject and also to discover that alot of work remains to be done Particularly interesting was inter-action with colleagues and students at the 2016 CIDER Workshopin Santa Barbara HRW is appreciative of discussions with RainerAbart Sanne Cottaar Patrick Cordier Thorne Lay Sebastien MerkelLowell Miyagi and Kaiqing Yuan CIDER is funded through NSF(FESD grant EAR 1135452) We acknowledge support from NSF(EAR 1343908 1417229 CSEDI-106751) DOE (DE-FG02-05ER15637) CDAC We acknowledge constructive reviews by MarkJellinek and Maureen Long

References

Abart R Kunze K Milke R Sperb R Heinrich W et al 2004 Silicon and oxygenself diffusion in enstatite polycrystals the Milke (2001) rim growthexperiments revisited Contrib Mineral Petrol 147 633ndash646 httpdxdoiorg101007s00410-004-0596-9

Alfegrave D Price GD Gillan MJ 2002 Iron under Earthrsquos core conditions Liquid-state thermodynamics and high pressure melting curve from ab initio

84 B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90

calculations Phys Rev B 65 (16) 165118 httpdxdoiorg101103PhysRevB65165118

Ammann M Brodholt J Wookey J Dobson D 2010 First-principles constraintson diffusion in lower-mantle minerals and a weak D00 layer Nature 465 462ndash465 httpdxdoiorg101038nature09052

Amodeo J Carrez P Cordier P 2012 Modelling the effect of pressure on thecritical shear stress of MgO single crystals Philos Mag 92 1523ndash1541 httpdxdoiorg101080147864352011652689

Amodeo J Devincre B Carrez P Cordier P 2014 Dislocation reactions plasticanisotropy and forest strengthening in MgO at high temperature Mech Mater71 62ndash73

Amodeo J Dancette S Delannay L 2016 Atomistically-informed crystalplasticity in MgO polycrystals under pressure Int J Plasticity 82 177ndash191httpdxdoiorg101016jijplas201603004

Anzellini S Dewaele A Mezouar M Loubeyre P Morard G 2013 Melting ofiron at Earthrsquos inner core boundary based on fast X-ray diffraction Science 340464ndash466 httpdxdoiorg101126science1233514

Ashby MF 1972 A first report on deformation-mechanism maps Acta Metall 20887ndash897

Auer L Boschi L Becker TW Nissen-Meyer T Giardini D 2014 Savani avariable resolution whole-mantle model of anisotropic shear-velocityvariations based on multiple data sets J Geophys Res 119 3006ndash3034httpdxdoiorg1010022013JB010773

Backus GE 1962 Long-wave elastic anisotropy produced by horizontal layering JGeophys Res 67 4427ndash4440

Badro J Fiquet G Guyot F Rueff J-P Struzhkin VV Vanko G Monaco G2003 Iron partitioning in Earthrsquos mantle toward a deep lower mantlediscontinuity Science 300 789ndash791 httpdxdoiorg101126science1081311

Badro J Cote AS Brodholt JP 2014 A seismologically consistent compositionalmodel of Earthrsquos core Proc Nat Acad Sci 111 7542ndash7545

Barton NR Bernier JV 2012 A method for intragranular orientation and latticestrain distribution determination J Appl Cryst 45 1145ndash1155 httpdxdoiorg101107S0021889812040782

Becker TW 2006 On the effect of temperature and strain-rate dependent viscosityon global mantle flow net rotation and plate-driving forces Geophys J Int167 943ndash957

Beghein C Trampert J 2003 Robust normal mode constraints on inner-coreanisotropy from model space search Science 299 552ndash555 httpdxdoiorg101126science1078159

Beghein C Trampert J Heijst HV 2006 Radial anisotropy in seismic referencemodels of the mantle J Geophys Res 111 (B2) B02303 httpdxdoiorg1010292005JB003728

Belonoshko AB Ahuja R Johansson B 2003 Stability of the body-centered-cubicphase of iron in the Earthrsquos inner core Nature 424 1032ndash1034 httpdxdoiorg101038nature01954

Belonoshko AB Isaev EI Skorodumova NV Johansson B 2006 Stability of thebody-centered-tetragonal phase of Fe at high pressure ground-state energiesphonon spectra and molecular dynamics simulations Phys Rev B 74 214102

Bercovici D Ricard Y 2016 Grain-damage hysteresis and plate-tectonic statesPhys Earth Planet Int 253 31ndash47 httpdxdoiorg101016jpepi201601005

Bergman MI 1997 Measurements of elastic anisotropy due to solidificationtexturing and the implications for the Earthrsquos inner core Nature 389 60ndash63httpdxdoiorg10103837962

Beyerlein IJ Lebensohn RA Tomeacute CN 2003 Modeling texture andmicrostructural evolution in the equal channel angular extrusion processMater Sci Eng A 345 122ndash138

Birch F 1952 Elasticity and constitution of the Earthrsquos interior J Geophys Res 57227ndash286

Blackman DK Kendall J-M Dawson PR Wenk H-R Boyce D Morgan JP1996 Teleseismic imaging of subaxial flow at mid-ocean ridges travel-timeeffects of anisotropic mineral texture in the mantle Geoph J Intern 127 415ndash426

Blackman DK Wenk H-R Kendall J-M 2002 Seismic anisotropy of the uppermantle 1 Factors that affect mineral texture and effective elastic propertiesGeochem Geophys Geosyst 3 (9) 8601 httpdxdoiorg1010292001GC000248

Boioli F Carrez P Cordier P Devincre B Marquille M 2015 Modeling the creepproperties of olivine by 25-dimensional dislocation dynamics simulationsPhys Rev B 92 (1) 014115 httpdxdoiorg101103PhysRevB92014115

Boioli F Carrez P Cordier P Devincre B Gouriet K Hirel P Kraych ARitterbex S 2017 Pure climb creep mechanism drives flow in Earthrsquos lowermantle Sci Adv 3 httpdxdoiorg101126sciadv1601958

Bolfan-Casanova N Keppler H Rubie DC 2003 Water partitioning at 660 kmdepth and evidence for very low water solubility in magnesium silicateperovskite Geophys Res Lett 30 1905 httpdxdoiorg1010292003GL017182

Borgeaud AFE Konishi K Kawai K Geller RJ 2016 Finite frequency effects onapparent S-wave splitting in the D00 layer comparison between ray theory andfull-wave synthetics Geophys J Int 207 12 httpdxdoiorg10193gjiggw254

Boschi L Dziewonski AM 2000 Whole earth tomography from delay times of PPcP and PKP phases lateral heterogeneities in the outer core or radialanisotropy in the mantle J Geophys Res 105 13675ndash13696

Bouchet J Mazavet S Morard G Guyot F Musella M 2013 Ab initio equationof state of iron up to 1500 GPa Phys Rev B 87 (9) 094102 httpdxdoiorg101103PhysRevB87094102

Breacutechet YJM Dawson P Embury JD Gsell C Suresh S Wenk H-R 1994Recommendations on modeling polyphase plasticity conclusions of paneldiscussions Mat Sci Eng A175 1ndash5

Breacuteger L Romanowicz B Tkalcic H 1999 PKP(BC-DF) travel time residuals andshort scale heterogeneity in the deep earth Geophys Res Lett 26 (20) 3169ndash3172 httpdxdoiorg1010291999GL008374

Breacuteger L Tkalcic H Romanowicz B 2000 The effect of D00 on PKP(AB-DF) traveltime residuals and possible implications for inner core structure Earth PlanetSci Lett 175 133ndash143 httpdxdoiorg101016S0012-821X(99)00286-1

Brown JM 2001 The equation of state of iron to 450 GPa Another high pressuresolid phase Geophys Res Lett 28 4339ndash4342 httpdxdoiorg1010292001GL013759

Buffett BA 2014 Geomagnetic fluctuations reveal stable stratification at the top ofthe Earthrsquos core Nature 507 484ndash487 httpdxdoiorg101038nature13122

Buffett BA Wenk HR 2001 Texturing of the Earthrsquos inner core by Maxwellstresses Nature 413 60ndash63 httpdxdoiorg10103835092543

Bunge H-P Richards MA Baumgardner JR 1996 Effect of depth-dependentviscosity on the planform of mantle convection Nature 379 436ndash438 httpdxdoiorg101038379436a0

Cann JR 1968 Geological processes at mid-oceanic ridge crests Geophys J RAstron Soc 15 331ndash341

Canova GR Wenk H-R Molinari A 1992 Deformation modelling of multiphasepolycrystals case of a quartz-mica aggregate Acta Metall 40 1519ndash1530

Cao A Romanowicz B 2007 Test of the innermost inner core models usingbroadband PKIKP travel time residuals Geophys Res Lett 34 L08303 httpdxdoiorg1010292007GL029384

Carrez P Ferreacute D Cordier P 2007 Implications for plastic flow in the deepmantle from modelling dislocations in MgSiO3 minerals Nature 446 68ndash70httpdxdoiorg101038nature05593

Castelnau O Blackman DK Becker TW 2009 Numerical simulations of texturedevelopment and associated rheological anisotropy in regions of complexmantle flow Geophys Res Lett 36 L12304 (1-6)

Catalli K Shim SH Prakapenka VB 2009 Thickness and Clapeyron slope of thepost-perovskite boundary Nature 462 782ndash785 httpdxdoiorg101038nature08598

Catalli K Shim SH Prakapenka VB Zhao JY Sturhahn W Chow P Xiao YMLiu HZ Cynn H Evans WJ 2010 Spin state of ferric iron in MgSiO3

perovskite and its effect on elastic properties Earth Planet Sci Lett 289 68ndash75httpdxdoiorg101016jepsl200910029

Chang S-J Ferreira AM Ritsema J van Heijst HJ Woodhouse JH 2014 Globalradially anisotropic mantle structure from multiple datasets a review currentchallenges and outlook Tectonophysics 617 1ndash19 httpdxdoiorg101016jtecto201401033

Chang S-J Ferreira AMG Ritsema J van Heijst HJ Woodhouse JH 2015Joint inversion for global isotropic and radially anisotropic mantle structureincluding crustal thickness perturbations J Geophys Res Solid Earth 120 (6)4278ndash4300 httpdxdoiorg1010022014JB011824

Chen I Argon A 1979 Grain boundary and interphase boundary sliding in powerlaw creep Acta Metall 27 749ndash754

Christensen U 1987 Some geodynamical effects of anisotropic viscosity GeophysJ Int 91 711ndash736 httpdxdoiorg101111j1365-246X1987tb01666x

Cobden L Thomas C Trampert J 2015 Seismic detection of post-perovskiteinside the Earth In Khan A Deschamps F (Eds) The earthrsquos heterogeneousmantle Springer Geophysics httpdxdoiorg101007978-3-319-15627-9_13 chapter 13

Conrad CP Lithgow-Bertelloni C 2004 The temporal evolution of plate drivingforces importance of lsquolsquoslab suctionrdquo versus lsquolsquoslab pullrdquo during the Cenozoic JGeophys Res 109 B10407 httpdxdoiorg1010292004JB002991

Cordier P Amodeo J Carrez P 2012 Modelling the rheology of MgO underEarthrsquos mantle pressure temperature and strain rates Nature 481 177ndash180httpdxdoiorg101038nature10687

Cormier VF Stroujkova A 2005 Waveform search for the innermost inner coreEarth Planet Sci Lett 236 (1ndash2) 96ndash105 httpdxdoiorg101016jepsl200505016

Cottaar S Li M McNamara A Romanowicz B Wenk H-R 2014 Syntheticseismic anisotropy models within a slab impinging on the core-mantleboundary Geophys J Int 199 164ndash177 httpdxdoiorg101093gjiggu244

Cottaar S Romanowicz B 2013 Observations of changing anisotropy across thesouthern margin of the African LLSVP Geophys J Int 195 (2) 1184ndash1195 httpdxdoiorg101093gjiggt285

Crampin S 1984 Evaluation of anisotropy by shear wave splitting Theorybackground and field studies Geophysics 20 23ndash33

Creager KC 1992 Anisotropy of the inner core from differential travel times of thephases PKP and PKiKP Nature 356 309ndash314 httpdxdoiorg101038356309a0

Creager KC 1999 Large-scale variations in inner core anisotropy J Geophys Res104 23127ndash23139

Dawson PR Wenk H-R 2000 Texturing of the upper mantle during convectionPhil Mag A 80 (3) 573ndash598 httpdxdoiorg10108001418610008212069

Debayle E Ricard Y 2013 Seismic observations of large-scale deformation at thebottom of fast moving plates Earth Planet Sci Lett 376 165ndash177 httpdxdoiorg101016jepsl201306025

B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90 85

De Bresser J ter Heege J Spiers C 2001 Grain size reduction by dynamicrecrystallization can it result in major rheological weakening Int J Earth Sci90 28ndash45

Deguen R 2012 Structure and dynamics of Earthrsquos inner core Earth Planet SciLett 333ndash334 211ndash225 httpdxdoiorg101016jepsl201204038

Deuss A 2014 Heterogeneity and anisotropy of Earthrsquos Inner Core Annu RevEarth Planet Sci 42 103ndash126

Deuss A Irving JCE Woodhouse JH 2010 Regional variation of inner coreanisotropy from seismic normal mode observations Science 328 1018ndash1020httpdxdoiorg101126science1188596

Devincre B Kubin LP 1997 The modelling of dislocation dynamics elasticbehavior versus core properties Phil Trans R Soc Lond A 355 2003ndash2012

De Wit RWL Trampert J 2015 Robust constraints on average radial lowermantle anisotropy and consequences for composition and texture Earth PlanetSci Lett 429 101ndash109 httpdxdoiorg101016jepsl201507057

DrsquoHalloy drsquoOmalius J-B 1833 Introduction agrave la Geacuteologie Levrault ParisDing X Helmberger DV 1997 Modelling D00 structure beneath Central America

with broadband seismic data Phys Earth Planet Inter 101 245ndash270 httpdxdoiorg101016S0031-9201(97)00001-0

Dobson DP Miyajima N Nestola F Alvaro M Casati N Liebske C Wood IGWalker AM 2013 Strong inheritance of texture between perovskite andpostperovskite in the D00 layer Nature Geosci 6 575ndash578 httpdxdoiorg101038ngeo1844]

Dubrovinsky L Dubrovinskaia N Prakapenka V Seifert F Langenhorst FDmitriev V Weber H Le Bihan T 2004 A class of new high-pressure silicapolymorphs Phys Earth Planet Inter 143 231ndash240

Dubrovinsky L Dubrovinskaia N Narygina O Kantor I Kuznetzov APrakapenka VB Vitos L Johansson B Mikhaylushkin AS Simak SIAbrikosov IA 2007 Body centered cubic iron nickel alloy in Earthrsquos coreScience 316 1880ndash1883 httpdxdoiorg101126science1142105

Dubrovinsky L Glazyrin K McCammon C Narygina O Greenberg E UbelhackS Chumakov AI Pascarelli S Prakapenka V Bock J Dubrovinskaia N 2009Portable laser-heating system for diamond anvil cells J Synchr Rad 16 (6)737ndash741 httpdxdoiorg101107S0909049509039065

Dziewonski AM Gilbert F 1971 Solidity of the inner core of the Earth inferredfrom normal mode observations Nature 234 465ndash466 httpdxdoiorg101038234465a0

Dziewonski AM Anderson DL 1981 Preliminary reference Earth model PhysEarth Planet Inter 25 297ndash356 httpdxdoiorg1010160031-9201(81)90046-7

Ekstroumlm G 2011 A global model of Love and Rayleigh surface wave dispersion andanisotropy 25ndash250s Geophys J Int 187 (3) 1668ndash1686 httpdxdoiorg101111j1365-246X201105225x

Engdahl ER van der Hilst R Buland R 1998 Global teleseismic earthquakerelocation with improved times and procedures for depth determination BullSeismol Soc Amer 88 722ndash743

Fei YW Zhang L Corgne A Watson H Ricolleau A Meng Y Prakapenka V2007 Spin transition and equations of state of (Mg Fe)O solid solutionsGeophys Res Lett 34 L17307 httpdxdoiorg1010292007GL030712

Ferreacute D Cordier P Carrez P 2009 Dislocation modeling in calcium silicateperovskite based on Peierls-Nabarro model Amer Mineral 94 (1) 135ndash142httpdxdoiorg102138am20093003

Fischer RA Campbell AJ Reaman DM Miller NA Heinz DL Dera PPrakapenka VB 2013 Phase relations in the Fe-FeSi system at high pressuresand temperatures Earth Planet Sci Lett 373 54ndash64 httpdxdoiorg101016jepsl201304035

Ford HA Long MD 2015 A regional test of global models for flow rheology andseismic anisotropy at the base of the mantle Phys Earth Planet Inter 245 71ndash75 httpdxdoiorg101016jpepi201505004

Ford SR Garnero EJ McNamara AK 2006 A strong lateral shear velocitygradient and anisotropy heterogeneity in the lowermost mantle beneath thesouthern Pacific J Geophys Res 111 B03306 httpdxdoiorg1010292004JB003574

Ford HA Long MD He X Lynner C 2015 Lowermost mantle flow at the easternedge of the African Large Low Shear Velocity Province Earth Planet Sci Lett420 12ndash22 httpdxdoiorg101016jepsl201503029

Fouch MJ Fischer KM Wysession ME 2001 Lowermost mantle anisotropybeneath the Pacific imaging the source of the Hawaiian plume Earth PlanetSci Lett 190 167ndash180 httpdxdoiorg101016S0012-821X(01)00380-6

French SW Romanowicz BA 2014 Whole-mantle radially anisotropic shearvelocity structure from spectral-element waveform tomography Geophys JInt 199 1303ndash1327 httpdxdoiorg101093gjiggu334

Frost DJ Liebske C Langenhorst F McCammon CA Tronnes RG Rubie DC2004 Experimental evidence for the existence of iron-rich metal in the Earthrsquoslower mantle Nature 428 409ndash412 httpdxdoiorg101038nature02413

Frost HJ Ashby MF 1982 Deformation mechanism maps The plasticity andcreep of metals and ceramics Pergamon Oxford

Gaidies F Milke R Heinrich W Abart R 2017 Metamorphic mineral reactionsporphyroblast corona and symplectic growth EMO Notes Mineral 16 (14)469ndash540 httpdxdoiorg101180EMU-notes1614

Garcia R 2002 Constraints on upper inner-core structure from waveforminversion of core phases Geophys J Int 150 651ndash664 httpdxdoiorg101046j1365-246X200201717x

Garnero EJ Lay T 1997 Lateral variations in lowermost mantle shear waveanisotropy beneath the North Pacific and Alaska J Geophys Res 102 (B4)8121ndash8135 httpdxdoiorg10102996JB03830

Garnero EJ Maupin V Lay T Fouch MJ 2004a Variable azimuthal anisotropyin Earthrsquos lowermost mantle Science 306 259ndash261 httpdxdoiorg101126science1103411

Garnero EJ Moore MM Lay T Fouch MJ 2004b Isotropy or weak verticaltransverse isotropy in D00 beneath the Atlantic Ocean J Geophys Res 109 (B8)B08308 httpdxdoiorg1010292004JB003004

Girard J Amulele G Farla R Mohiuddin A Karato S-I 2016 Shear deformationof bridgmanite and magnesiowuestite aggregates at lower mantle conditionsScience 351 144ndash147 httpdxdoiorg101126scienceaad3113

Godwal BK Gonzalez-Cataldo F Verma AK Stixrude L Jeanloz R 2015Stability of iron crystal structures at 03ndash15 TPa Earth Planet Sci Lett 409299ndash306 httpdxdoiorg101016jepsl201410056

Goryaeva AM Carrez P Cordier P 2015 Modeling defects and plasticity inMgSiO3 post-perovskite Part 2mdashscrew and edge [100] dislocations PhysChem Min 42 793ndash803 httpdxdoiorg101007s00269-015-0763-8

Green G 2016 Low viscosity and high attenuation in MgSiO3 post-perovskiteinferred from atomic-scale calculations Nature Sci Rep 6 34771 doi101038srep34771

Green G 1838 On the reflexion and refraction of sound Trans Philos Soc London7 24 p

Green HW 1980 On the thermodynamics of non-hydrostatically stressed solidsPhil Mag A 41 637ndash647

Griggs DT 1936 Deformation of rocks under high confining pressure J Geol 44541ndash577

Grocholski B Shim SH Prakapenka VB 2013 Stability metastability and elasticproperties of a dense silica polymorph seifertite J Geophys Res E Planets 1184745ndash4757 httpdxdoiorg101002jgrb5036

Gurnis M Hager BH 1988 Controls on the structure of subducted slabs Nature335 317ndash321

Gutenberg B 1913 Uumlber die Konstitution des Erdinnern erschlossen ausErdbebenbeobachtungen Physikalische Zeitschrift 14 1217ndash1218

Haessner F 1978 Recrystallization of metallic materials Riederer StuttgartHager BH OrsquoConnell RJ 1981 A simple model of plate dynamics and mantle

convection J Geophys Res 86 4843ndash4868Hall S Kendall J van der Baan M 2004 Some comments on the effects of lower-

mantle anisotropy on SKS and SKKS phases Phys Earth Planet Inter 146 (3ndash4)469ndash481

Handy M 1994 Flow laws for rocks containing two non-linear viscous phases aphenomenological approach J Struct Geol 16 (3) 287ndash301 httpdxdoiorg1010160191-8141(94)90035-3

Hansen LN Zimmerman ME Kohlstedt DL 2011 Grainboundary sliding in SanCarlos olivine flow law parameters and crystallographic-preferred orientationJ Geophys Res 116 (B8) httpdxdoiorg1010292011JB008220

Hansen LN Zimmerman ME Kohlstedt DL 2012 The influence ofmicrostructure on deformation of olivine in the grain-boundary slidingregime J Geophys Res 117 B09201 httpdxdoiorg1010292012JB009305

He X Long MD 2011 Lowermost mantle anisotropy beneath the northwest-ernPacific evidence from PcS ScS SKS and SKKS phases Geochem GeophysGeosyst 12 Q12012 httpdxdoiorg1010292011GC003779

Hernlund JW Thomas C Tackley PJ 2005 A doubling of the post-perovskitephase boundary and structure of the Earthrsquos lowermost mantle Nature 434882ndash886

Herwegh M Linckens J Ebert A Berger A Brodhag SH 2011 The role ofsecond phases for controlling microstructural evolution in polymineralic rocksa review J Struct Geol 33 (12) 1728ndash1750 httpdxdoiorg101016jjsg201108011

Hess HH 1964 Seismic anisotropy of the uppermost mantle under oceans Nature203 629ndash631

Hill R 1952 The elastic behaviour of a crystalline aggregate Proc Phys SocLondon Sect A 65 349ndash354

Hirose K Labrosse S Hernlund J 2013 Composition and state of the core AnnRev Earth Planet Sci 41 657ndash691

Hornby BE Schwartz LM Hudson JA 1994 Anisotropic effective-mediummodeling of the elastic properties of shales Geophysics 59 (10) 1570ndash1583httpdxdoiorg10119011443546

Hunt SA Weidner DJ Li L Wang L Walte NP Brodholt JP Dobson DP2009 Weakening of calcium iridate during its transformation from perovskiteto postperovskite Nature Geosci 2 794ndash797 httpdxdoiorg101038ngeo663

Irifune T Ringwood AE 1993 Phase transformations in subducted oceanic crustand buoyancy relationships at depths of 600ndash800 km in the mantle EarthPlanet Sci Lett 117 101ndash110 httpdxdoiorg1010160012-821X(93)90120-X

Irifune T Tsuchiya T 2015 Phase transitions and mineralogy of the lower mantle 2nd ed Treatise on Geophysics 2nd ed vol 2 pp 33ndash60

Irving JCE 2016 Imaging the inner core under Africa and Europe Phys EarthPlanet Inter 254 12ndash24 httpdxdoiorg101016jpepi201603001

Irving JCE Deuss A 2011 Hemispherical structure in inner core velocityanisotropy J Geophys Res 116 B04307 httpdxdoiorg1010292010JB007942

Ishii M Tromp J 1999 Normal mode and free-air gravity constraints on lateralvariations in velocity and density of Earthrsquos mantle Science 285 1231ndash1236httpdxdoiorg101126science28554311231

Ishii M Dziewonski AM 2002 The innermost inner core of the earth Evidencefor a change in anisotropic behavior at the radius of about 300 km Proc NatlAcad Sci 99 14026ndash14030

86 B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90

Ishii M Dziewonski AM 2005 Constraints on the outer-core tangent cylinderusing normal-mode splitting measurements Geophys J Int 162 787ndash792httpdxdoiorg101111j1365-246X200502587x

Jackson I Faul UH 2010 Grainsize-sensitive viscoelastic relaxation in olivinetowards a robust laboratory-based model for seismological applications PhysEarth Planet Inter 183 151ndash163 httpdxdoiorg101016jpepi201009005

Jeanloz R Wenk H-R 1988 Convection and anisotropy of the inner coreGeophys Res Lett 15 72ndash75 httpdxdoiorg101029GL015i001p00072

Jeong T Pickett WE 2004 Implications of the B20 crystal structure for themagnetoelectronic structure of MnSi Phys Rev B 70 075114 doiorg101103PhysRevB70075114

Jones CA 2011 Planetary magnetic fields and fluid dynamos Annual Rev FluidMech 43 583ndash614

Jung H Karato S 2001 Water-induced fabric transitions in olivine Science 2931460ndash1463 httpdxdoiorg101126science1062235

Jung H Katayama I Jiang Z Hiraga T Karato S 2006 Effects of water and stresson the lattice preferred orientation in olivine Tectonophysics 421 1ndash22

Kaercher P Miyagi L Kanitpanyacharoen W Zepeda-Alarcon E Wang YParkinson D Lebensohn RA De Carlo F Wenk HR 2016 Two phasedeformation of lower mantle mineral analogs Earth Planet Sci Lett 456 134ndash145 doiorg101016jepsl201609030

Kamb WB 1961 The thermodynamic theory of nonhydrostatically stressed solidsJ Geoph Res 66 259ndash271

Kaminski E Ribe NM 2001 A kinematic model for recrystallization and texturedevelopment in olivine polycrystals Earth Planet Sci Lett 189 253ndash267httpdxdoiorg101016S0012-821X(01)00356-9

Karato S 1999 Seismic anisotropy of the Earthrsquos inner core resulting from flowinduced Maxwell stresses Nature 402 871ndash873 httpdxdoiorg10103847235

Karato S Jung H Katayama I Skemer P 2008 Geodynamic significance ofseismic anisotropy of the upper mantle new insights from laboratory studiesAnnu Rev Earth Planet Sci 36 59ndash95

Karki B Wentzcovitch RM De Gironcoli S Baroni S 2000 High pressure latticedynamics and thermoelasticity of MgO Phys Rev B 61 (13) 8793ndash8800 httpdxdoiorg101103PhysRevB

Kawai K Geller RRJ 2010 The vertical flow in the lowermost mantle beneath thePacific from inversion of seismic waveforms for anisotropic structure EarthPlanet Sci Lett 297 (1ndash2) 190ndash198 httpdxdoiorg101016jepsl201005037

Kawai K Tsuchiya T 2015 Small shear modulus of cubic CaSiO3 perovskiteGeophys Res Lett 42 2718ndash2736 httpdxdoiorg1010022015GL063442

Kawazoe T Nishiyama N Nishihara Y Irifune T 2010 Deformation experimentat P-T conditions of the mantle transition zone using D-DIA apparatus PhysEarth Planet Inter 183 190ndash195

Kendall J Silver P 1996 Constraints from seismic anisotropy on the nature of thelowermost mantle Nature 381 409ndash412 httpdxdoiorg101038381409a0

Kendall J-M Silver PG 1998 Investigating causes of D00 anisotropy In GurnisM Wysession ME Knittle E Buffett BA (Eds) The core-mantle boundaryregion geodynamics series American Geophysical Union Washington pp 97ndash118

Kennett BLN Widyantoro S 1998 Joint seismic tomography for bulk sound andshear wave speed in the Earthrsquos mantle J Geophys Res 103 (12) 469ndash493httpdxdoiorg10102909JB00150

Kern H Ivankina TI Nikitin AN Lokajicek T Pros Z 2008 The effect oforiented microcracks and crystallographic and shape preferred orientation onbulk elastic anisotropy of a foliated biotite gneiss from OutokumpuTectonophysics 457 143ndash149

Kern H Wenk HR 1990 Fabric-related velocity anisotropy and shear wavesplitting in rocks from the Santa Rosa mylonite zone California J Geophys Res95 (B7) 11213ndash11223 httpdxdoiorg101029JB095iB07p11213

Kingma KJ Cohen RE Hemley RJ Mao H-k 1995 Transformation of stishoviteto a denser phase at lower-mantle pressures Nature 374 243ndash245 httpdxdoiorg101038374243a0

Koci L Vitos L Ahuja R 2007 Ab initio calculations of the elastic properties offerropericlase Mg1-xKexO (xfrasl025) Phys Earth Planet Inter 164 177ndash185

Kohlstedt DT Goetze C 1974 Low-stress high-temperature creep in olivinesingle crystals J Geophys Res 79 2045ndash2051

Komatitsch D Vinnik LP Chevrot S 2010 SHdiff-SVdiff splitting in an isotropicEarth J Geophys Res 115 B07312 httpdxdoiorg1010292009JB006795

Kraych A Carrez P Hirel P Clouet E Cordier P 2016 On dislocation glide inMgSiO3 bridgmanite at high-pressure and high-temperature Earth Planet SciLett 452 60ndash68 httpdxdoiorg101016jepsl201607035

Kubin LP Canova G Condat M Devincre B Pontikis V Breacutechet Y 1992Dislocation microstructures and plastic flow A 3D simulation Solid StatePhenomena 23ndash24 455ndash472 httpdxdoiorg104028wwwscientificnetSSP23-24455

Kuwayama Y Hirose K Sata N Ohishi Y 2005 The pyrite-type high-pressureform of silica Science 309 923ndash925 httpdxdoiorg101126science1114879

Kustowski B Ekstroumlm G Dziewonski A 2008 Anisotropic shear-wave velocitystructure of the Earthrsquos mantle a global model J Geophys Res 113 (B6)B06306 httpdxdoiorg1010292007JB005169

Langdon TG Mohamed FA 1978 A simple method of constructing Ashby-typedeformation mechanism maps J Mater Sci 13 473ndash482 httpdxdoiorg101007BF00544735

Langrand C Hilairet N Nisr C Roskosz M Ribaacuterik G Vaughan GBM MerkelS 2017 Reliability of multigrain indexing for orthorhombic polycrystals above1 Mbar application to MgSiO3-post-perovskite J Appl Crystallog 50 120ndash130httpdxdoiorg101107S1600576716018057

Lay T 2015 Deep earth structure Lower mantle and D00 In Romanowicz BDziewonski AM (Eds) Treatise on Geophysics Vol 122 pp 684ndash723

Lay T Helmberger DV 1983 The shear-wave velocity gradient at the base of themantle J Geophys Res 88 8160ndash8170 httpdxdoiorg101029JB088iB10p08160

Lay T Young CJ 1991 Analysis of seismic SV waves in the corersquos penumbraGeophys Res Lett 18 1373ndash1376 httpdxdoiorg10102991GL01691

Lay T Williams Q Garnero EJ Kellogg L Wysession ME 1998 Seismic waveanisotropy in the D00 region and its implications In Gurnis M Wysession MEKnittle E Buffett BA (Eds) The core-mantle boundary region geodynamicsseries 28 American Geophysical Union Washington USA pp 299ndash318

Lay T Garnero EJ Williams Q 2004 Partial melting in a thermo-chemicalboundary layer at the base of the mantle Phys Earth Planet Inter 146 441ndash467 httpdxdoiorg101126science1133280

Lebensohn RA Tomeacute CN 1993 A self-consistent anisotropic approach for thesimulation of plastic deformation and texture development of polycrystals ndashapplication to zirconium alloys Acta Metall Mater 41 2611ndash2624 httpdxdoiorg1010160956-7151(93)90130-K

Lebensohn RA 2001 N-site modeling of a 3D viscoplastic polycrystal using fastfourier transform Acta Mater 49 2723ndash2737 httpdxdoiorg101016S1359-6454(01)00172-0

Lehmann I 1936 Prsquo Bureau Central Seacuteismologique International StrasbourgPublications du Bureau Central Scientifiques A 14 (3) 87ndash115

Lekic V Cottaar S Dziewonski A Romanowicz B 2012 Cluster analysis of globallower mantle tomography a new class of structure and implications forchemical heterogeneity Earth Planet Sci Lett 357 68ndash77 httpdxdoiorg101016jepsl201209014

Levitas VI Ma Y Hashemi J Holtz M Guven N 2006 Strain-induced disorderphase transformations and transformation-induced plasticity in hexagonalboron nitride under compression and shear in a rotational diamond anvil cellIn situ x-ray diffraction study and modeling J Chem Phys 125 044507 httpdxdoiorg10106312208353

Leykam D Tkalcic H Reading AM 2010 Core structure re-examined using newteleseismic data recorded in Antarctica evidence for at most weak cylindricalseismic anisotropy in the inner core Geophys J Int 180 (3) 1329ndash1343 httpdxdoiorg101111j1365-246X201004488x

Li M McNamara AK Garnero EJ 2014 Chemical complexity of hotspots causedby cycling oceanic crust through mantle reservoirs Nature Geosci 7 366ndash370httpdxdoiorg101038ngeo2120

Li J Struzhkin VV Mao H-K Shu J Hemley RJ Fei Y Mysen B Dera PPrakapenka V Shen G 2004 Electronic spin state of iron in lower mantleperovskite Proc Nat Acad Sci 101 14027ndash14030 101073 pnas0405804101

Li X-D Romanowicz B 1995 Comparison of global waveform inversions with andwithout considering cross-branch modal coupling Geophys J Int 121 (3) 695ndash709 101111j1365-246X1995tb06432x

Li Y Deschamps F Tackley PJ 2014 Effects of low-viscosity post-perovskite onthe stability and structure of primitive reservoirs in the lower mantle GeophysRes Lett 41 httpdxdoiorg1010022014GL061362

Liermann H-P Merkel S Miyagi L Wenk H-R Shen G Cynn H Evans WJ2009 Experimental method for in situ determination of material textures atsimultaneous high-pressure and high temperature by means of radialdiffraction in the diamond anvil cell Rev Scient Instrum 80 (104501) 1ndash8httpdxdoiorg10106313236365

Lin J-F Watson H Vanko G Alp EE Prakapenka VB Dera P Struzhkin VKubo A Zhao J McCammon C Evans WJ 2008 Intermediate-spin ferrousiron in lowermost mantle post-perovskite and perovskite Nature Geosci 1688ndash691 httpdxdoiorg101038ngeo310

Lin J-F Wenk H-R Voltolini M Speziale S Shu J Duffy T 2009 Deformationof lower mantle ferropericlase (Mg Fe)O across the electronic spin transitionPhys Chem Mineral 36 585ndash592 httpdxdoiorg101007s00269-009-0303-5

Lin J-F Alp EE Mao Z Inoue T McCammon C Xia YM Chow P Zhao JY2012 Electronic spin states of ferric and ferrous iron in the lower-mantlesilicate perovskite Amer Mineral 97 592ndash597 httpdxdoiorg102138am20124000

Linckens J Herwegh M Muumlntener O Mercolli I 2011 Evolution of apolymineralic mantle shear zone and the role of second phases in thelocalization of deformation J Geophys Res 116 B06210 httpdxdoiorg1010292010JB008119

Lincot A Merkel S Cardin P 2015 Is inner core seismic anisotropy a marker forplastic flow of cubic iron Geophys Res Lett 42 1326ndash1333 httpdxdoiorg1010022014GL062862

Lincot A Merkel S Deguen P Cardin P 2016 Multiscale model of global inner-core anisotropy induced by hcp alloy plasticity Geophys Res Lett 43 1084ndash1091 httpdxdoiorg1010022015GL067019

Liu L-G 1974 Silicate perovskite from phase transformations of pyrope-garnet athigh pressure and temperature Geophys Res Lett 1 277ndash280 httpdxdoiorg101029GL001i006p00277

Long MD 2009 Complex anisotropy in D00 beneath the eastern Pacific from SKSndashSKKS splitting discrepancies Earth Planet Sci Lett 283 181ndash189 httpdxdoiorg101016jepsl200904019

B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90 87

Long MD 2013 Constraints on subduction geodynamics from seismic anisotropyRev Geophys 51 76ndash112 httpdxdoiorg101002rog20008

Long MD Silver PG 2009 Shear wave splitting and mantle anisotropymeasurements interpretations and new directions Surv Geophys 30 407ndash461 httpdxdoiorg101007s10712-009-9075-1

Long MD Becker TW 2010 Mantle dynamics and seismic anisotropy EarthPlanet Sci Lett 297 341ndash354 httpdxdoiorg101016jepsl201006036

Long MD Lynner C 2015 Seismic anisotropy in the lowermost mantle near thePerm Anomaly Geophys Res Lett 42 7073ndash7080 httpdxdoiorg1010022015GL065506

Long MD Xiao X Jiang Z Evans B Karato S 2006 Lattice preferred orientationin deformed polycrystalline (Mg Fe)O and implications for seismic anisotropyin D00 Phys Earth Planet Inter 156 (1ndash2) 75ndash88 httpdxdoiorg101016jpepi200602006

Lutterotti L Vasin R Wenk H-R 2014 Rietveld texture analysis fromsynchrotron diffraction images I Basic analysis Powder Diffraction 29 76ndash84 httpdxdoiorg101007s00269-011-0439-y

Lynner C Long MD 2012 Evaluating contributions to SK(K)S splitting from lowermantle anisotropy a case study from station DBIC Cocircte DrsquoIvoire Bull SeismolSoc Am 102 1030ndash1040 httpdxdoiorg101785-12-11-0255

Lynner C Long MD 2014 Lowermost mantle anisotropy and deformation alongthe boundary of the African LLSVP Geophys Res Lett 41 3447ndash3454 httpdxdoiorg1010022014GL059875

Lythgoe KH Deuss A Rudge JF Neufeld JA 2014 Earthrsquos inner core Innermostinner core or hemispherical variations Earth Planet Sci Lett 385 181ndash189httpdxdoiorg101016jepsl201310049

Mainprice D Tommasi A Ferreacute D Carrez P Cordier P 2008 Predicted glidesystems and crystal preferred orientations of polycrystalline silicate Mg-perovskite at high pressure Implications for the seismic anisotropy in thelower mantle Earth Planet Sci Lett 271 135ndash144 httpdxdoiorg101016jepsl200803058

Mao HK Bassett WA Takahashi T 1967 Effect of pressure on crystal structureand lattice parameters of iron up to 300 kbars J Appl Phys 38 272ndash276

Marquardt H Miyagi L 2015 Slab stagnation in the shallow lower mantle linkedto an increase in mantle viscosity Nature Geosci 8 311ndash314 httpdxdoiorg101038ngeo2393

Masters G Laske G Bolton H Dziewonski A 2000 The relative behavior of shearvelocity bulk sound speed and compressional velocity in the mantleimplications for chemical and thermal structure In Karato S-I (Ed) EarthrsquosDeep Interior Minreal Physics and Tomography from the atomic to the globalscale American Geophysical Union Washington DC pp 63ndash88 httpdxdoiorg101029GM117p0063

Martorell B Vocadlo L Brodholdt J Wood IG 2013 Strong premelting effect inthe elastic properties of hcp-Fe under inner core conditions Science 342 466ndash468 httpdxdoiorg101126science1243651

Mattesini M Belonoshko AB Buforn E Ramirez M Simak SI Udias A MaoH-K Ahuja R 2010 Hemispherical anisotropic patterns of the Earthrsquos innercore Proc Nat Acad Sci 107 9507ndash9512

Matthies S 2012 GEO-MIX-SELF calculations of the elastic properties of a texturedgraphite sample at different hydrostatic pressures J Appl Crystallog 45 (1) 1ndash16 httpdxdoiorg101107S002188981104338X

Matthies S Humbert M 1995 On the principle of a geometric mean of even-ranksymmetric tensors for textured polycrystals J Appl Crystallog 28 (3) 254ndash266httpdxdoiorg101107S0021889894009623

Matzel E Sen MK Grand SP 1996 Evidence for anisotropy in the deep mantlebeneath Alaska Geophys Res Lett 23 2417ndash2420 httpdxdoiorg10102996GL02186

Maupin V 1994 On the possibility of anisotropy in the D00 layer as inferred fromthe polarization of diffracted S waves Phys Earth Planet Inter 87 (1ndash2) 1ndash32httpdxdoiorg1010160031-9201(94)90019-1

Maupin V Garnero EJ Lay T Fouch MJ 2005 Azimuthal anisotropy in the D00

layer beneath the Caribbean J Geophys Res 110 B08301 httpdxdoiorg1010292004JB003506

McCammon C 1997 Perovskite as a possible sink for ferric iron in the lowermantle Nature 387 694ndash696

McKenzie DP 1969 Speculations on the consequences and causes of platemotions Geophys J R Astron Soc 18 1ndash32

McNamara A van Keken P Karato S 2002 Development of anisotropic structurein the Earthrsquos lower mantle by solid-state convection Nature 416 (6678) 310ndash314 httpdxdoiorg101038416310a

McNamara A van Keken P Karato S 2003 Development of finite strain in theconvecting lower mantle and its implications for seismic anisotropy J GeophysRes 108 (B5) 2230 httpdxdoiorg1010292002JB001970]

Meade C Silver PG Kaneshima S 1995 Laboratory and seismologicalobservations of lower mantle isotropy Geophys Res Lett 22 1293ndash1296httpdxdoiorg10102995GL01091

Meacutegnin C Romanowicz B 2000 The three-dimensional shear velocity structure ofthe mantle from the inversion of body surface and higher-mode waveformsGeophys J Int 143 (3) 709ndash728 httpdxdoiorg101046j1365-246X200000298x

Merkel S Wenk H-R Shu J Shen G Gillet P Mao H-K Hemley RJ 2002Deformation of polycrystalline MgO at pressures of the lower mantle JGeophys Res 107 (B11) 2271 httpdxdoiorg1010292001JB000920

Merkel S Wenk H-R Badro J Montagnac J Gillet P Mao Hk Hemley RJ2003 Deformation of (Mg09 Fe01)SiO3 perovskite aggregates up to 32 GPa

Earth Planet Sci Lett 209 351ndash360 httpdxdoiorg101016S0012-821X(03)00098-0

Merkel S Wenk H-R Gillet P Mao H-K Hemley RJ 2004 Deformation ofpolycrystalline iron up to 30 GPa and 1000 K Phys Earth Planet Inter 145239ndash251 httpdxdoiorg101016jpepi200404001

Merkel S Kubo A Miyagi L Speziale S Duffy TS Mao H-K Wenk H-R 2006Plastic deformation of MgGeO3 post-perovskite at lower mantle pressuresScience 311 644ndash646 httpdxdoiorg101126science1121808

Merkel S McNamara AK Kubo A Speziale S Miyagi L Meng Y Duffy TSWenk H-R 2007 Deformation of (Mg Fe)SiO3 post-perovskite and D00

anisotropy Science 316 1729ndash1732 httpdxdoiorg101126science1140609

Merkel S Liermann HP Miyagi L Wenk H-R 2013 In-situ radial X-raydiffraction study of texture and stress during phase transformations in bcc- fcc- and hcp-iron up to 36 GPa and 1000K Acta Mater 61 5144ndash5151 httpdxdoiorg101016jactamat201304068

Mika DP Dawson PR 1999 Polycrystal plasticity modeling of intracrystallineboundary textures Acta Mater 47 (4) 1355ndash1369 httpdxdoiorg101016S1359-6454(98)00386-3

Mitrovica JX Forte AM 2004 A new inference of mantle viscosity based uponjoint inversion of convection and glacial isostatic adjustment data Earth PlanetSci Lett 225 177ndash189

von Mises R 1928 Mechanik der plastischen Formaumlnderung von Kristallen ZAngew Math Mech 8 161ndash185

Mitchell BJ Helmberger DV 1973 Shear velocities at the base of the mantle fromobservations of S and ScS J Geophys Res 78 6009ndash6020 httpdxdoiorg101029JB078i026p06009

Miyagi L Merkel S Yagi T Sata N Ohishi Y Wenk H-R 2006 QuantitativeRietveld texture analysis of CaSiO3 perovskite deformed in a diamond anvil cellJ Phys Cond Matter 18 S995ndashS1005 httpdxdoiorg1010880953-89841825S07

Miyagi L Merkel S Yagi T Oshishi Y Wenk H-R 2009 Diamond anvil celldeformation of CaSiO3 perovskite up to 49 GPa Phys Earth Planet Inter 174159ndash164 httpdxdoiorg101016jpepi200805018

Miyagi L Wenk H-R 2016 Texture development and slip systems in bridgmaniteand bridgmanite + ferropericlase aggregates Phys Chem Minerals 43 597ndash613 httpdxdoiorg101007s00269-016-0820-y

Miyagi L Kunz M Nasiatka J Voltolini M Knight J Wenk H-R 2008 In-situstudy of texture development in polycrystalline iron during phasetransformations and deformation at high pressure and temperature J ApplPhys 104 103510 httpdxdoiorg10106313008035

Miyagi L Kanitpanyacharoen W Kaercher P Lee KKM Wenk HR 2010 Slipsystems in MgSiO3 post-perovskite Implications for D00 anisotropy Science 3291639ndash1641 httpdxdoiorg101126science1192465

Miyagi L Kanitpanyacharoen W Stackhouse S Militzer B Wenk H-R 2011The enigma of post-perovskite anisotropy deformation versus transformationtextures Phys Chem Minerals 38 665ndash678 httpdxdoiorg101007s00269-011-0439-y

Miyagi L Kanitpanyacharoen W Raju V Kaercher P Knight J McDowell AWenk HR Williams Q Zepeda E 2013 Combined resistive and laser heatingtechnique for in situ radial X-ray diffraction in the diamond anvil cellexperiments at high pressure and temperature Rev Sci Instr 84 (025118)1ndash9 httpdxdoiorg10106314793398

Miyajima N Yagi T Ichihara M 2009 Dislocation microstructures of MgSiO3

perovskite at a high pressure and temperature condition Phys Earth PlanetInter 174 153ndash158 httpdxdoiorg101016jpepi200804004

Molinari A Canova GR Ahzi S 1987 A self-consistent approach of the largedeformation polycrystal viscoplasticity Acta Metall 35 2983ndash2994

Montagner JP 2002 Upper mantle low anisotropy channels below the Pacificplate Earth Planet Sci Lett 202 263ndash274

Montagner JP Anderson DL 1989 Petrological constraints on seismicanisotropy Phys Earth Planet Inter 54 82ndash105

Montagner JP Tanimoto T 1990 Global anisotropy in the upper mantle inferredfrom the regionalization of phase velocities J Geophys Res 95 4797ndash4819httpdxdoiorg101029JB095iB04p04797

Montagner JP Tanimoto T 1991 Global upper mantle tomography of seismicvelocities and anisotropies J Geophys Res 96 20337ndash20351 httpdxdoiorg10102991JB01890

Montagner J-P Kennett BLN 1996 How to reconcile body-wave and normal-mode reference Earth models Geophys J Int 125 229ndash248 101111j1365-246X1996tb06548x

Monteiller V Chevrot S 2010 How to make robust splitting measurements forsingle-station analysis and three-dimensional imaging of seismic anisotropyGeophys J Int 182 httpdxdoiorg101111j1365246X201004608

Morelli A Dziewonski AM Woodhouse JH 1986 Anisotropy of the inner coreinferred from PKIKP travel times Geophys Res Lett 13 1545ndash1548 httpdxdoiorg101029GL013i013p01545

Morris GB Raitt RW Shor GG 1969 Velocity anisotropy and delay-time mapsof the mantle near Hawaii J Geophys Res 17 4300ndash4316

Moulik P Ekstroumlm G 2014 An anisotropic shear velocity model of the Earthrsquosmantle using normal modes body waves surface waves and long-periodwaveforms Geophys J Int 199 1713ndash1738 httpdxdoiorg101029JB078i026p06009

Murakami M Hirose K Kawamura K Sata N Ohishi Y 2004 Post-perovskitephase transition in MgSiO3 Science 304 855ndash858 httpdxdoiorg101126science1095932

88 B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90

Nataf HC Nakanishi I Anderson DL 1984 Anisotropy and shear velocities in theupper mantle Geophys Res Lett 11 109ndash112 httpdxdoiorg101029GL011i002p00109

Naumann CF 1850 Lehrbuch der Geognosie Engelmann LeipzigNisr C Ribarik G Ungar T Vaughan GBM Cordier P Merkel S 2012 High

resolution three-dimensional X-ray diffraction study of dislocations in grains ofpost-perovskite at 90 GPa J Geophys Res 117 B03201 httpdxdoiorg1010292011JB008401

Niu F Wen L 2002 Seismic anisotropy in the top 400 km of the inner corebeneath the lsquolsquoeasternrdquo hemisphere Geophys Res Lett 29 (12) 1611 15-1-53-5[doi1010292001GL014118]

Niu F Perez AM 2004 Seismic anisotropy in the lower mantle a comparison ofwaveform splitting of SKS and SKKS Geophys Res Lett 31 L24612 httpdxdoiorg1010292004GL021196

Nobre Silva IG Weis D Scoates JS 2013 Isotopic systematics of the early MaunaKea shield phase and insight into the deep mantle beneath the Pacific OceanGeochem Geophys Geosyst 14 (3) 659ndash676 httpdxdoiorg101002ggge20047

Nowacki A Wookey J 2016 The limits of ray theory when measuring shear wavesplitting in the lowermost mantle with ScS waves Geophys J Int 207 (3)1573ndash1583 httpdxdoiorg101093gjiggw358

Nowacki A Wookey J Kendall J-M 2010 Deformation of the lowermost mantlefrom seismic anisotropy Nature 467 1091ndash1094 httpdxdoiorg101038nature09507

Nowacki A Wookey J Kendall J-M 2011 New advances in using seismicanisotropy mineral physics and geodynamics to understand deformation in thelowermost mantle J Geodyn 52 205ndash228 httpdxdoiorg101016jjog201104003

Nowacki A Walker A Wookey J Kendall J 2013 Evaluating post-perovskite as acause of D00 anisotropy in regions of palaeosubduction Geophys J Int 192 (3)1085ndash1090 httpdxdoiorg101093gjiggs068

Oganov A Ono S 2004 Theoretical and experimental evidence for a post-perovskite phase of MgSiO3 in Earthrsquos D00 layer Nature 430 (6998) 445ndash448httpdxdoiorg101038nature02701

Ohtami E Sakai T 2008 Recent advances in the study of mantle phase transitionsPhys Earth Planet Inter 170 240ndash247 httpdxdoiorg101016jpepi200807024

Oldham RD 1906 The constitution of the interior of the Earth as revealed byearthquakes Quart J Geol Soc 62 (1ndash4) 456ndash475

Onodera A 1987 Octahedral-anvil high-pressure devices High Temperature-HighPressure 19 579ndash609

Oreshin S Vinnik L 2004 Heterogeneity and anisotropy of seismic attenuation inthe inner core Geophys Res Lett 31 L02613 httpdxdoiorg1010292003GL018591

Pamato MG Myhill R Boffa Balaran T Frost DJ Heidelbach F Miyajima N2014 Lower-mantle water reservoir implied by the extreme stability of ahydrous aluminosilicate Nature Geosci 8 75ndash79 httpdxdoiorg101038ngeo2306

Panning MP Romanowicz B 2004 Inferences on flow at the base of Earthrsquosmantle based on seismic anisotropy Science 303 351ndash353 httpdxdoiorg101126science1091524

Panning MP Romanowicz B 2006 A three-dimensional radially anisotropicmodel of shear velocity in the whole mantle Geophys J Int 167 361ndash379httpdxdoiorg101111j1365-246X200603100x

Panning MP Lekic V Romanowicz BA 2010 Importance of crustal correctionsin the development of a new global model of radial anisotropy J Geophys Res115 B12325 httpdxdoiorg1010292010JB007520

Paterson MS 1973 Nonhydrostatic thermodynamics and its geologic applicationsRev Geophys 11 355ndash389

Paterson MS Olgaard DL 2000 Rock deformation tests to large shear strains intorsion J Struct Geol 22 (8) 1341ndash1358 httpdxdoiorg101016S0191-8141(00)00042-0

Petrova AE Krasnorussky VN Stishov SM 2010 Elastic properties of FeSi JExp Theor Physics 111 427ndash430

Pfaff F 1859 Versuche uber den Einfluss des Drucks auf die optischenEigenschaften doppeltbrechender Krystalle Ann Phys 107 333ndash338

Ping Y Coppari F Hicks DG Yaakobi B Fratanduono DE Hamel S Eggert JHRygg JR Smith RF Swift DC Braun DG Boehly TR Collins GW 2013Solid iron compressed up to 560GPa Phys Rev Lett 111 (6) 065501 httpdxdoiorg101103PhysRevLett 111065501

Polanyi M 1934 Lattice distortion which originates plastic flow Z Phys 89 660Prakapenka VB Kubo A Kuznetsov A Laskin A Shkurikhin O Dera P Rivers

ML Sutton SR 2008 Advanced flat top laser heating system for high pressureresearch at GSECARS application to the melting behavior of germanium HighPressure Research 28 (3) 225ndash235 httpdxdoiorg10108008957950802050718

Pulliam J Sen M 1998 Seismic anisotropy in the corendashmantle transition zoneGeophys J Int 135 113ndash128 httpdxdoiorg101046j1365-246X199800612x

Raitt RW 1963 Marine physics laboratory Scripps Inst Oceanography Univ CalifSan Diego MPL-U-2363

Raleigh CB 1968 Mechanisms of plastic deformation in olivine J Geophys Res73 5391ndash5406

Restivo A Helffrich G 2006 Core-mantle boundary structure investigated usingSKS and SKKS polarization anomalies Geophys J Int 165 288ndash302

Reuss A 1929 Berechnung der Flieszliggrenze von Mischkristallen auf Grund derPlastizitaumltsbedingung fuumlr Einkristalle Z Angew Math Mech 9 49ndash58

Ringwood AE 1962 Mineralogical constitution of the deep mantle J GeophysRes 67 4005ndash4010

Ringwood AE 1975 Composition and Petrology of the Earthrsquos Mantle McGraw-Hill New York 618 pp

Ritsema J Lay T Garnero EJ Benz H 1998 Seismic anisotropy in the lowermostmantle beneath the Pacific Geophys Res Lett 25 1229ndash1232 httpdxdoiorg10102998GL00913

Ritsema J 2000 Evidence for shear wave anisotropy in the lowermost mantlebeneath the Indian Ocean Geophys Res Lett 27 1041ndash1044 httpdxdoiorg1010291999GL011037

Rokosky JM Lay T Garnero EJ Russell S 2004 High-resolution investigation ofshear wave anisotropy in D00 beneath the Cocos Plate Geophys Res Lett 31L0760 httpdxdoiorg1010292003GL018902

Rokosky JM Lay T Garnero EJ 2006 Small-scale lateral variations inazimuthally anisotropic D structure beneath the Cocos Plate Earth Planet SciLett 248 (1ndash2) 411ndash425 httpdxdoiorg101016jepsl200606005

Romanowicz B Breacuteger L 2000 Anomalous splitting of free oscillations a re-evaluation of possible interpretations J Geophys Res 105 (B9) 21559ndash21578httpdxdoiorg1010292000JB900144

Romanowicz B Li X-D Durek J 1996 Anisotropy in the inner core could it bedue to low-order convection Science 274 (5289) 963ndash966 httpdxdoiorg101126science27452951988f

Romanowicz B Tkalcic H Breacuteger L 2003 On the origin of complexity in PKPtravel time data 1st ed In Dehant V et al (Eds) Earthrsquos Core DynamicsStructure Rotation 1st ed vol 31 AGU Washington DC pp 31ndash44

Romanowicz B Cao A Godwal B Wenk R Ventosa S Jeanloz R 2016 Seismicanisotropy in the Earthrsquos innermost inner core testing structural modelsagainst mineral physics predictions Geophys Res Lett 43 93ndash100 httpdxdoiorg1010022015GL066734

Rosa AD Hilairet N Ghosh S Garbarino G Jacobs J Perrillat J-P Vaughan GMerkel S 2015 In situ monitoring of phase transformation microstructures atEarthrsquos mantle pressure and temperature using multi-grain XRD J ApplCrystallog 48 1346ndash1354 httpdxdoiorg101107S1600576715012765

Rozel A Ricard Y Bercovici D 2011 A thermodynamically self-consistentdamage equation for grain size evolution during dynamic recrystallizationGeophys J Int 184 (2) 719ndash728

Rudolph ML Lekic VL Lithgow-Bertelloni C 2015 Viscosity jump in Earthrsquosmid-mantle Science 350 1349ndash1352 httpdxdoiorg101126scienceaad1929

Rudzki MP 1897 Ueber die Gestalt elastischer Wellen in Gesteinen Bull AcadSci Cracow 387ndash393

Rudzki MP 1911 Parametrische Darstellung der elastischen Welle in anisotropenMedien Bull Acad Sci Cracow (A) 503ndash536

Russell SA Lay T Garnero EJ 1998 Seismic evidence for small-scale dynamicsin the lowermost mantle at the root of the Hawaiian hotspot Nature 396 255ndash258 httpdxdoiorg10103824364

Russell SA Lay T Garnero EJ 1999 Small-scale lateral shear velocity andanisotropy heterogeneity near the core-mantle boundary beneath the centralPacific imaged using broadband ScS waves J Geophys Res 104 (B6) 13183ndash13199 httpdxdoiorg1010291999JB900114

Sachs G 1928 Zur Ableitung einer Fliessbedingung Z Ver Dtsch Ing 72 734ndash736Saha S Bengtson A Crispin K Morgan D 2011 Effects of spin transition on

diffusion of Fe2+ in ferropericlase in Earthrsquos lower mantle Phys Rev B 84184102 httpdxdoiorg101103PhysRevB84184102

Sakai T Ohtani E Hiro N Ohishi Y 2011 Stability field of the hcp-structure forFe Fe-Ni and Fe-Ni-Si alloys up to 3 Mbar Geophys Res Lett 38 L09302httpdxdoiorg1010292011GL047178

Sayers CM 1994 The elastic anisotropy of shales J Geophys Res 99 767ndash774httpdxdoiorg10102993JB02579

Schmandt B Jacobson SD Becker TW Liu Z Duecker KG 2014 Dehydrationmelting at the top of the lower mantle Science 344 1265ndash1268 httpdxdoiorg101126science1253358

Schmid E 1924 Zn-normal stress law Proc Int Congr Appl Mech (Delft) p 342Shi CY Zhang L Yang W Liu Y Wang J Meng Y Andrews JC Mao WL

2013 Formation of an interconnected network of iron melt at Earthrsquos lowermantle conditions Nature Geosci 6 971ndash975 httpdxdoiorg101038ngeo1956

Shieh SR Duffy TS Shen G 2004 Elasticity and strength of calcium silicateperovskite at lower mantle pressures Phys Earth Planet Int 143ndash144 93ndash105httpdxdoiorg101016jpepi200310006

Shim SH Jeanloz R Duffy TS 2002 Tetragonal structure of CaSiO3 perovskiteabove 20 GPa Geophys Res Lett 29 (24) 2166 httpdxdoiorg1010292002GL016148

Shimizu I 1999 A stochastic model of grain size distribution during dynamicrecrystallization Philos Mag A 79 1217ndash1231

Shimizu I 2008 Theories and applicability of grain size piezometers The role ofdynamic recrystallization mechanisms J Struct Geol 30 899ndash917 101016jjsg200803004

Simmons NA Forte AM Grand SP 2009 Joint seismic geodynamic and mineralphysical constraints on three-dimensional mantle heterogeneity implicationsfor the relative importance of thermal versus compositional heterogeneityGeophys J Int 177 1284ndash1304 httpdxdoiorg101111j1365-246X200904133x

B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90 89

Simmons NA Myers SC Johannesson G Matzel E 2012 LLNL-G3Dv3 global Pwave tomography model for improved regional and teleseismic travel timeprediction J Geophys Res 117 B10302 httpdxdoiorg1010292012JB009525

Soderlund KM King EM Aurnou JM 2012 The influence of magnetic fields inplanetary dynamo models Earth Planet Sci Lett 333ndash334 9ndash20 httpdxdoiorg101016jepsl201203038

Souriau A 2015 Deep earth structure the Earthrsquos cores In Romanowicz BDziewonski AM (Eds) Treatise on Geophysics Vol 1 pp 656ndash693 chap 119

Souriau A Romanowicz B 1996 Anisotropy in inner core attenuation A new typeof data to constrain the nature of the solid core Geophys Res Lett 23 1ndash4httpdxdoiorg10102995GL03583

Souriau A Romanowicz B 1997 Anisotropy in the inner core relation between P-velocity and attenuation Phys Earth Planet Inter 101 33ndash47 httpdxdoiorg101016S0031-9201(96)03242-6

Souriau A Teste A Chevrot S 2003 Is there structure inside the liquid outercore Geophys Res Lett 30 (11) 1567 httpdxdoiorg1010292003GL017008

Speziale S Marquardt H Duffy TS 2014 Brillouin scattering and its applicationin geosciences Rev Mineral Geochem 78 543ndash603

Stackhouse S Brodholt JP Wookey J Kendall J-M Price GD 2005 The effectof temperature on the seismic anisotropy of the perovskite and post-perovskitepolymorphs of MgSiO3 Earth Planet Sci Lett 230 (1ndash2) 1ndash10 httpdxdoiorg101016jepsl200411021

Stevenson DJ 1987 Limits on lateral density and velocity variations in the Earthrsquosouter core Geophys J R Astron Soc 88 (1) 311ndash319 httpdxdoiorg101111j1365-246X1987tb01383x

Stretton I Heidelbach F Mackwell S Langenhorst F 2001 Dislocation creep ofmagnesiowuestite (Mg08Fe02O) Earth Planet Sci Lett 194 229ndash240 httpdxdoiorg101016S0012-821X(01)00533-7

Su W-J Dziewonski AM 1997 Simultaneous inversion for 3-D variations inshear and bulk velocity in the mantle Phys Earth Planet Inter 100 135ndash156httpdxdoiorg101016S0031-9201(96)03236-0

Sumita I Bergman MI 2015 Inner-core dynamics In Treatise on Geophysics vol8 (chap 810)

Sun XL Song XD 2008a Tomographic inversion for three-dimensionalanisotropy of Earthrsquos inner core Phys Earth Planet Inter 167 53ndash68 httpdxdoiorg101016jpepi200802011

Sun XL Song XD 2008b The inner inner core of the Earth texturing of ironcrystals from three dimensional seismic anisotropy Earth Planet Sci Lett 26956ndash65 httpdxdoiorg101016jepsl200801049

Sun XY Cordier P Taupin V Fressengeas C Jahn S 2016 Continuousdescription of a grain boundary in forsterite from atomic scale simulationsthe role of disclinations Phil Mag 96 1757ndash1772 httpdxdoiorg1010801478643520161177232

Tackley PJ 1993 Effects of strongly temperature-dependent viscosity on time-dependent three-dimensional models of mantle convection Geophys Res Lett20 2187ndash2190 httpdxdoiorg10102993GL02317

Tanaka S Hamaguchi H 1997 Degree one heterogeneity and hemisphericalvariation of anisotropy in the inner core from PKP(BC)-PKP(DF) times JGeophys Res 102 2925ndash2938 httpdxdoiorg10102996JB03187

Tanimoto T Anderson DL 1984 Mapping convection in the mantle GeophysRes Lett 11 (4) 287ndash290 httpdxdoiorg101029GL011i004p00287

Tanimoto T Anderson DL 1985 Lateral heterogeneity and azimuthal anisotropyof the upper mantle Love and Rayleigh Waves 100ndash250s J Geophys Res 901842ndash1858 httpdxdoiorg101029JB090iB02p01842

Tamura N 2014 XMAS a versatile tool for analyzing synchrotron X-raymicrodiffraction data In Ice GE Barabash R (Eds) Strain and DislocationGradients from Diffraction London Imperial College Press pp 125ndash155 httpdxdoiorg1011429781908979636_fmatter

Tateno S Hirose K Sata N Ohishi Y 2009 Determination of post-perovskitephase transition boundary up to 4400 K and implications for the thermalstructure of D00 layer Earth Planet Sci Lett 277 130ndash136 httpdxdoiorg101016jepsl200810004

Tateno S Hirose K Ohishi Y Tatsumi Y 2010 The structure of iron in Earthrsquosinner core Science 330 359ndash361 httpdxdoiorg101126science1194662

Tateno S Hirose K Komabayashi T Ozawa H Ohishi Y 2012 The structure ofFe-Ni alloy in Earthrsquos inner core Geophys Res Lett 39 (L12305) 1ndash4 httpdxdoiorg1010292012GL052103

Tateno S Kuwayama Y Hirose K Ohishi Y 2015 The structure of FendashSi alloy inEarthrsquos inner core Earth Planet Sci Lett 418 11ndash19 httpdxdoiorg101016jepsl201502008

Taylor GI 1934 The mechanism of plastic deformation of crystals Proc R SocLondon 145 362ndash404

Taylor GI 1938 Plastic strain in metals J Inst Metals 62 307ndash324Thomas C Kendall JM 2002 The lowermost mantle beneath northern Asia (2)

Evidence for D00 anisotropy Geophys J Int 151 296ndash308 httpdxdoiorg101046j1365-246X200201760x

Thomas C Wookey J Simpson M 2007 D00 anisotropy beneath Southeast AsiaGeophys Res Lett 34 (4) L04301 httpdxdoiorg1010292006GL028965

Thomas C Wookey J Brodholt J Fieseler T 2011 Anisotropy as cause forpolarity reversals of D00 reflections Earth Planet Sci Lett 307 369ndash376 httpdxdoiorg101016jepsl201105011

Thomsen L 1986 Weak elastic anisotropy Geophysics 51 (10) 1954ndash1966 httpdxdoiorg10119011442051

Tkalcic H 2010 Large variations in travel times of mantle-sensitive seismic wavesfrom the South Sandwich Islands Is the Earthrsquos inner core a conglomerate ofanisotropic domains Geophys Res Lett 37 L14312 httpdxdoiorg1010292010GL043841

Tkalcic H 2015 Complex inner core of the Earth the last frontier of globalseismology Rev Geophys 53 59ndash94 httpdxdoiorg1010022014RG000469

Tkalcic H Romanowicz B Houy N 2002 Constraints on D00 structure using PKP(AB-DF) PKP(BC-DF) and PcP-P traveltime data from broad-band recordsGeophys J Int 148 599ndash616 httpdxdoiorg101046j1365-246X200201603x

To A Romanowicz B Capdeville Y Takeuchi N 2005 3D effects of sharpboundaries at the borders of the African and Pacific Superplumes Observationand modeling Earth Planet Sci Lett 233 137ndash153 httpdxdoiorg101016jepsl200501037

Trampert J Woodhouse JH 2003 Global anisotropic phase velocity maps forfundamental mode surface waves between 40 and 150s Geophys J Int 154154ndash165 httpdxdoiorg101046j1365-246X200301952x

Trampert J van Heijst HJ 2002 Global azimuthal anisotropy in the transitionzone Science 296 1297ndash1299 httpdxdoiorg101126science1070264

Tschauner O Ma C Beckett JR Prescher C Prakapenka VB Rossman GR2014 Discovery of bridgmanite the most abundant mineral in Earth in ashocked meteorite Science 346 1100ndash1102 1100 [doi101126science1259369]

Tsuchiya J Tsuchiya T 2008 Postperovskite phase equilibria in the MgSiO3-Al2O3

system Proc Nat Acad Sci 105 19160ndash19164 httpdxdoiorg101073pnas0805660105

Tsuchiya J Tsuchiya T 2011 First-principles prediction of a high-pressurehydrous phase of AlOOH Physical Review B 83 054115 httpdxdoiorg1010292010JB008018

Tsuchiya T Wentzcovitch RM da Silva CRS de Gironcoli S 2006 Spintransition in magnesiowstite in Earthrsquos lower mantle Phys Rev Lett 96198501 doiorg101103PhysRevLett 96198501

Tsujino N Nishihara Y Yamazaki D Seto Y Higo Y Takahashi E 2016 Mantledynamics inferred from the crystallographic preferred orientation ofbridgmanite Nature 539 81ndash85 httpdxdoiorg101038nature19777

Tullis J Wenk H-R 1994 Effect of muscovite on the strength and lattice preferredorientations of experimentally deformed quartz aggregates Mat Sci Eng A175209ndash220

Ullemeyer K Siegesmund S Rasolofosaon PNJ Behrmann JH 2006Experimental and texture-derived P-wave anisotropy of principal rocks fromthe TRANSALP traverse an aid for the interpretation of seismic field dataTectonophysics 414 97ndash116 httpdxdoiorg101016jtecto200510024

Usui Y Hiramatsu Y Furumoto M Kanao M 2008 Evidence of seismicanisotropy and a lower temperature condition in the D00 layer beneath PacificAntarctic Ridge in the Antarctic Ocean Phys Earth Planet Inter 167 205ndash216

Van den Berg AP De Hoop MV Yuen DA Duchkov A van der Hilst RD JacobsMHG 2010 Geodynamical modeling and multiscale seismic expression ofthermo-chemical heterogeneity and phase transitions in the lowermost mantlePhys Earth Planet Inter 180 244ndash257 101016jpepi201002008

Vanacore E Niu F 2011 Characterization of the D00 layer beneath the GalapagosIslands using SKKS and SKS waveforms Earthquake Sci 24 87ndash99 httpdxdoiorg101007s11589-011-0772-8

Vasin R Wenk H-R Kanitpanyacharoen W Matthies S Wirth R 2013Anisotropy of Kimmeridge shale J Geophys Res 118 1ndash26 httpdxdoiorg101002jgrb50259

Vilella K Shim S-H Farnetani CG Badro J 2015 Spin state transition andpartitioning of iron effects on mantle dynamics Earth Planet Sci Lett 417 57ndash66 httpdxdoiorg101016jepsl201502009

Vine FJ Matthews DH 1963 Magnetic anomalies over oceanic ridges Nature199 947ndash949

Vinnik L Farra V Romanowicz B 1989 Observational evidence for diffracted SVin the shadow of the Earthrsquos core Geophys Res Lett 16 (6) 519ndash522 httpdxdoiorg101029GL016i006p00519

Vinnik L Romanowicz B Breacuteger L 1994 Anisotropy in the center of the innercore Geophys Res Lett 21 (16) 1671ndash1674 httpdxdoiorg10102994GL01600

Vinnik L Romanowicz B Le Stunff Y Makeyeva L 1995 Seismic anisotropy inthe D00 layer Geophys Res Lett 22 (13) 1657ndash1660 httpdxdoiorg10102995GL01327

Vinnik L Breacuteger L Romanowicz B 1998a On the inversion of Sd particle motionfor seismic anisotropy in D00 Geophys Res Lett 25 (5) 679ndash682 httpdxdoiorg10102998GL00190

Vinnik LP Breacuteger L Romanowicz B 1998b Anisotropic structures at the base ofthe Earthrsquos mantle Nature 393 564ndash567 httpdxdoiorg10103831208

Vocadlo L Alfegrave D Gillan MJ Wood IG Brodholt JP Price GD 2003 Possi-blethermal and chemical stabilization of body centered-cubic iron in the Earthrsquoscore Nature 424 536ndash539 httpdxdoiorg101038nature01829

Vocadlo L Wood IG Gillan MJ Brodholt J Dobson DP Price GD Alfe D2008 The stability of bcc-Fe at high pressures and temperatures with respect totetragonal strain Phys Earth Planet Inter 170 52ndash59 httpdxdoiorg101016j pepi200807032

Vocadlo L Dobson DP Wood IG 2009 Ab initio calculations of the elasticity ofhcp-Fe as a function of temperature at inner- core pressure Earth Planet SciLett 288 534ndash538 httpdxdoiorg101016jepsl200910015

90 B Romanowicz H-R Wenk Physics of the Earth and Planetary Interiors 269 (2017) 58ndash90

Voigt W 1887 Theoretische Studien uumlber die Elasticitaumltsverhaumlltnisse der KrystalleAbh Kgl Ges Wiss Goumlttingen Math Kl 34 3ndash51

Walker AM Forte AM Wookey J Nowacki A Kendall J-M 2011 Elasticanisotropy of D00 predicted from global models of mantle flow GeochemGeophys Geosystems 12 Q10006 httpdxdoiorg1010292011GC003732

Wang Y Weidner DJ Guyot F 1996 Thermal equation of state of CaSiO3

perovskite J Geophys Res 101 661ndash672 httpdxdoiorg10102995JB03254

Wang Y Wen L 2007 Complex seismic anisotropy at the border of a very lowvelocity province at the base of the Earthrsquos mantle J Geophys Res 112 B09305httpdxdoiorg1010292006JB004719

Wang Y Durham WB Getting IC Weidner DJ 2003 The deformation-DIA Anew apparatus for high temperature triaxial deformation to pressures up to 15GPa Rev Sci Instrum 74 3002 httpdxdoiorg10106311570948

Wang Y Lesher C Fiquet G Rivers ML Nishiyama N Siebert J Roberts JMorard G Gaudio S Clark A Watson H Menguy N Guyot F 2011 In situhigh-pressure and high-temperature X-ray microtomographic imaging duringlarge deformation A new technique for studying mechanical behavior ofmultiphase composites Geosphere 7 (1) 40ndash53 httpdxdoiorg101130GES005601

Wang T Song X Xia HH 2015 Equatorial anisotropy in the inner part of theEarthrsquos inner core from autocorrelation of earthquake coda Nature Geosci 8224ndash227 httpdxdoiorg101038ngeo2354

Waszek L Irving J Deuss A 2011 Reconciling the hemispherical structure ofEarthrsquos inner core with its super-rotation Nat Geosci 4 264ndash267 httpdxdoiorg101038ngeo1083

Wegener A 1915 Die Entstehung der Kontinente und Ozeane ViewegBraunschweig

Weidner DJ Li L 2015 Methods for the study of high P-T deformation andrheology 2nd ed Treatise on Geophysics 2nd ed pp 351ndash368

Weis D Garcia MO Rhodes JM Jellinek M Scoates JS 2011 Role of the deepmantle in generating bilateral the compositional asymmetry of the Hawaiianmantle plume Nature Geosci 4 831ndash838 httpdxdoiorg101038ngeo1328

Wenk H-R Canova G Brechet Y Flandin L 1997 A deformation-based modelfor recrystallization of anisotropic materials Acta Mater 45 3283ndash3296

Wenk H-R Tomeacute C 1999 Simulation of deformation and recrystallization ofolivine deformed in simple shear J Geophys Res 104 25513ndash25527 httpdxdoiorg1010291999JB900261

Wenk H-R Matthies S Hemley RJ Mao H-K Shu J 2000a The plasticdeformation of iron at pressures of the Earthrsquos inner core Nature 405 1044ndash1047 httpdxdoiorg101016jepsl200407033

Wenk H-R Baumgardner J Lebensohn R Tomeacute C 2000b A convection model toexplain anisotropy of the inner core J Geophys Res 105 5663ndash5677 httpdxdoiorg1010291999JB900346

Wenk H-R Lonardelli I Pehl J Devine J Prakapenka V Shen G Mao H-K2004 In situ observation of texture development in olivine ringwooditemagnesiowuestite and silicate perovskite at high pressure Earth Planet SciLett 226 507ndash519 httpdxdoiorg101016j epsl200407033

Wenk H-R Speziale S McNamara AK Garnero EJ 2006 Modeling lowermantle anisotropy development in a subducting slab Earth Planet Sci Lett 245302ndash314 httpdxdoiorg101016jepsl200602028

Wenk H-R Armann M Burlini L Kunze K Bortolotti M 2009 Large strainshearing of halite experimental and theoretical evidence for dynamic texturechanges Earth Planet Sci Lett 280 205ndash210 httpdxdoiorg101016jepsl200901036

Wenk H-R Cottaar S Tomeacute C McNamara A Romanowicz B 2011Deformation in the lowermost mantle From polycrystal plasticity to seismicanisotropy Earth Planet Sci Lett 306 33ndash45 httpdxdoiorg101016jepsl201103021

Wenk H-R Lutterotti L Kaercher P Kanitpanyacharoen W Miyagi L Vasin R2014 Rietveld texture analysis from synchrotron diffraction images IIComplex multiphase materials and diamond anvil cell experiments PowderDiffraction 29 220ndash232 httpdxdoiorg101017S0885715614000360

Wentzcovitch R Karki B Cococcioni M de Gironcoli S 2004 Thermoelasticproperties of MgSiO3-perovskite insights on the nature of the Earthrsquos lowermantle Phys Rev Lett 92 (1) 1ndash4

Wentzcovitch RM Tsuchiya T Tsuchiya J 2005 MgSiO3 postperovskite at D00

conditions Proc Nat Acad Sci 103 543ndash546 httpdxdoiorg101073pnas0506879103

White WM 2015 Probing the Earthrsquos deep interior through geochemistryGeochem Perspect 4 (2) 95ndash251

Williams Q Garnero EJ 1996 Seismic evidence for partial melt at the base ofEarthrsquos mantle Science 273 1528ndash1530 httpdxdoiorg101126science27352811528

Woodhouse JH Giardini D Li X-D 1986 Evidence for inner core anisotropyfrom free oscillations Geophys Res Lett 13 1549ndash1552 httpdxdoiorg101029GL013i013p01549

Wookey J Kendall J-M 2007 Seismic anisotropy of post-perovskite and thelowermost mantle In Post-Perovskite The Last Mantle Phase Transition InHirose K Brodholt J Lay T Yuen D (Eds) Geophysical Monograph Seriesvol 174 AGU 984 Washington DC pp 171ndash189

Wookey J Kendall J 2008 Constraints on lowermost mantle mineralogy andfabric beneath Siberia from seismic anisotropy Earth Planet Sci Lett 275 32ndash42 httpdxdoiorg101016jepsl200807049

Wookey J Kendall J Ruumlmpker G 2005a Lowermost mantle anisotropy beneaththe north Pacific from differential S-ScS splitting Geophys J Int 161 829ndash838httpdxdoiorg101111j1365-246X200502623x

Wookey J Stackhouse S Kendall J-M Brodholt J Price GD 2005b Efficacy ofthe post-perovskite phase as an explanation for lowermost-mantle seismicproperties Nature 438 1004ndash1007 httpdxdoiorg101038nature-04345

Wu X Lin J-F Kaercher P Mao Z Wenk H-R Prakapenka V 2017 Seismicanisotropy of the D00 layer induced by (001) deformation of post-perovskiteNature Commu 8 httpdxdoiorg1010038ncomms14669 14669

Wysession M Lay T Revenaugh J Williams Q Garnero EJ Jeanloz R KelloggLH 1998 The D00 discontinuity and its implications In Gurnis M WysessionME Knittle E Buffett BA (Eds) The core-mantle boundary region AmericanGeophysical Union Washington DC pp 273ndash298 httpdxdoiorg101029GD028p0273

Yamasaki D Karato SI 2001 Some mineral physics constraints on the rheologyand geothermal structure of Earthrsquos lower mantle - Amer Mineral 86 385ndash391 httpdxdoiorg102138am-2001-0401

Yamazaki D Ito E Yoshino T Tsujino N Yoneda A Guo X Xu F Higo YFunakoshi K 2014 Over 1 Mbar generation in the Kawai-type multianvilapparatus and its application to compression of (Mg092Fe008)SiO3 perovkite andstishovite Phys Earth Planet Int 228 262ndash267 httpdxdoiorg101016jpepi201401013

Yoshida S Sumita I Kumazawa M 1996 Growth model of the inner core coupledwith outer core dynamics and the resulting elastic anisotropy J Geophys Res101 28085ndash28103

Yuan K Beghein C 2013 Seismic anisotropy changes across upper mantle phasetransitions Earth Planet Sci Lett 374 132ndash144 httpdxdoiorg101016jepsl201305031

Zhang Z Stixrude L Brodholt J 2013 Elastic properties of MgSiO3-perovskiteunder lower mantle conditions and the composition of the deep Earth EarthPlanet Sci Lett 379 1ndash12 httpdxdoiorg101016jepsl201307034

Zhang L Popov D Meng Y Wang J Ji C Li B Mao H-K 2016 In-situ crystalstructure determination of seifertite SiO2 at 129 GPa Studying a minor phasenear Earthrsquos core-mantle boundary Amer Mineral 101 231ndash234 doiorg102138am-2016-5525