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LETTERSPUBLISHED ONLINE: 26 JUNE 2011 | DOI: 10.1038/NGEO1187

Spatial and temporal variability in Hawaiianhotspot volcanism induced bysmall-scale convectionMaxim D. Ballmer1,2*, Garrett Ito1, Jeroen van Hunen3 and Paul J. Tackley2

Volcanism far from plate boundaries is often attributed to anunderlying mantle plume1–6. However, enigmatic observationsof Hawaiian volcanism, such as variations in the volumeof erupted volcanic material through time7,8, a geographicalasymmetry in the geochemistry of the lavas9–18 and secondaryvolcanism that occurs far away from the hotspot15–20, cannotbe explained by the classical mantle plume concept. Here wepresent a numerical model of mantle plume upwelling beneathHawaii. We find that small-scale convection in the ambientmantle can erode the base of the lithosphere, creating awashboard topography on the underside of the plate. As theplate migrates over the upwelling plume, the plume interactswith alternating thicker and thinner sections of lithosphereto generate temporal variations in the flux of eruptedvolcanic material. The pre-existing washboard topography alsocauses the plume to spread and melt asymmetrically. In oursimulations, this asymmetry in mantle flow generates anasymmetry in the chemistry of the erupted lavas. Finally, amore vigorous type of small-scale convection develops withinthe spreading plume, generating localized zones of upwellingwell away from the hotspot. The associated magmatism is fedby chemically distinct material originating from the edges ofthe plume conduit. Our results show that shallow processeshave an important influence on the character of volcanism fedby deep-rooted mantle plumes.

Classical plumes are typically described as purely thermallydriven, narrow upwellings rising through the entire mantle andbeing deflected into a thin ‘pancake’ beneath the overridingplate1. Such an upwelling dynamically generates an elongated,parabolically shaped swelling of seafloor topography2–4. Associ-ated ‘hotspot’ volcanism is localized and stationary, thereforeentailing an age-progressive island chain. This classical theoryhas indeed successfully predicted first-order observations at manyhotspot chains, Hawaii being among the most prominent andbest studied examples.

A set of enigmatic observations ofHawaiian volcanism, however,are not explained by the above idealized description. First, averagevolcanic flux as documented along the Hawaii–Emperor chainhas varied by a factor of >2 over typical timescales of ∼15Myr(refs 7,8). Mechanisms involving intrinsic variations in buoyancyflux or tilt of the rising plume stem have been proposed as anexplanation5–8, but not yet tested. Second, the origin of the bilateralasymmetry in lava geochemistry, as documented by compositionaldistinctions between the southern (‘Loa’) and northern (‘Kea’)volcano sub-chains (Fig. 1a), is not well understood. One set

1School of Ocean and Earth Sciences and Technology, University of Hawaii, Honolulu, Hawaii 96822, USA, 2Institute of Geophysics, ETH Zürich, 8092Zürich, Switzerland, 3Department of Earth Sciences, Durham University, Durham, DH1 3LE, UK. *e-mail: [email protected].

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Figure 1 | Overview and concept. a, Geographic overview and bathymetryof the Hawaiian Islands. Shield volcanoes are marked with triangles andarch volcanic fields with strong acoustic reflectivity19,20 are shaded. Theshallow seafloor surrounding the islands is referred to as the Hawaiian arch(black dashed). b, Conceptual illustration of small-scale convection (SSC)interacting with the Hawaiian plume. Undulations on the base of thelithosphere (washboard pattern; dashed yellow line) were created by SSCin the ambient mantle.

of interpretations invokes some form of compositional zoningin the upwelling plume stem9–11. Other studies emphasize thatif the mantle is a fine-scale mixture of different lithologicalcomponents, spatial variations in pressure and temperature overthe hotspot melting zone can create geographical patterns ofmagma composition that differ from those for an isochemicalsource12. Finally, widespread secondary volcanism17–20 occurring

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Figure 2 | Visualization of the central part of the reference model. a, Horizontal (at 130 km depth) and vertical cross-sections are coloured by potentialtemperature Tpot. The hotspot and secondary melting zones are in black. Isotherms of 1,550 and 1,620 ◦C are white. Black arrows show the direction andstrength of ambient-mantle SSC 800 km upstream of the plume. See also Supplementary Movie. b, Vertical cross-section of Tpot and viscosity η throughthe upwelling plume oriented perpendicular to plate-motion with contours denoting log10(η). Upper panel shows a blow-up of the yellow-shaded area.Light blue arrows show the schematic flow field indicating that the plume pancake spreads asymmetrically as guided by undulations inlithospheric thickness.

well away from the Hawaiian hotspot (Fig. 1a) has so far beenattributed to lateral spreading of the pancake3 or flexural uplift18,but even a combination of both mechanisms cannot account forthe large volumes of secondary volcanism as observed on thenorth arch19, and Kauai17 (cf. Supplementary Information SC).We use three-dimensional numerical simulations to show that theinteraction of small-scale sublithospheric convection (SSC) withthe Hawaiian plume (Fig. 1b)—a combination of two well-studiedgeodynamic phenomena2–5,21–23—can explain many key aspects ofthese three observations together.

Compared to previous geodynamic modelling studies3–5,24 ofmantle plumes, this study involves numerical simulations ofsignificantly larger model boxes and a strongly temperature-dependent mantle rheology, advances that for the first time enablesimulations of vigorous SSC both inside and outside the plumepancake. The effective ambientmantle viscosity, excess temperatureand radius of the plume are fixed at 1.8 × 1019 Pa s, 300Kand 68 km, respectively (Supplementary Table S1; for methodssee Supplementary Information SA). These parameters result ina flux of upwelling buoyant plume material of ∼4,000 kg s−1and a predicted seafloor swell of width ∼1,300 and height∼1.2 km. A volcanic flux of ∼150,000 km3 Myr−1 predominantly(>99%) occurs at the hotspot centre of width ∼110 km andlength ∼125 km. Thus, the island-building shield stage volcanismlasts ∼1.5Myr on the plate overriding the hotspot. We assumethe mantle source to be a fine-scale mixture of 80% dryperidotite, 15% hydrous peridotite, and 5% pyroxenite. Each ofthese lithologies has a distinct melting behaviour with hydrousperidotite and pyroxenite having the deepest solidi, and pyroxenitemelting much more extensively than peridotite. Thus, pyroxenitemelting contributes >50% to shield stage volcanism, whereasthe much more voluminous dry-peridotite matrix contributesonly ∼38%. These predictions are robust and fall close to theuncertainty of constraints for Hawaii as based on published dataand/or models7,8,25–27.

The numerical models predict two types of SSC to occur(Fig. 2a). In the ambientmantle, SSC self-organizes beneathmatureoceanic lithosphere as convection rolls aligned with plate motionand spaced ∼300 km. This form of SSC is thought to be theprimary mechanism for limiting the maximum thickness of matureoceanic lithosphere globally, thus slowing the subsidence of seafloor

of ages ≥70Myr (ref. 22). SSC is therefore likely to be alreadywell established beneath the ∼90Myr-old Hawaiian lithosphere.A different form of SSC develops inside the pancake of hotplume material ponding beneath the lithosphere (cf. ref. 24). This‘plume-pancake SSC’ is more vigorous, of smaller scale, and formsa more variable pattern owing to lower viscosities in the hotpancake (Supplementary Fig. S1). Its occurrence does not requireambient-mantle SSC, but its pattern and strength in detail aresensitive to the style of the latter (Supplementary InformationSB, Figs S2 and S3).

SSC in the ambient mantle upstream of the plume createssublithospheric topography and hence affects plume-lithosphereinteraction. It shapes a ‘washboard’ pattern into the base of thelithosphere (of wavelength ∼300 km), which is thinned aboveSSC upwellings and thickened above downwellings (Fig. 2b). TheHawaiian plume impacts this pre-shaped lithosphere, and in allcases with the impact site not precisely beneath a minimumin lithospheric thickness, the pancake spreads asymmetrically:the buoyant and hot core of the ponding plume is deflectedtowards the nearest minimum in lithospheric thickness, resultingin slightly higher temperatures within one flank of the pancake—hereinafter referred to as the ‘Kea’ flank—compared with theopposite ‘Loa’ flank (Fig. 2b).

With the compositionally heterogeneous mantle source mod-elled, such asymmetry in mantle flow gives rise to asymmetry in thetype of material that melts, with important implications for magmageochemistry. The hotter Kea half of themain hotspot melting zoneexperiences higher maximum and mean extents12,28 of peridotitemelting than the less hot Loa half, whereas pyroxenite melts 100%on both halves. Such a situation implies higher volcanic flux anda lower fractional contribution of pyroxenite-derived melts XPX onthe Kea side than on the Loa side. Figure 3 shows for our referencemodel that shield stage volcanic flux totals 86,800 km3 Myr−1 withXPX≈49% on the Kea side, whereas it totals 65,700 km3 Myr−1 withXPX≈53%on the Loa side. These predictions are consistent with thegeological record of average volcanic flux along the Hawaiian Keaand Loa trends (94,400 and 75,400 km3 Myr−1, respectively26), aswell as with evidence for mafic materials being an important sourcecomponent of Hawaiian hotspot volcanism, and even more so inthe Kea than in the Loa volcanoes17,27. In our models, the differencein XPX between the Kea and Loa sides arises purely from interaction

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NATURE GEOSCIENCE DOI: 10.1038/NGEO1187 LETTERS

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Figure 3 | Source and volume flux of surface volcanism. a, Colours give thepyroxenite contribution to volcanism (grey is no volcanism), and contoursdenote the rate of volcanism per area of seafloor. From outside to inside,dashed contours are at 0.01, 0.1, 1, and 10 km3 km−2 Myr−1. The solidcontours follow the same log scale shifted by 100.5. Pyroxenite contributionXPX in the centre of the hotspot is∼50%, but is slightly higher and loweralong the Kea and Loa trends, respectively. This distinction persists throughthe postshield stage, as does the geochemical distinction between the twotrends10. Rejuvenated and arch volcanism shows relatively low (∼40%)and high (>97%, not shown) XPX, respectively. b, Dashed lines denotevolcanic fluxes (km3 Myr−1 per km of distance along the chain) for the Keatrend (red), the Loa trend (blue), and the total of both trends (black). Theassumed feeding zones for the two trends are denoted light grey in a. Solidlines show the pyroxenite contribution for the same colour code, andelucidate the asymmetry of shield and postshield volcanism arising fromthe distribution shown in the map view in a. The bold black numberindicates the total flux of hotspot volcanism in (km3 Myr−1). Green andgrey shadings denote the predicted durations of the major phases ofHawaiian volcanism (as defined by volume flux).

of the plume with SSC, and a source with fine-scale compositionalheterogeneity; it is independent of any large-scale compositionalzoning in the plume conduit, as has been previously implied9–11.

Moreover, the total volcanic flux at Hawaii is sensitive to thepattern and strength of ambient-mantle SSC. Model calculationsshow thatmodest (∼100 km) changes in the relative position of SSCand the plume alone can alter volcanic flux by >25% (numbers inFig. 3b, Supplementary Information S4 and SB). The main reasonis that the spreading of and convection within the pancake aresensitive to lithospheric thickness undulations (washboard) createdby ambient-mantle SSC. In nature, fracture zones, other sourcesof mantle density heterogeneity, and changes in plate motion canalter the position as well as the amplitude of the lithosphericthickness undulations23, and hence influence magma production.Plume interaction with these undulations is a mechanism withinthe shallow, rather than deep mantle for creating some of the largevariations inHawaiian volcanic flux seen in the geologic record7,8.

SSC in the plume-pancake gives rise to decompression meltingwell awayfrom the hotspot centre, thus explaining the occurrenceof widespread secondary volcanism (Fig. 3a). At the distal flanks ofthe pancake, SSC occurs as short rolls perpendicular to platemotion(Supplementary Information SB and Fig. S1); associated meltingcan explain the expansive North Arch Volcanic Fields19 (cf. Fig. 1a).Directly upstream of the hotspot melting zone, a localized SSC up-welling is predicted to support arch volcanism south of the islands20.Moreover, downstream of the main melting zone, a prominentupwelling erodes the lithosphere (by 10–15 km) and inducesdecompression melting, which would appear as the rejuvenatedvolcanic stage13,17,18. The most productive part of this secondarymelting zone spans an along-chain distance of ∼300 km, and ispreceded by a pronouncedminimum inmelting, thereby producinga near ‘gap’ in magmatism spanning ∼80 km. These length-scalesagree well with observations17,18. The fluxes of the predicted archand rejuvenated volcanism total 0.36–0.6% and 0.08–0.4% ofthe hotspot volcanic flux, respectively (i.e. ∼0.5–1% combined);therefore our model has no difficulty in explaining voluminoussecondary volcanism on the north arch19 and Kauai17 (details inSupplementary Information SB and SC). The precise fluxes ofsecondary volcanism, however, are sensitive to the rheologicaland melt extraction parameters applied (Supplementary Fig. S7).Finally, those of arch volcanism critically depend on the action ofambient-mantle SSC to thin the lithosphere. A separate calculationidentical to the reference case, but without ambient-mantle SSC,predicts no arch volcanism at all (Supplementary Fig. S3).

Two distinct sources are predicted to feed secondary volcanism.The first involves relatively shallow melting (125–135 km) ofharzburgitic peridotite; it accounts for ∼60% of the rejuvenatedvolcanism but a negligible amount to arch volcanism (cf. Fig. 3a)and therefore should influence the major-element signature ofrejuvenated lavas only (cf. ref. 17). The second source is pyroxenite:a deepermelting (135–150 km) fertile lithology, which can be tracedback to the periphery of the plume stem. In contrast to the harzbur-gitic peridotite, this peripheral fertile source bypassed the mainhotspot melting zone to avoid depletion and retain incompatibleelements. Therefore, it is expected to control incompatible-elementratios andmany isotope systems of both arch and rejuvenated lavas.

To satisfy isotopic evidence for distinct source materials inshield and secondary volcanism13–16, the centre (which feeds theshields) and periphery of the plume stem would have to differcompositionally. As previously suggested, the peripheral sourcemay be isotopically depleted ambient-mantle material as entrainedby the mantle plume9,15. Trace-element signatures of secondaryvolcanism require that such peripheral material was metasomatizedby incipient melts from the plume centre14,16, whereas Os-isotopesignatures point to pyroxenitic ambient-mantle heterogeneity13.Both these scenarios emphasize the importance of peripheral fertilematerial that starts melting deeper than dry peridotite (perhaps butnot necessarily pyroxenite), and such behaviour is key to our modelpredictions of secondary volcanism.

Geophysical evidence lends additional credibility to our models.Recent high-resolution seismic tomography reveals a broad low-velocity body in the upper mantle beneath the Hawaiian swellwith pronounced small-scale variability29,30. These variationsare asymmetric about the islands29,30, an observation that—incombination with asymmetric swell topography25 (Fig. 1a)—isconsistent with higher densities in the mantle northeast thansouthwest of Hawaii. Such constraints are well explained by thepredicted effects of SSC on the Hawaiian plume—particularly byasymmetric plume-pancake spreading, and SSC in the pancake.

This study elucidates that shallow processes such as SSC affectplume-lithosphere interaction to induce temporal, spatial andgeochemical variability in hotspot volcanism. SSC may not justaffect the Hawaiian plume and associated volcanism, but also

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other plumes impacting mature lithosphere or spreading withinlow-viscosity asthenosphere (for example, in the South Pacific),where SSC is thought to develop beneath younger seafloor thanelsewhere21,23. Future efforts are therefore needed to distinguishbetween shallow versus deep controls on hotspot magmatism,which is important for understanding patterns of heterogeneity andconvection in the mantle.

Received 4 December 2010; accepted 20May 2011;published online 26 June 2011

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8. Vidal, V. & Bonneville, A. Variations of the Hawaiian hot spot activityrevealed by variations in the magma production rate. J. Geophys. Res. 109,B03104 (2004).

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10. Hanano, D., Weis, D., Scoates, J. S., Aciego, S. & DePaolo, D. J. Horizontaland vertical zoning of heterogeneities in the Hawaiian mantle plume from thegeochemistry of consecutive postshield volcano pairs: Kohala-Mahukona andMauna Kea-Hualalai. Geochem. Geophys. Geosyst. 11, Q01004 (2010).

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12. Bianco, T. A., Ito, G., van Hunen, J., Ballmer, M. D. & Mahoney, J. J.Geochemical variation at the Hawaiian hot spot caused by upper mantledynamics and melting of a heterogeneous plume. Geochem. Geophys. Geosyst.9, Q11003 (2008).

13. Lassiter, J. C., Hauri, E. H., Reiners, P. W. & Garcia, M. O. Generation ofHawaiian post-erosional lavas by melting of a mixed lherzolite/pyroxenitesource. Earth Planet. Sci. Lett. 178, 269–284 (2000).

14. Yang, H. J., Frey, F. A. & Clague, D. A. Constraints on the source componentsof lavas forming the Hawaiian North Arch and Honolulu volcanics. J. Petrol.44, 603–627 (2003).

15. Fekiacova, Z., Abouchami, W., Galer, S. J. G., Garcia, M. O. & Hofmann, A. W.Origin and temporal evolution of Ko’olau Volcano, Hawai’i: Inferences fromisotope data on the Ko’olau Scientific Drilling Project (KSDP), the HonoluluVolcanics and ODP Site 843. Earth Planet. Sci. Lett. 261, 65–83 (2007).

16. Dixon, J., Clague, D. A., Cousens, B., Monsalve, M. L. & Uhl, J. Carbonatiteand silicate melt metasomatism of the mantle surrounding the Hawaiianplume: Evidence from volatiles, trace elements, and radiogenic isotopes inrejuvenated-stage lavas from Niihau, Hawaii. Geochem. Geophys. Geosyst. 9,Q09005 (2008).

17. Garcia,M. O. et al. Petrology, Geochemistry andGeochronology of Kaua’i Lavasover 4 center dot 5 Myr: Implications for the Origin of Rejuvenated volcanismand the evolution of the Hawaiian plume. J. Petrol. 51, 1507–1540 (2010).

18. Bianco, T. A., Ito, G., Becker, J. M. & Garcia, M. O. Secondary Hawaiianvolcanism formed by flexural arch decompression. Geochem. Geophys. Geosyst.6, Q08009 (2005).

19. Clague, D. A., Uto, K., Satake, K., Davis, A. S. & Eruption, in HawaiianVolcanoes: Deep Underwater Perspective Vol. 128 (ed. Takahashi, E.) 65–84(Geophys. Monogr. Series, AGU, 2002).

20. Lipman, P. W., Clague, D. A., Moore, J. G. & Holcomb, R. T. South ArchVolcanic Field—newly identified young lava flows on the sea-floor south of theHawaiian Ridge. Geology 17, 611–614 (1989).

21. Ballmer, M. D., Ito, G., van Hunen, J. & Tackley, P. J. Small-scalesublithospheric convection reconciles geochemistry and geochronologyof ‘Superplume’ volcanism in the western and south Pacific. Earth Planet.Sci. Lett. 290, 224–232 (2010).

22. van Hunen, J., Zhong, S. J., Shapiro, N. M. & Ritzwoller, M. H. New evidencefor dislocation creep from 3-D geodynamic modeling of the Pacific uppermantle structure. Earth Planet. Sci. Lett. 238, 146–155 (2005).

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AcknowledgementsM.D.B. has been supported by SNF-grants PBEZP2-127810 and 20020-119922/1, andG.I by grants NSF-0510482 and NSF-0855814. We are grateful to C. J. Wolfe andM. O. Garcia for input on earlier versions of the manuscript. Calculations were done atthe Hawaii Open Supercomputing Center (HOSC).

Author contributionsM.D.B. carried out the numerical experiments. M.D.B. and G.I. led the interpretation ofmodel results and writing, followed by J.v.H. and P.J.T.

Additional informationThe authors declare no competing financial interests. Supplementary informationaccompanies this paper on www.nature.com/naturegeoscience. Reprints and permissionsinformation is available online at http://www.nature.com/reprints. Correspondence andrequests for materials should be addressed to M.D.B.

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Spatial and temporal variability in Hawaiian hotspot volcanism induced by small-scale convection

Maxim D. Ballmer1,2,*, Garrett Ito1, Jeroen van Hunen3, and Paul J. Tackley2

(1) School of Ocean and Earth Sciences and Technology, University of Hawaii, Honolulu, USA (2) Institute of Geophysics, ETH Zürich, Zürich, Switzerland (3) Department of Earth Sciences, Durham University, Durham, UK (*) corresponding author: [email protected]

Supplemental Information

SA. MethodsIn order to discretize and solve the equations of conservation of mass, momentum and

energy, we use an extended version of the finite element code Citcom31,32. The most important extensions include formulations for compositional rheology (Eq. S3), and compositional buoyancy (Eq. S4), both being sensitive to partial melting processes. Related time-dependent feedback mechanisms between consumption of latent heat of fusion L, buoyancy, partial melting and rheology require application of the extended Boussinesq approximation33 and of a 2nd-order Runge-Kutta time-integration scheme34,35. Details of the numerical method used are described elsewhere21,35.

The Cartesian model box spans dimensions 4818x3300x660 km (Fig. 1) with 672x384x96 rectangular elements, and element sizes ranging from 8.4x9.9x6.6 km to 4.6x4.3x3.4 km. An imposed, constant horizontal motion on the top boundary simulates 80 km/Myr of Pacific plate-motion36. In order to accommodate this motion, one vertical side of the box is free to inflow and the opposite side to outflow. The other sides are closed. The bottom is also closed except for a small circular region of radius of 4rP (rp = 68 km) wide enough to allow a mantle plume to rise into the box, and centered 3135 km downstream from inflow boundary. At the same location, a Gaussian thermal anomaly of amplitude TP and of half-width rP is imposed to supply excess temperature to the plume4. Otherwise, temperatures at the top and bottom remain fixed at 0 °C and the reference temperature Tm = 1350 °C, respectively. On the inflow boundary, temperatures are maintained based on a simple cooling profile for 50 Myr-old lithosphere plus an adiabatic gradient γ = 0.3 K/km and a random thermal noise of ±5°C.

In order to simulate melting of a heterogeneous mantle, we apply the marble cake mantle hypothesis28,37,38. Accordingly, we assume that the mantle is compositionally heterogeneous on a scale smaller than the finite element mesh. We take a marble cake recipe of bimineralic silica-deficient pyroxenite (PX; cf. ref. 27) making up ΦPX = 5% of

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the mass of the mantle39, and of two flavors of peridotite: a depleted component (DC) for dry peridotite and a hydrous component (HC) for peridotite with high volatile content (we model a bulk water content cO = 0.03 wt.-%, and no CO2 content for simplicity) with ΦDC

= 80% and ΦHC = 15%. We neglect any larger-scale heterogeneity, except for that PX is restricted to the plume. The radius of the compositional plume is fixed at rP, outside of which ΦPX is initially 0%. Our model results are however independent of this restriction.

Each of these lithologies has a distinct melting behavior. HC and PX start melting significantly deeper (or at lower temperatures) than DC with PX clearly having the highest melt productivity. In order to simulate melting of PX and DC, we use the parametrizations of Pertermann and Hirschmann40, and Hirschmann et al.41, respectively. We apply the dynamic melting approximation for each lithology individually: melt accumulates in small pores in any lithology until a critical porosity φC is reached, beyond which melt is assumed to be extracted instantaneously to maintain the porosity at φC in that lithology42. In most of our cases we take φC = 1%, but we also vary φC between 0.5% and 0.9% (cf. Suppl. Inf. SC). For HC, we reduce melting temperatures relative to DC by ∆Tsol according to the hydrous peridotite melting parametrization of Katz et al.43:

0.75

2

HCSol

H O

c∆T K

D

=

(S1)

with the bulk distribution coefficient for water DH2O = 0.01, and K = -43 wt.-%-0.75K. When the depletion (i.e., extent of melting) in HC, FHC, exceeds φC, the water content in the HC solid residue cHC is efficiently reduced by melt extraction according to Zou44:

( )

( )

2

1 11

2

2

11

1

c c H Oφ φ DHC c

H Oc

HC OH O HC

F φDφ

c cF D F

−

+ − −−

− =+ −

(S2)

Consequently, the altered water content of the solid affects the solidus (cf. equation S1). As olivines in DC and HC dominate the rheology of the lithological assemblage

(since ΦDC + ΦHC = 95%), we apply an experimentally calibrated olivine rheology45-47. An activation energy of E* = 300 kJ/mol45 leads to strong temperature dependence of viscosity. We also include compositional effects such as melt lubrication48, and more importantly, stiffening due to dehydration of the solid with ongoing depletion in HC46:

( )( )

( )* * *

0

0

expECΦ

dry mm DC DC HC HC

mHC dry HC

ξ c c E ρ gzV Eη η ζ Φ φ Φ φ

RT RTξ c c c c

− + = − − + − + −

(S3)

Table S1: Notations. parameter description value or range; unit cdry water concentration in the solid HC, below which

hydrous olivine behaves like dry olivine 6 wt.-ppm

cHC water concentration in the solid HC [wt.-ppm] cO initial water concentration in the solid HC 300 wt.-ppm E* activation energy 3·105 J/mol FDC depletion in DC - FHC depletion in HC - g gravity acceleration 9.8 kg/s2

L latent heat of fusion 5.6·105 J/kg p lithostatic pressure [Pa] rP radius of the plume 68 km T temperature [K] Tm mantle potential temperature 1350 °C TP plume potential temperature 1650 °C Tsol dry solidus temperature [K] V* activation volume 5·10-6 m3/mol α thermal expansivity 3·10-5 K-1

γ adiabatic gradient 0.3 K/km ∆Tsol hydrous solidus reduction [K] ∆ρF density anomaly related to 100% depletion in peridotite -165 kg/m3

∆ρφ density anomaly related to 100% melting -500 kg/m3

ζ melt lubrication exponent 40 η viscosity [Pa·s] ηeff effective mantle viscosity 1.8·1019 Pa·s ξ dehydration stiffening coefficient 310.6383 ρ0 reference mantle density 3300 kg/m3

φC critical porosity 0.5-1.0 % φDC, φHC, φPX porosities in DC, HC and PX (respectively) - ФDC mass fraction of DC 80% ФHC mass fraction of HC 15% ФPX initial mass fraction of PX 5%

with R, η, ηm, φDC, φHC, ξ, ζ, V*, ρm, g, z, T, Tm, and cdry the ideal gas constant, viscosity, reference mantle viscosity, porosity in DC, porosity in HC, dehydration stiffening coefficient, melt lubrication coefficient, activation volume, reference mantle density, gravity acceleration, depth, temperature, and the water content below which hydrous olivine behaves like dry olivine, respectively (see Table S1 for values). The effective viscosity ηeff ≡ 0.00155ηm corresponds to the minimum viscosity in the upper mantle column at the onset of small-scale convection (SSC), and is a better representation for the rheology of the ambient mantle than ηm. The dehydration stiffening coefficient ξ is scaled such that dehydrating HC from cHC = 100 ppm to cHC = cdry increases the viscosity of HC by a factor of 100 (ref. 47). Substituting equation (S2) into equation (S3) elucidates that rheology is dependent on variables T, z, FHC, and φHC only.



the mass of the mantle39, and of two flavors of peridotite: a depleted component (DC) for dry peridotite and a hydrous component (HC) for peridotite with high volatile content (we model a bulk water content cO = 0.03 wt.-%, and no CO2 content for simplicity) with ΦDC

= 80% and ΦHC = 15%. We neglect any larger-scale heterogeneity, except for that PX is restricted to the plume. The radius of the compositional plume is fixed at rP, outside of which ΦPX is initially 0%. Our model results are however independent of this restriction.

Each of these lithologies has a distinct melting behavior. HC and PX start melting significantly deeper (or at lower temperatures) than DC with PX clearly having the highest melt productivity. In order to simulate melting of PX and DC, we use the parametrizations of Pertermann and Hirschmann40, and Hirschmann et al.41, respectively. We apply the dynamic melting approximation for each lithology individually: melt accumulates in small pores in any lithology until a critical porosity φC is reached, beyond which melt is assumed to be extracted instantaneously to maintain the porosity at φC in that lithology42. In most of our cases we take φC = 1%, but we also vary φC between 0.5% and 0.9% (cf. Suppl. Inf. SC). For HC, we reduce melting temperatures relative to DC by ∆Tsol according to the hydrous peridotite melting parametrization of Katz et al.43:

0.75

2

HCSol

H O

c∆T K

D

=

(S1)

with the bulk distribution coefficient for water DH2O = 0.01, and K = -43 wt.-%-0.75K. When the depletion (i.e., extent of melting) in HC, FHC, exceeds φC, the water content in the HC solid residue cHC is efficiently reduced by melt extraction according to Zou44:

( )

( )

2

1 11

2

2

11

1

c c H Oφ φ DHC c

H Oc

HC OH O HC

F φDφ

c cF D F

−

+ − −−

− =+ −

(S2)

Consequently, the altered water content of the solid affects the solidus (cf. equation S1). As olivines in DC and HC dominate the rheology of the lithological assemblage

(since ΦDC + ΦHC = 95%), we apply an experimentally calibrated olivine rheology45-47. An activation energy of E* = 300 kJ/mol45 leads to strong temperature dependence of viscosity. We also include compositional effects such as melt lubrication48, and more importantly, stiffening due to dehydration of the solid with ongoing depletion in HC46:

( )( )

( )* * *

0

0

expECΦ

dry mm DC DC HC HC

mHC dry HC

ξ c c E ρ gzV Eη η ζ Φ φ Φ φ

RT RTξ c c c c

− + = − − + − + −

(S3)

Table S1: Notations. parameter description value or range; unit cdry water concentration in the solid HC, below which

hydrous olivine behaves like dry olivine 6 wt.-ppm

cHC water concentration in the solid HC [wt.-ppm] cO initial water concentration in the solid HC 300 wt.-ppm E* activation energy 3·105 J/mol FDC depletion in DC - FHC depletion in HC - g gravity acceleration 9.8 kg/s2

L latent heat of fusion 5.6·105 J/kg p lithostatic pressure [Pa] rP radius of the plume 68 km T temperature [K] Tm mantle potential temperature 1350 °C TP plume potential temperature 1650 °C Tsol dry solidus temperature [K] V* activation volume 5·10-6 m3/mol α thermal expansivity 3·10-5 K-1

γ adiabatic gradient 0.3 K/km ∆Tsol hydrous solidus reduction [K] ∆ρF density anomaly related to 100% depletion in peridotite -165 kg/m3

∆ρφ density anomaly related to 100% melting -500 kg/m3

ζ melt lubrication exponent 40 η viscosity [Pa·s] ηeff effective mantle viscosity 1.8·1019 Pa·s ξ dehydration stiffening coefficient 310.6383 ρ0 reference mantle density 3300 kg/m3

φC critical porosity 0.5-1.0 % φDC, φHC, φPX porosities in DC, HC and PX (respectively) - ФDC mass fraction of DC 80% ФHC mass fraction of HC 15% ФPX initial mass fraction of PX 5%

with R, η, ηm, φDC, φHC, ξ, ζ, V*, ρm, g, z, T, Tm, and cdry the ideal gas constant, viscosity, reference mantle viscosity, porosity in DC, porosity in HC, dehydration stiffening coefficient, melt lubrication coefficient, activation volume, reference mantle density, gravity acceleration, depth, temperature, and the water content below which hydrous olivine behaves like dry olivine, respectively (see Table S1 for values). The effective viscosity ηeff ≡ 0.00155ηm corresponds to the minimum viscosity in the upper mantle column at the onset of small-scale convection (SSC), and is a better representation for the rheology of the ambient mantle than ηm. The dehydration stiffening coefficient ξ is scaled such that dehydrating HC from cHC = 100 ppm to cHC = cdry increases the viscosity of HC by a factor of 100 (ref. 47). Substituting equation (S2) into equation (S3) elucidates that rheology is dependent on variables T, z, FHC, and φHC only.



Lateral density variations, which drive convection, depend on temperature, bulk porosity φ (with φ = φDCΦDC + φHCΦHC + φPXΦPX) and depletion in peridotite:

( )( )m m m φ F DC DC HC HCρ ρ αρ T T ∆ρ φ ∆ρ Φ F Φ F− = − + + + (S4)

with ∆ρφ, ∆ρF, α, ρ, FDC, and φPX the density changes with melt retention and peridotite depletion, thermal expansivity, density, depletion in DC, and porosity in PX, respectively. We ignore the small density variations related to the consumption of PX by melting, since the density of pyroxenite is close to that of the mantle, and since ΦPX is just 5%.

SB. Controls on plume-pancake SSC and related effects on volcanismAs opposed to SSC in the ambient mantle self-organizing as regularly spaced, linear

rolls parallel to plate motion, SSC in the hot plume pancake is more complex in flow geometries (cf. ref. 24). In both places, SSC rolls are aligned according to the differential motion between the low-viscosity mantle and the overriding plate49. Whereas this differential motion is dominated by the plate motion in the ambient mantle, it is strongly affected by the gravitational spreading of the plume in the pancake. Figure S1 shows the horizontal flow at a depth of 140 km minus 80 km/Myr of plate motion. The overall differential flow radiates outward away from the plume stem. Directly downstream of the plume stem, gravitational spreading drives flow that is parallel to but faster than plate motion; far away from the axis of the hypothetical hotspot track, gravitational spreading results in a strong component of flow perpendicular to plate motion. Accordingly, SSC rolls tend to align parallel to plate motion along the central axis of the plume pancake, and perpendicular to plate motion on the flanks of the pancake (Fig. S1).

Plume-pancake SSC controls locations of decompression melting and related secondary volcanism. Stable upwellings directly downstream of the hotspot oriented parallel to plate motion give rise to rejuvenated stage volcanism. Transient upwellings (cf. movie supplement) on the distal flanks of the pancake (oriented perpendicular to plate motion) spawn arch volcanism ~300 km away from the central axis of the hypothetical island chain. Another type of arch volcanism is predicted to emerge ~250 km upstream of the hotspot above a localized upwelling of plume-pancake SSC. This upwelling is triggered by a nearby downwelling of ambient-mantle SSC that carves into the plume pancake to focus the otherwise diffuse flow (Fig. S2).

The predicted sites and volumes agree well with the observed geographic distributions of rejuvenated stage volcanism, and arch volcanism around Hawaii. In particular, our models display a near-gap between the hotspot and the rejuvenated melting zones of ~80 km (cf. Fig. 3b) that addresses the observed gap of 1-2 Myrs17,18,50 between the shield and rejuvenated phases of Hawaiian volcanism. In addition, a length-scale of

~300 km for the rejuvenated melting zone can readily explain occurrences of coeval rejuvenated volcanism on Niihau and Maui16-18,50. In terms of arch volcanism, the models predict volcanic fluxes as high as ~1000 km3/Myr occurring ~300 km away from the central axis of the island chain, fluxes and locations that are consistent with observations for the Hawaiian North Arch Volcanic Field19 (cf. Fig. 1a). Predicted arch volcanism occurring 200-300 km upstream of the hotspot displays a smaller volume flux (~25 km3/Myr) and can thus account for the South Arch Volcanic Field20. The precise patterns of secondary volcanism however may be influenced by various mechanisms not modelled. These may include a possible recent change in Pacific plate motion51, associated complications in the pattern of SSC52, localized intermediate-scale fertile anomalies in the mantle source10, and lateral flow of magma.

The importance of ambient-mantle SSC for the symmetry of flow and temperature in the plume pancake as well as for the occurrence of secondary volcanism is explored by comparing the predictions of the reference case (Fig. S2a) with a case that has ambient-mantle SSC artificially switched off (Fig. S3). The latter case is governed by the same model parameters as the first, and differs only in the length of the box in the direction of plate motion, which is just 2376 km, instead of 4818 km for the first. Such a short box does not allow enough time for ambient-mantle SSC to organize upstream of the plume. The large-scale pattern of temperature and flow in the plume pancake are similar for both the reference case (Fig. S2a) and the short-box case (Fig. S3a), independent of the occurrence of ambient-mantle SSC. However, the pancake is much more symmetric in the short-box case because there are no pre-existing undulations in lithospheric thickness (“washboard”-pattern) to trigger asymmetric flow. Likewise, the pyroxenite contribution in hotspot volcanism (Fig. S3b) and the pattern of plume-pancake SSC are almost completely symmetric. Also, without the effects of ambient-mantle SSC to shape and remove parts of the base of the incoming lithosphere in the short-box case, plume-pancake SSC does not produce arch volcanism (Fig. S3). Along these lines, the occurrence of ambient-mantle SSC is critical for widespread secondary volcanism and asymmetry of plume-lithosphere interaction.

For the more realistic large-box models, the pattern of ambient-mantle SSC relative to the location of the plume controls plume-pancake SSC and volcanism. The three cases shown in Figures S2b-d are similar to the reference case shown in Figure S2a. They are governed by the same parameters, and only differ in the position of the hot patch at the base of the model box, which is shifted perpendicular to plate motion in 50 km increments from case to case. Such a setup simulates distinct positions of the plume relative to the pattern of ambient-mantle SSC, since the latter is similar for all cases (being influenced by the model boundaries with SSC downwellings typically organizing at the sides of the box). Figure S2 highlights that the temperature distribution and pattern of convection in the plume pancake are sensitive to the position of the plume relative to



the pattern of SSC. Related effects on magma generation further imply that geographical distributions and geochemical signatures of volcanism are affected by shifts in the position of the plume relative to ambient-mantle SSC. Figures S4-S6 show that such shifts indeed alter rejuvenated volcanic flux (Figs. 3b, S4), average pyroxenite contribution and duration of rejuvenated stage volcanism (Figs. 3b, S4, S6), volcanic flux and geographical distribution of arch volcanism (Figs. 3a, S5), geochemical contrast between the Kea and Loa trends (solid lines in Figs. 3b, S6), and most notably hotspot volcanic flux (numbers in Figs. 3b and S4). Top-down driven ambient-mantle SSC induces variability of hotspot volcanic flux through the effects of lithospheric thickness undulations (“washboard”) on plume-lithosphere interaction. Both hotspot volcanic flux and the extent of the Kea/Loa geochemical asymmetry are influenced by the position of the plume relative to the washboard (Figs. S4, S6). Thus, they are sensitive to a change in the pattern of ambient-mantle SSC. We speculate that a change in the pattern of SSC upstream of the Hawaiian hotspot as induced by the Molokai Fracture Zone23,53 or by a recent change in plate motion51,52 contributed to the sudden appearance of the geochemically asymmetric Kea and Loa sub-chains11,54 at ~2 Ma and a coeval boost in Hawaiian hotspot volcanism7,8,26.

SC. Controls of melt extraction on secondary volcanismFigure S7 shows that the predicted total volume of rejuvenated stage volcanism and

its duration (or distance, over which it simultaneously occurs) are sensitive to the critical porosity φC. For instance, rejuvenated volcanic flux triples when φC increases from just 0.8% to 1%. Whereas higher φC reduces the fraction of extracted melt in magma produced, the dominating effects in boosting magma production are to increase the mantle buoyancy as more melt is retained, and to keep viscosity low as more water remains in the mantle (cf. equation (S2) and ref. 35). These important effects boost decompression melting by fueling plume-pancake SSC and related erosion at the base of the lithosphere.

Our model predictions can be tested with the geological record of the rejuvenated “Koloa volcanics” on Kauai. Alternative models for the origin of rejuvenated volcanism include decompression melting due to lithospheric flexure18, and due to lateral spreading of the plume pancake3. Given that widespread rejuvenated volcanism also occurred on the seafloor around Kauai55, we neglect major melt focusing towards the island of Kauai during extraction of rejuvenated melts. With this assumption, the lithospheric flexure and pancake spreading models can just account for 6 km³ and 8 km³ of rejuvenated volcanism on Kauai, respectively (cf. refs. 3, 18). Therefore, even a combination of both mechanisms is insufficient to explain the large observed volumes of ~60 km³ of Koloa volcanics17. Our models instead predict higher volumes of about 210 km³, 170 km³,

135 km³, 90 km³ and 55 km³ over the area of Kauai for critical porosities of 1%, 0.9%, 0.8%, 0.75% and 0.7%, respectively. Depending on the actual ratio of intrusive versus extrusive rejuvenated volcanism, our model predictions for φC ≥ 0.75% thus have no difficulty in explaining the large volume of Koloa volcanics.

For the same reasons (above) increasing φC boosts rejuvenated volcanism, it also tends to boost volcanic flux of arch volcanism. By fueling SSC on the flanks of the pancake, increasing φC from 0.5% to 1% boosts arch volcanic flux from ~550 km/Myrs to ~1000 km/Myrs. To a greater extent, however, SSC on the flanks of the pancake and related arch volcanism are expected to be sensitive to rheological parameters (cf. ref. 24).


SUPPLEMENTARY INFORMATION DOI: 10.1038/NGEO1187BALLMER ET AL. (2011): SPATIO-TEMPORAL VARIABILITY IN HAWAIIAN VOLCANISM INDUCED BY SSC

Figure S1. Differential horizontal flow field between the plume pancake and the plate for the reference case. Arrows denote direction and color denote the amplitude of differential flow as computed by subtracting of plate motion (i.e. 80 km/Myr from left to right) from horizontal flow at 140 km. Arrows pointing to the left/right indicate horizontal flow that is slower/faster than plate motion. The shear associated with this differential motion appears to influence the alignment of SSC in the pancake.

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BALLMER ET AL. (2011): SPATIO-TEMPORAL VARIABILITY IN HAWAIIAN VOLCANISM INDUCED BY SSC

Figure S2. Horizontal cross-sections of temperature at 140 km depth for different models with contours of the rate of surface volcanism. From outside to inside, black dashed contours denote 0.01, 0.1, 1, and 10 km³/km²/Myr (average over 1000 timesteps). Upwellings and downwellings typically occur where temperatures are relatively high and low, respectively. The light blue and dark blue stripes reveal the pattern of ambient-mantle SSC. Warm colors (and white) are the plume-pancake. The different models simulate different positions of the plume relative to the pattern of ambient-mantle SSC. The position of SSC is influenced by the boundaries of the model box and is similar for all cases; therefore, the model conditions differ only in where the center of the plume is positioned: (a) y = 1650, (b) y = 1700 km, (c) y = 1750 km, and (d) y = 1800 km. The original position (i.e., at the bottom boundary of the model box) of the plume on the y-axis is marked by the white dashed line (green dashed line for position of the plume in (a)). The model in (a) is the reference case as also shown in Figs. 2-3. The pattern of SSC in the pancake is sensitive to undulations in lithosphere thickness relative to the plume, which was shaped by SSC in the ambient mantle upstream of the plume.

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SUPPLEMENTARY INFORMATIONDOI: 10.1038/NGEO1187BALLMER ET AL. (2011): SPATIO-TEMPORAL VARIABILITY IN HAWAIIAN VOLCANISM INDUCED BY SSC

Figure S1. Differential horizontal flow field between the plume pancake and the plate for the reference case. Arrows denote direction and color denote the amplitude of differential flow as computed by subtracting of plate motion (i.e. 80 km/Myr from left to right) from horizontal flow at 140 km. Arrows pointing to the left/right indicate horizontal flow that is slower/faster than plate motion. The shear associated with this differential motion appears to influence the alignment of SSC in the pancake.

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Figure S2. Horizontal cross-sections of temperature at 140 km depth for different models with contours of the rate of surface volcanism. From outside to inside, black dashed contours denote 0.01, 0.1, 1, and 10 km³/km²/Myr (average over 1000 timesteps). Upwellings and downwellings typically occur where temperatures are relatively high and low, respectively. The light blue and dark blue stripes reveal the pattern of ambient-mantle SSC. Warm colors (and white) are the plume-pancake. The different models simulate different positions of the plume relative to the pattern of ambient-mantle SSC. The position of SSC is influenced by the boundaries of the model box and is similar for all cases; therefore, the model conditions differ only in where the center of the plume is positioned: (a) y = 1650, (b) y = 1700 km, (c) y = 1750 km, and (d) y = 1800 km. The original position (i.e., at the bottom boundary of the model box) of the plume on the y-axis is marked by the white dashed line (green dashed line for position of the plume in (a)). The model in (a) is the reference case as also shown in Figs. 2-3. The pattern of SSC in the pancake is sensitive to undulations in lithosphere thickness relative to the plume, which was shaped by SSC in the ambient mantle upstream of the plume.

depth = 140 km

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Figure S3. Model results for case without SSC in the ambient mantle (small-box case). This case is similar to the reference case, and differs only in box length (2376 km instead of 4818 km). Such a setup prohibits self-organization of ambient-mantle SSC. Panels (a) and (b) show a horizontal cross-section of temperature (cf. Fig. S2), and the origin of volcanism in terms of source lithology (cf. Fig. 3a), respectively. Both panels display contours of surface volcanism (same contour spacing as in Fig. S2). For this case, plume-pancake SSC appears to be insufficient to support arch volcanism.

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Figure S4. Volcanic flux versus seafloor age for different positions of the plume relative to the pattern of ambient-mantle SSC. The 3 cases shown correspond to those in Figs. S2b-d (i.e., the plume is centered at (a) y = 1700 km [cf. Fig. S2b], (b) y=1750 km [cf. Fig. S2c], and (c) y=1800 km [cf. Fig. S2d]). Numbers denote total hotspot volcanic flux in [km³/Myr]. The above curves should be compared to the dashed lines in Fig. 3b, which represent volcanic flux for the reference case with the plume centered at y = 1650 km. Black curves display total volcanic flux. Red and blue curves indicate the volcanic fluxes along the Kea and Loa trends, respectively. The feeding zones for these trends are shown as light grey boxes in Fig. S5. The boundary between the two zones is chosen such that the Kea trend displays ~25% more volcanism than the Loa-trend—as consistent with the geological record over the past 2 Myrs (ref. 26).

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Figure S3. Model results for case without SSC in the ambient mantle (small-box case). This case is similar to the reference case, and differs only in box length (2376 km instead of 4818 km). Such a setup prohibits self-organization of ambient-mantle SSC. Panels (a) and (b) show a horizontal cross-section of temperature (cf. Fig. S2), and the origin of volcanism in terms of source lithology (cf. Fig. 3a), respectively. Both panels display contours of surface volcanism (same contour spacing as in Fig. S2). For this case, plume-pancake SSC appears to be insufficient to support arch volcanism.

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Figure S4. Volcanic flux versus seafloor age for different positions of the plume relative to the pattern of ambient-mantle SSC. The 3 cases shown correspond to those in Figs. S2b-d (i.e., the plume is centered at (a) y = 1700 km [cf. Fig. S2b], (b) y=1750 km [cf. Fig. S2c], and (c) y=1800 km [cf. Fig. S2d]). Numbers denote total hotspot volcanic flux in [km³/Myr]. The above curves should be compared to the dashed lines in Fig. 3b, which represent volcanic flux for the reference case with the plume centered at y = 1650 km. Black curves display total volcanic flux. Red and blue curves indicate the volcanic fluxes along the Kea and Loa trends, respectively. The feeding zones for these trends are shown as light grey boxes in Fig. S5. The boundary between the two zones is chosen such that the Kea trend displays ~25% more volcanism than the Loa-trend—as consistent with the geological record over the past 2 Myrs (ref. 26).

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b

145,000156,000

182,000




Figure S5. Composition and volume flux of surface volcanism for different positions of the plume relative to the pattern of ambient-mantle SSC. The 3 cases (a, b, c) correspond to those as shown in Fig. S4 with the plume centered at (a) y = 1700 km, (b) y = 1750 km, and (c) y = 1800 km, respectively. Colors denote contribution of pyroxenite in surface volcanism; black contours denote the rate of surface volcanism (same contour spacing as in Fig. S2). The above plot should be compared with Fig. 3a that represents the reference case with the plume centered at y = 1650 km.

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a)

b)

c)


Figure S6. Pyroxenite contribution versus seafloor age for different positions of the plume relative to the pattern of ambient-mantle SSC. The 3 cases (a, b, c) correspond to those as shown in Figs. S4-S5 with the plume centered at (a) y = 1700 km, (b) y = 1750 km, and (c) y = 1800 km, respectively. The above curves should be compared to the solid lines in Fig. 3b, which represent pyroxenite contribution for the reference case with the plume centered at y = 1650 km. All cases (including the reference case) except for the case in panel (a) display a distinction in pyroxenite contribution between the Kea and Loa trends of about 5%. This distinction persists through the postshield stage, as does the geochemical distinction between the two trends10.

pre

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96 98 [Myrs]88 90 92 94


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88 90 9692 94

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Figure S7. Volcanic flux versus seafloor age for cases with different critical porosity φC . Black

dashed line is the same as that in Fig. 3b for the reference case with φ C = 1%. Numbers denote total rejuvenated volcanic flux in km³/Myr for the different cases.

References 31 Moresi, L. & Gurnis, M. Constraints On the Lateral Strength Of Slabs From 3-

Dimensional Dynamic Flow Models. Earth Plan. Sci. Lett. 138, 15-28, (1996). 32 Zhong, S., Zuber, M. T., Moresi, L. & Gurnis, M. Role of temperature-dependent

viscosity and surface plates in spherical shell models of mantle convection. J. Geophys. Res. 105, 11063-11082, (2000).

33 Christensen, U. R. & Yuen, D. A. Layered convection induced by phase transitions. J. Geophys. Res. 90, 10291-10300, (1985).

34 Ballmer, M. D. Small-scale sublithospheric convection - an alterna tive mechanism for oceanic intraplate volcanism Ph.D. thesis, Diss. ETH No. 18425, ETH Zürich, (2009).

35 Ballmer, M. D., van Hunen, J., Ito, G., Bianco, T. A. & Tackley, P. J. Intraplate volcanism with complex age-distance patterns – a case for small-scale sublithospheric convection. Geochem. Geophys. Geosyst. 10, Q06015, (2009).

36 Schellart, W. P., Stegman, D. R. & Freeman, J. Global trench migration velocities and slab migration induced upper mantle volume fluxes: Constraints to find an Earth reference frame based on minimizing viscous dissipation. Earth-Science Reviews 88, 118-144, (2008).

37 Allègre, C. J., Hamelin, B. & Dupré, B. Statistical analysis of isotopic ratios in MORB: the mantle blob cluster model and the convective regime of the mantle. Earth Planet. Sci. Lett. 71, 71-84, (1984).

38 Phipps Morgan, J. Isotope topology of individual hotspot basalt arrays: Mixing curves or melt extraction trajectories? Geochem. Geophys. Geosyst. 1, 1003, (1999).

tsteps: 110600-110800vo

lcan

ic fl

ux

[km

³/km

/Myr

]

1

10

100

1000

pre

-shi

eld

pos

tshi

eld

shie

ld

reju

vena

ted

98

seafloor age [Myrs]92 969088

500200 300 400-100 0 100 600distance [km]

1%0.9%0.8%0.75%0.7%0.6%0.5% cr

itic

al p

oro

sity

661

470

205

191

105

39 Hirschmann, M. M. & Stolper, E. M. A possible role for garnet pyroxenite in the origin of the ''garnet signature'' in MORB. Contrib. Mineral. Petrol. 124, 185-208, (1996).

40 Pertermann, M. & Hirschmann, M. M. Partial melting experiments on a MORB-like pyroxenite between 2 and 3 GPa: Constraints on the presence of pyroxenite in basalt source regions from solidus location and melting rate. J. Geophys. Res. 108, 2125, (2003).

41 Hirschmann, M. M., Ghiorso, M. S., Wasylenki, L. E., Asimow, P. D. & Stolper, E. M. Calculation of Peridotite Partial Melting from Thermodynamic Models of Minerals and Melts - I - Review of Methods and Comparison with Experiments. J. Petrol. 39, 1091-1115, (1998).

42 McKenzie, D. Th-230-U-238 Disequilibrium and the Melting Processes Beneath Ridge Axes. Earth Planet. Sci. Lett. 72, 149-157, (1985).

43 Katz, R. F., Spiegelman, M. & Langmuir, C. H. A new parameterization of hydrous mantle melting. Geochem. Geophys. Geosyst. 4, 1073, (2003).

44 Zou, H. B. Trace element fractionation during modal and nonmodal dynamic melting and open-system melting: A mathematical treatment. Geochem. Cosmochem. Acta 62, 1937-1945, (1998).

45 Karato, S. & Wu, P. Rheology of the upper mantle - a synthesis. Science 260, 771-778, (1993).

46 Hirth, G. & Kohlstedt, D. L. Rheology of the upper mantle and mantle wedge: A view from the experimentalists. in: Inside the subduction factory (ed J. Eiler) 83-105 (AGU, 2003).

47 Hirth, G. & Kohlstedt, D. L. Water in the Oceanic Upper-Mantle - Implications For Rheology, Melt Extraction and the Evolution of the Lithosphere. Earth Planet. Sci. Lett.144, 93-108, (1996).

48 Kohlstedt, D. L. & Zimmerman, M. E. Rheology of partially molten mantle rocks. Ann. Rev. Earth Planet. Sci. 24, 41-62, (1996).

49 Richter, F. M. & Parsons, B. On the interaction of two scales of convection in the mantle. J. Geophys. Res. 80, 2529-2541, (1975).

50 Clague, D. A. & Dalrymple, G. B. Age and Petrology of Alkalic Postshield and Rejuvenated-Stage Lava from Kauai, Hawaii. Contrib. Mineral. Petrol. 99, 202-218, (1988).

51 Wessel, P. & Kroenke, L. W. Ontong Java Plateau and late Neogene changes in Pacific plate motion. J. Geophys. Res. 105, 28255-28277, (2000).

52 van Hunen, J. & Zhong, S. Influence of rheology on realignment of mantle convective structure with plate motion after a plate reorganization. Geochem., Geophys., Geosyst. 7, Q08008, (2006).

53 Dumoulin, C., Choblet, G. & Doin, M. P. Convective interactions between oceanic lithosphere and asthenosphere: Influence of a transform fault. Earth Planet. Sci. Lett. 274, 301-309, (2008).

54 Tanaka, R., Makishima, A. & Nakamura, E. Hawaiian double volcanic chain triggered by an episodic involvement of recycled material: Constraints from temporal Sr-Nd-Hf-Pb isotopic trend of the Loa-type volcanoes. Earth Planet. Sci. Lett. 265, 450-465, (2008).

55 Garcia, M. O. et al. Widespread Secondary Volcanism Near Northern Hawaiian Islands. Eos, Transactions, AGU 89, 525, (2008).



Figure S7. Volcanic flux versus seafloor age for cases with different critical porosity φC . Black

dashed line is the same as that in Fig. 3b for the reference case with φ C = 1%. Numbers denote total rejuvenated volcanic flux in km³/Myr for the different cases.

References 31 Moresi, L. & Gurnis, M. Constraints On the Lateral Strength Of Slabs From 3-

Dimensional Dynamic Flow Models. Earth Plan. Sci. Lett. 138, 15-28, (1996). 32 Zhong, S., Zuber, M. T., Moresi, L. & Gurnis, M. Role of temperature-dependent

viscosity and surface plates in spherical shell models of mantle convection. J. Geophys. Res. 105, 11063-11082, (2000).

33 Christensen, U. R. & Yuen, D. A. Layered convection induced by phase transitions. J. Geophys. Res. 90, 10291-10300, (1985).

34 Ballmer, M. D. Small-scale sublithospheric convection - an alterna tive mechanism for oceanic intraplate volcanism Ph.D. thesis, Diss. ETH No. 18425, ETH Zürich, (2009).

35 Ballmer, M. D., van Hunen, J., Ito, G., Bianco, T. A. & Tackley, P. J. Intraplate volcanism with complex age-distance patterns – a case for small-scale sublithospheric convection. Geochem. Geophys. Geosyst. 10, Q06015, (2009).

36 Schellart, W. P., Stegman, D. R. & Freeman, J. Global trench migration velocities and slab migration induced upper mantle volume fluxes: Constraints to find an Earth reference frame based on minimizing viscous dissipation. Earth-Science Reviews 88, 118-144, (2008).

37 Allègre, C. J., Hamelin, B. & Dupré, B. Statistical analysis of isotopic ratios in MORB: the mantle blob cluster model and the convective regime of the mantle. Earth Planet. Sci. Lett. 71, 71-84, (1984).

38 Phipps Morgan, J. Isotope topology of individual hotspot basalt arrays: Mixing curves or melt extraction trajectories? Geochem. Geophys. Geosyst. 1, 1003, (1999).

tsteps: 110600-110800

volc

anic

flu

x [k

m³/

km/M

yr]

1

10

100

1000

pre

-shi

eld

pos

tshi

eld

shie

ld

reju

vena

ted

98

seafloor age [Myrs]92 969088

500200 300 400-100 0 100 600distance [km]

1%0.9%0.8%0.75%0.7%0.6%0.5% cr

itic

al p

oro

sity

661

470

205

191

105

39 Hirschmann, M. M. & Stolper, E. M. A possible role for garnet pyroxenite in the origin of the ''garnet signature'' in MORB. Contrib. Mineral. Petrol. 124, 185-208, (1996).

40 Pertermann, M. & Hirschmann, M. M. Partial melting experiments on a MORB-like pyroxenite between 2 and 3 GPa: Constraints on the presence of pyroxenite in basalt source regions from solidus location and melting rate. J. Geophys. Res. 108, 2125, (2003).

41 Hirschmann, M. M., Ghiorso, M. S., Wasylenki, L. E., Asimow, P. D. & Stolper, E. M. Calculation of Peridotite Partial Melting from Thermodynamic Models of Minerals and Melts - I - Review of Methods and Comparison with Experiments. J. Petrol. 39, 1091-1115, (1998).

42 McKenzie, D. Th-230-U-238 Disequilibrium and the Melting Processes Beneath Ridge Axes. Earth Planet. Sci. Lett. 72, 149-157, (1985).

43 Katz, R. F., Spiegelman, M. & Langmuir, C. H. A new parameterization of hydrous mantle melting. Geochem. Geophys. Geosyst. 4, 1073, (2003).

44 Zou, H. B. Trace element fractionation during modal and nonmodal dynamic melting and open-system melting: A mathematical treatment. Geochem. Cosmochem. Acta 62, 1937-1945, (1998).

45 Karato, S. & Wu, P. Rheology of the upper mantle - a synthesis. Science 260, 771-778, (1993).

46 Hirth, G. & Kohlstedt, D. L. Rheology of the upper mantle and mantle wedge: A view from the experimentalists. in: Inside the subduction factory (ed J. Eiler) 83-105 (AGU, 2003).

47 Hirth, G. & Kohlstedt, D. L. Water in the Oceanic Upper-Mantle - Implications For Rheology, Melt Extraction and the Evolution of the Lithosphere. Earth Planet. Sci. Lett.144, 93-108, (1996).

48 Kohlstedt, D. L. & Zimmerman, M. E. Rheology of partially molten mantle rocks. Ann. Rev. Earth Planet. Sci. 24, 41-62, (1996).

49 Richter, F. M. & Parsons, B. On the interaction of two scales of convection in the mantle. J. Geophys. Res. 80, 2529-2541, (1975).

50 Clague, D. A. & Dalrymple, G. B. Age and Petrology of Alkalic Postshield and Rejuvenated-Stage Lava from Kauai, Hawaii. Contrib. Mineral. Petrol. 99, 202-218, (1988).

51 Wessel, P. & Kroenke, L. W. Ontong Java Plateau and late Neogene changes in Pacific plate motion. J. Geophys. Res. 105, 28255-28277, (2000).

52 van Hunen, J. & Zhong, S. Influence of rheology on realignment of mantle convective structure with plate motion after a plate reorganization. Geochem., Geophys., Geosyst. 7, Q08008, (2006).

53 Dumoulin, C., Choblet, G. & Doin, M. P. Convective interactions between oceanic lithosphere and asthenosphere: Influence of a transform fault. Earth Planet. Sci. Lett. 274, 301-309, (2008).

54 Tanaka, R., Makishima, A. & Nakamura, E. Hawaiian double volcanic chain triggered by an episodic involvement of recycled material: Constraints from temporal Sr-Nd-Hf-Pb isotopic trend of the Loa-type volcanoes. Earth Planet. Sci. Lett. 265, 450-465, (2008).

55 Garcia, M. O. et al. Widespread Secondary Volcanism Near Northern Hawaiian Islands. Eos, Transactions, AGU 89, 525, (2008).

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