Lecture 1

Historical Background

1.1 Introduction 3

Figure 1.2. James Hutton (1726–1797), thefather of Geology and proponent of internalheat as the driving force for Earth’s evolution.

The idea that flow in the Earth’s interior is a form of thermal convection developedslowly. Recognition of the significance of thermal convection as a primary fluid mechanicalphenomenon in nature came from physicists. Count Rumford is usually given credit forrecognizing the phenomenon around 1797 (Brown, 1957), although the term convection(derived from convectio, to carry) was first used by Prout (1834) to distinguish it from theother known heat transfer mechanisms, conduction and radiation. Subcrustal convection inthe Earth was first suggested by W. Hopkins in 1839 and the first interpretations of geologicalobservations using convection were made by Osmond Fisher (1881). Both of these presumeda fluid interior, so when the solidity of the mantle was established, these ideas fell out offavor.

The earliest experiments on convection in a layer of fluid heated from below and cooledfrom above were reported by J. Thompson (1882), who observed a “tesselated structure” inthe liquid when its excess temperature, compared to that of the overlying air, was sufficientlylarge. But the name most closely associated with convection is Henri Bénard (Figure 1.3).Bénard (1900, 1901) reported the first quantitative experiments on the onset of convection,including the role of viscosity, the cellular planform, and the relationship between cell sizeand fluid layer depth. Bénard produced striking photographs of the convective planform inthin layers of viscous fluids heated from below (Figure 1.4). The regular, periodic, hexagonalcells in his photographs are still referred to as Bénard cells. Since Bénard used fluid layers incontact with air, surface tension effects were surely present in his experiments, as he himselfrecognized. It has since been shown that Bénard’s cells were driven as much by surfacetension gradients as by gradients in buoyancy. Still, he correctly identified the essentials ofthermal convection, and in doing so, opened a whole new field of fluid mechanics. Motivatedby the “interesting results obtained by Bénard’s careful and skillful experiments,” LordRayleigh (1916; Figure 1.5) developed the linear stability theory for the onset of convection

- James Hutton

“The fundamental physical process behind all major geological events is heat transfer from the deep interior to the surface.”

Theory of isostacy that allowed for vertical adjustment

•  Earliest experiment: Benjamin Thomson

•  Also developed the science of thermodynamics

4 Historical Background

Figure 1.3. Henri Bénard (1880–1939) (on the left) madethe first quantitative experiments on cellular convection inviscous liquids. The picture was taken in Paris about 1920with Reabouchansky on the right.

Figure 1.4. Photograph of hexagonal con-vection cells in a viscous fluid layer heatedfrom below, taken by Bénard (1901).

in a horizontally infinite fluid layer between parallel surfaces heated uniformly from belowand cooled uniformly from above, and isolated the governing dimensionless parameter thatnow bears his name. It was unfortunate that these developments in fluid mechanics were notfollowed more widely in Earth Science, for they might have removed a stumbling block toacceptance of the milestone concept of continental drift.

Bénard cells (1901)

1.2 Continental Drift 5

Figure 1.5. Lord Rayleigh (1842–1919) developed thetheory of convective instability in fluids heated frombelow.

1.2 Continental Drift

The earliest arguments for continental drift were largely based on the fit of the continents.Ever since the first reliable maps were available, the remarkable fit between the east coastof South America and the west coast of Africa has been noted (e.g., Carey, 1955). Indeed,the fit was pointed out as early as 1620 by Francis Bacon (Bacon, 1620). North America,Greenland, and Europe also fit as illustrated in Figure 1.6 (Bullard et al., 1965).

Geological mapping in the southern hemisphere during the nineteenth century revealedthat the fit between these continents extends beyond coastline geometry. Mountain belts inSouth America match mountain belts in Africa; similar rock types, rock ages, and fossilspecies are found on the two sides of the Atlantic Ocean. Thus the southern hemispheregeologists were generally more receptive to the idea of continental drift than their northernhemisphere colleagues, where the geologic evidence was far less conclusive.

Further evidence for continental drift came from studies of ancient climates. Geologistsrecognized that tropical climates had existed in polar regions at the same times that arc-tic climates had existed in equatorial regions. Also, the evolution and dispersion of plantand animal species was best explained in terms of ancient land bridges, suggesting directconnections between now widely separated continents.

As previously indicated, most geologists and geophysicists in the early twentieth centuryassumed that relative motions on the Earth’s surface, including motions of the continentsrelative to the oceans, were mainly vertical and generally quite small – a few kilometersin extreme cases. The first serious advocates for large horizontal displacements were twovisionaries, F. B. Taylor and Alfred Wegener (Figure 1.7). Continental drift was not widelydiscussed until the publication of Wegener’s famous book (Wegener, 1915; see also Wegener,1924), but Taylor deserves to share the credit for his independent and somewhat earlieraccount (Taylor, 1910). Wegener’s book includes his highly original picture of the breakup

•  Lord Rayleigh: Linear stability theory

•  Rayleigh-Bénard

convection

1.2 Continental Drift 7

Figure 1.7. Alfred Wegener (1880–1930), the father ofcontinental drift.

Figure 1.8. Harold Jeffreys (1891–1989), themost influential theorist in the early debate overcontinental drift and mantle convection.

rotational forces were also responsible for driving the mantle flows resulting in continentaldrift.) At the same time, seismologists were exploring the Earth’s deep interior, and wereimpressed by the high elastic rigidity of the mantle. In his influential book, The Earth(Jeffreys, 1929), Sir Harold Jeffreys (Figure 1.8) referred to the mantle as the “shell,” arguingthat this term better characterized its elastic strength. Paradoxically, Jeffreys was at the same

How can mantle be both elastic and viscous?

“Thermal convection in the highly rigid mantle not possible on mechanical grounds”

- Harold Jeffreys

1.3 The Concept of Subsolidus Mantle Convection 9

Figure 1.9. Arthur Holmes (1890–1965), the firstprominent advocate for subsolidus mantle convection.

Figure 1.10. Arthur Holmes’ (1931) depiction of mantle convection as the cause of continental drift, thirtyyears prior to the discovery of seafloor spreading.

than that required for the onset of convection. He also outlined a general relation betweenthe ascending and descending limbs of mantle convection cells and geological processes,illustrated in Figure 1.10. Holmes argued that radioactive heat generation in the continentsacted as a thermal blanket inducing ascending thermal convection beneath the continents.Holmes was one of the most prominent geologists of the time, and in his prestigious textbookPrinciples of Physical Geology (Holmes, 1945), he articulated the major problems of mantleconvection much as we view them today.

The creep viscosity of the solid mantle was first determined quantitatively by Haskell(1937). Recognition of elevated beach terraces in Scandinavia showed that the Earth’s surface

Arthur Holmes’ (1931)

(Credit: Finnish Geospatial Research Institute)

•  Viscosity of mantle first determined quantitatively by Haskell •  Explained the uplift of Fennoscandia •  GIA

How to reconcile both solid and fluid behavior of mantle?

•  Slow creep of crystalline materials At temperatures less than melt temperatures rocks can

flow at low stress levels on timescales greater than 10,000 years

14 Historical Background

E

W

(a)

Reversed Profile

Observed Profile

150 0 150 km

500γ

GilbertGauss

Matuyama

Brunhes

Matuyama

GaussGilbert

Mid-Ocean Ridge

3.3 Million Years3.3

Brunhes

Zone of Cooling and Magnetization

(b)

Figure 1.13. (a) Magnetic profile across the East Pacific Rise at 51◦S; the lower profile shows the observedprofile reversed for comparison. (b) The spreading ocean floor. Hot material wells up along the oceanic ridge.It acquires a remanent magnetism as it cools and travels horizontally away from the ridge. At the top of thediagram are shown the known intervals of normal (gray) and reversed (white) polarity of the Earth’s magneticfield, with their names. The width of the ocean-floor stripes is proportional to the duration of the normal andreversed time intervals.

Carey (1958, 1976) had been concerned about the geometrical reconstruction of formercontinental masses. These studies led him to view the Earth as undergoing rapid expansion.This view did not receive wide support and it will not be considered further. There is nosatisfactory physical explanation of how such a large volume expansion might have occurredand it is inconsistent both with estimates of the change in the Earth’s rate of rotation andwith paleomagnetic constraints on changes in the Earth’s radius.

Magnetic profile across the East Pacific Rise

Rayleigh number: •  Measures the vigor of convection •  Measure of the competition between gravitational thermal buoyance forces that acts to drive convective flow and the resistive effects of fluid viscosity that retards convective motion and thermal diffusion which acts to diminish thermal anomalies

•  Very high viscosity of mantle

•  Various complex rheologies and deformation mechanisms

BERCOVICI ET AL.: MANTLE DYNAMICS AND PLATE TECTONICS 19

45

1

2

3

0

0.2

0.4

0.6

0.8

1

0 0.1 0.2 0.3 0.4 0.5

0

0.2

0.4

0.6

0.8

1

0 0.1 0.2 0.3 0.4 0.5

strain rate

stre

ss

Figure 10. Constitutive (stress versus strain-rate) laws for (1) plastic,(2) non-Newtonian power law, (3) Newtonian, (4) brittle stick-slip and (5)self-lubricating (also called continuous stick-slip) rheologies.

layer will tend to be weakest at the divergent zone (wherethe boundary layer is thinnest) which approaches plate-likebehavior. However, the viscosity will be highest over thecold convergent zone, tending to immobilize it and eventu-ally the entire boundary layer, which is of course one of theroot causes for the subduction initiation problem (see 4.6);in the end, this also leads to a thermal boundary layer withlittle plateness. Therefore, it is a reasonable assumption thatplate-like strength distributions – or high plateness – requirea lithospheric rheology that permits boundaries to be weak,regardless of temperature.At high stresses mantle rocks undergo non-Newtonian

creep wherin deformation responds nonlinearly to the ap-plied stress; i.e., the stress–strain-rate constitutive law isnonlinear through a power-law relation such that

(10)

where is strain-rate, is stress, and is the power-law in-dex (see Fig. 10); for mantle rocks, , typically [Weert-man and Weertman, 1975; Evans and Kohlstedt, 1995]. Theeffective viscosity is

(11)

which means that for viscosity decreases with in-creasing strain-rate. The power-law rheology causes regionsof the material that are rapidly deformed to become softer,while slowly-deforming regions become relatively stiff. Thisrheology not only yields reasonable plateness, but also leadsto a feedback effect: as the deformed parts of the fluid soften

they become more readily deformed, causing further strainto concentrate there, thereby inducing further softening, etc.(Comparable effects can be caused with other rheologiessuch as Bingham plastics and bi-viscous laws; however,these are just further mathematical models for essentially thesame strain-softening effect represented by a power-law rhe-ology.) Such non-Newtonian rheologies have been incorpo-rated into numerous 2-D convection models for andhave found little plate like behavior [e.g., Parmentier et al.,1976; Christensen, 1984c]. Other models, concentrating onplate formation, placed a thin non-Newtonian “lithospheric”fluid layer atop a thicker convecting layer, or mathemati-cally confined the non-Newtonian behavior to a near-surfacelayer [Weinstein and Olson, 1992; Weinstein, 1996; Moresiand Solomatov, 1998; see also Schmeling and Jacoby, 1981](Fig. 11). In these latter models, the non-Newtonian ef-fect does indeed yield an upper layer with reasonably highplateness for basally heated convection: the layer becomesweaker over both divergent zones (i.e. over upwellings) andconvergent zones (downwellings), and is relatively immo-bile and strong in between the these two zones. Moreover, asnoted by King et al. [1992], 2D models with non-Newtonianrheology are often indistinguishable in some respects fromthose with imposed plate geometries [e.g., Olson and Cor-cos, 1980; Davies, 1988a] and lithospheric weak zones [e.g.,King and Hager, 1990; Zhong and Gurnis, 1995a]. How-ever, to obtain sufficient plateness with the non-Newtonianmodels, it is necessary to use a power-law index con-siderably higher than inferred from rheological experiments(typically is needed). Thus, it seems that a generalstrain-weakening type rheology is a plausible and simple so-lution to generating high plateness, i.e. weak boundariesand strong plate interiors, in a convection model. However,when the convective flow is driven by internally heated con-vection, which has little or no concentrated upwellings, thenthe divergent zones in the lithospheric layer tend to be broadand diffuse, i.e., not at all like narrow, passively spreadingridges [Weinstein and Olson, 1992] (Fig. 11).It is undoubtedly naive to assert that plate-like behavior

simply requires the generation of weak boundaries; in facteach type of boundary, i.e., convergent, divergent and strike-slip, develops under very different deformational and ther-mal environments. Obtaining sufficient plateness is invari-ably related to the the nature of how the different boundariesform. As each type of boundary is uniquely enigmatic, theywarrant individual discussion. These will be the focus of thefollowing sections.

4.6. Convergent margins: initiation and asymmetry ofsubduction

The downwelling currents in simple convection are forthe most part very symmetric; i.e., one downwelling is com-posed of two cold thermal boundary layers converging oneach other (Plate 1). In the Earth, the downwellings associ-ated with plate motions – i.e., subducting slabs – are highlyasymmetric, i.e., only one side of the convergent zone – only

Bercovici et al., 2000

•  Is mantle layered at 660 km?

•  Is mantle layered at 660 km?

http://instruct.uwo.ca/earth-sci/240a/Part_D.htm

Vol. 7, No. 4 April 1997

GSA TODAYA Publication of the Geological Society of America

ABSTRACT

Two new global high-resolutionmodels of the P-wave and S-waveseismic structure of the mantle werederived independently using differentinversion techniques and different datasets, but they show excellent correlationfor many large-scale as well as smallerscale structures throughout the lowermantle. The two models show thathigh-velocity anomalies in the lowermantle are dominated by long linearfeatures that can be associated with thesites of ancient subduction. The imagessuggest that most subduction-relatedmantle flow continues well into thelower mantle and that slabs may ulti-mately reach the core-mantle boundary.The models are available from anony-mous ftp at maestro.geo.utexas.edu indirectory pub/grand and at brolga.mit.edu in directory pub/GSAtoday.

INTRODUCTION

Since forming about 4.5 Ga, planetEarth has been cooling by means of rela-tively vigorous convection in its interiorand by conductive heat loss across thecold thermal boundary layer at the topof the mantle (mainly the oceanic litho-sphere). The primary force driving convec-tion is the downward pull of gravity onthe cold, dense lithosphere resulting indownwellings of slabs of subducted litho-sphere. Understanding the nature of the

Figure 1. Cross sections of mantle P-wave (A) and S-wave (B) velocity variations along a sectionthrough the southern United States. The endpoints of the section are 30.1°N, 117.1°W and 30.2°N,56.4°W. The images show variations in seismic velocity relative to the global mean at depths from thesurface to the core-mantle boundary. Blues indicate faster than average and reds slower than averageseismic velocity. The large tabular blue anomaly that crosses the entire lower mantle is probably thedescending Farallon plate that subducted over the past ~100 m.y. Differences in structure between thetwo models in the transition zone (400 to 660 km depth) and at the base of the mantle are probablydue to different data sampling in the two studies.

A

BFARALLON SLAB

2700 km depth

2770 km depth

Global Seismic Tomography: A Snapshot of Convection in the Earth Stephen P. Grand, Department of Geological Sciences, University of Texas,

Austin, TX 78712Rob D. van der Hilst, Department of Earth and Planetary Sciences, Massachussetts Institute of Technology, Cambridge, MA 02139Sri Widiyantoro, Research School of Earth Sciences, Australian National University, Canberra, ACT 0200, Australia

Tomography continued on p. 2

120°W 100°W 80°W 60°W 40°W

40°N

20°N

1997AnnualMeetingCall for Papers

page 13

Electronic Abstracts Submission

page 14

Registration Issue June GSA Today

Vol. 7, No. 4 April 1997

GSA TODAYA Publication of the Geological Society of America

ABSTRACT

Two new global high-resolutionmodels of the P-wave and S-waveseismic structure of the mantle werederived independently using differentinversion techniques and different datasets, but they show excellent correlationfor many large-scale as well as smallerscale structures throughout the lowermantle. The two models show thathigh-velocity anomalies in the lowermantle are dominated by long linearfeatures that can be associated with thesites of ancient subduction. The imagessuggest that most subduction-relatedmantle flow continues well into thelower mantle and that slabs may ulti-mately reach the core-mantle boundary.The models are available from anony-mous ftp at maestro.geo.utexas.edu indirectory pub/grand and at brolga.mit.edu in directory pub/GSAtoday.

INTRODUCTION

Since forming about 4.5 Ga, planetEarth has been cooling by means of rela-tively vigorous convection in its interiorand by conductive heat loss across thecold thermal boundary layer at the topof the mantle (mainly the oceanic litho-sphere). The primary force driving convec-tion is the downward pull of gravity onthe cold, dense lithosphere resulting indownwellings of slabs of subducted litho-sphere. Understanding the nature of the

Figure 1. Cross sections of mantle P-wave (A) and S-wave (B) velocity variations along a sectionthrough the southern United States. The endpoints of the section are 30.1°N, 117.1°W and 30.2°N,56.4°W. The images show variations in seismic velocity relative to the global mean at depths from thesurface to the core-mantle boundary. Blues indicate faster than average and reds slower than averageseismic velocity. The large tabular blue anomaly that crosses the entire lower mantle is probably thedescending Farallon plate that subducted over the past ~100 m.y. Differences in structure between thetwo models in the transition zone (400 to 660 km depth) and at the base of the mantle are probablydue to different data sampling in the two studies.

A

BFARALLON SLAB

2700 km depth

2770 km depth

Global Seismic Tomography: A Snapshot of Convection in the Earth Stephen P. Grand, Department of Geological Sciences, University of Texas,

Austin, TX 78712Rob D. van der Hilst, Department of Earth and Planetary Sciences, Massachussetts Institute of Technology, Cambridge, MA 02139Sri Widiyantoro, Research School of Earth Sciences, Australian National University, Canberra, ACT 0200, Australia

Tomography continued on p. 2

120°W 100°W 80°W 60°W 40°W

40°N

20°N

1997AnnualMeetingCall for Papers

page 13

Electronic Abstracts Submission

page 14

Registration Issue June GSA Today

Grand et al., GSA, 1997

P-wave

S-wave

Figure 2. Structure of subducted slabs as inferred from mantle tomography (from Karason and van der Hilst[2000]). Red lines show the surface projection of each section. The base of each section is the core-mantleboundary (CMB); dashed lines show the location of mantle discontinuities at 410, 660, and 1700 km. Red andblue colors in each section denote regions where the P wave velocities are relatively slow and fast, respectively,compared to average mantle at the same depth. Fast regions are most easily interpreted as relatively cool areascorresponding to the subducted slab and its viscous mantle blanket. This allows the cool, subducted slab to betraced well below the deepest earthquake. Note that some slabs penetrate the 660 km discontinuity anddescend into the lower mantle (e.g., Central America, central Japan, and Indonesia), while other slabs seemto stagnate in the upper mantle (such as Izu-Bonin). The subducted slab beneath Tonga seems to stagnate atthe 660 km discontinuity for a while, then cascade into the lower mantle.

Figure 6. (opposite) Geophysical images of subduction zones. (a) P wave tomographic image of NE Japan(modified after Zhao et al. [1994]). There is no vertical exaggeration. (b) P wave tomographic image of Tongasubduction zone (modified after Zhao et al. [1997]). There is no vertical exaggeration. For both Figures 6a and6b, red and blue colors denote regions where the P wave velocities are relatively slow and fast, respectively,compared to average mantle at the same depth. (c) P wave velocity structure across the Cascadia SubductionZone (modified after Parsons et al. [1998]). Yellow dots show earthquakes during 1970–1996 between 45! and47! latitude, " M1 at depths " 25 km and " M4 at shallower depths. Note vertical exaggeration is 2x. Note thatthe subduction zones in Figure 6a and 6b subduct old, cold lithosphere, which is relatively easy to identifytomographically, whereas the subduction zone in Figure 6c subducts young lithosphere, which differs less invelocity relative to the surrounding mantle and is more difficult to image tomographically.

40, 4 / REVIEWS OF GEOPHYSICS STERN: SUBDUCTION ZONES

● 3-5 and 3-11 ●

Karason & Van der Hilst, Geophys. Monograph, 2000

•  Is mantle layered at 660 km?

•  Do plumes exist?

•  Do plumes exist?

Montelli et al., G3, 2006