Plates,Plates, slabs,slabs, andand keelskeels DecipheringDeciphering Earth'sEarth's convectiveconvective historyhistory fromfrom seismology,seismology, mineralmineral physicsphysics andand geodynamicsgeodynamics

ThorstenThorsten WW BeckerBecker UniversityUniversity ofof SouthernSouthern CaliforniaCalifornia LosLos Angeles,Angeles, CaliforniaCalifornia

DGG C.-F.-Gauß Lecture European Geosciences Union General Assembly Vienna, April 16, 2008 2/51 PreviousPrevious GaußGauß LecturesLectures

 HeinerHeiner IgelIgel (2007)(2007) Rupture,Rupture, WavesWaves andand ImagesImages

 UlrichUlrich ChristensenChristensen (2006)(2006) GeodynamoGeodynamo ModelingModeling 3/51

PlatePlate tectonicstectonics –– Top,Top, coldcold boundaryboundary layerlayer

temperature hot MantleMantle convectionconvection

cold

CoreCore heatheat flowflow –– Bottom,Bottom, hothot boundaryboundary layerlayer 4/51 Problem:Problem: MantleMantle  thermalthermal convectionconvection

 RheologicalRheological controlscontrols onon plateplate tectonics?tectonics? – WhyWhy doesdoes (only)(only) EarthEarth havehave plateplate tectonics?tectonics? – HowHow areare platesplates coupledcoupled toto mantlemantle flow?flow?  ChemicalChemical controlscontrols onon boundaryboundary layers?layers? – RoleRole andand evolutionevolution ofof thethe continents?continents? – RoleRole ofof volatilevolatile variationsvariations andand fractionation?fractionation? 5/51

ContentContent ofof thisthis talktalk

 AppliedApplied GeodynamicsGeodynamics approachapproach – CombineCombine disciplinarydisciplinary constraintsconstraints andand modelingmodeling toto understandunderstand mantlemantle systemsystem interactionsinteractions – EstablishEstablish aa geodynamicgeodynamic referencereference modelmodel  SeismicSeismic anisotropyanisotropy ofof thethe upperupper mantlemantle – TectonicTectonic strainstrain gaugegauge – ConstrainingConstraining laterallateral viscosityviscosity variationsvariations – ExploringExploring thethe rolerole ofof continentalcontinental keelskeels – VolatileVolatile variationsvariations inin thethe asthenosphereasthenosphere 6/51 SurfaceSurface constraintsconstraints –– plateplate tectonicstectonics

Crustal velocities in HS-3 Hot spot reference frame

e.g. DeMets et al. (1991); Gripp & Gordon (2002);Sella et al. (2002); Kreemer et al. (2003) 7/51 GlobalGlobal circulationcirculation modelsmodels

Tractions from plate motions acting on asthenosphere  MantleMantle viscousviscous StokesStokes flow,flow, nono inertiainertia – InstantaneousInstantaneous solutionsolution forfor boundaryboundary conditionsconditions andand internalinternal loadsloads – Semi-analytical,Semi-analytical, ifif viscosityviscosity isis NewtonianNewtonian andand onlyonly depthdepth dependentdependent  ForceForce modelmodel – PlatePlate motionsmotions prescribedprescribed – EvaluateEvaluate mantlemantle tractionstractions andand plateplate drivingdriving forcesforces

Hager & O'Connell (1981) 8/51 DeepDeep structuralstructural constraints:constraints: SeismologicalSeismological mappingmapping 9/51

SeismicSeismic tomographytomography

 CAT-scanCAT-scan likelike techniquetechnique  EarthquakesEarthquakes :: sourcessources SeismometersSeismometers :: receiversreceivers  MeasureMeasure traveltravel timestimes toto invertinvert forfor 3-D3-D velocityvelocity structurestructure 10/51 MantleMantle shearshear velocityvelocity anomaliesanomalies MapMap atat 12001200 kmkm depthdepth

e.g. Grand and van der Hilst (1997); Becker and Boschi (2001) 11/51 MantleMantle temperaturetemperature anomaliesanomalies MapMap atat 12001200 kmkm depthdepth

 UseUse mineralmineral physicsphysics toto convertconvert velocityvelocity intointo temperaturetemperature (density)(density) anomaliesanomalies 12/51 MantleMantle flowflow drivendriven byby tomographytomography IsoviscousIsoviscous geoidgeoid predictionprediction ObservedObserved geoidgeoid anomaliesanomalies

 FlowFlow modelmodel drivendriven byby densitydensity ViscosityViscosity increaseincrease geoidgeoid predictionprediction anomalies,anomalies, surfacesurface freefree slipslip  ObservedObserved geoidgeoid anomaliesanomalies requirerequire lowerlower mantlemantle viscosityviscosity increaseincrease  Overall,Overall, geopotentialgeopotential (stress(stress related)related) constraintsconstraints non-uniquenon-unique e.g. Richards & Hager (1984); Hager (1984); Forte & Mitrovica (2000); Moucha et al. (2006) 13/51 VelocitiesVelocities asas aa constraintconstraint forfor laterallateral viscosityviscosity variationsvariations

FlowFlow modelmodel withwith onlyonly radialradial viscosityviscosity variationsvariations PoloidalPoloidal componentcomponent  NoNo toroidaltoroidal flowflow withoutwithout laterallateral viscosityviscosity variationsvariations  Strain-ratesStrain-rates notnot veryvery plate-likeplate-like ObservedObserved plateplate velocitiesvelocities inin hothot spotspot referencereference frameframe PoloidalPoloidal componentcomponent ToroidalToroidal componentcomponent

Sources and sinks Strike slip motion, spin

O'Connell et al. (1991); Ricard et al. (1991); Forte & Peltier (1993); Thoraval & Richards (1997) 14/51 TheThe rolerole ofof thethe plateplate boundariesboundaries Observed plate motions  VelocityVelocity modelmodel – PrescribePrescribe weakweak plateplate boundariesboundaries – ComputeCompute plateplate dragdrag couplingcoupling andand drivingdriving torquestorques

– SolveSolve forfor EulerEuler Modeled plate motions vectorsvectors forfor rigidrigid platesplates  CorrelationsCorrelations good,good, butbut oceanicoceanic platesplates movemove asas fastfast asas continentalcontinental onesones

Ricard & Vigny (1989)

Ricard & Vigny (1989); Lithgow-Bertelloni & Richards (1998); Becker & O'Connell (2001); Conrad & Lithgow-Bertelloni (2002) 15/51 AdditionalAdditional constraints:constraints: SeismicSeismic anisotropyanisotropy

 RadialRadial :: LoveLove (SH(SHorizontal))

vs.vs. RayleighRayleigh (SV(SVertical)) surfacesurface waveswaves

PREM radial average

Radial average from S362WMANI model depth depth [km]

(V /V )2 SH SV

core mantle

e.g. Dziewonski & Anderson (1981); Debayle et al. (2005); Panning & Romanowicz (2006); Kustowski et al. (2008) 16/51 AdditionalAdditional constraints:constraints: SeismicSeismic anisotropyanisotropy  RadialRadial :: LoveLove (SH)(SH) Azimuthal vs.vs. RayleighRayleigh (SV)(SV) anisotropy surfacesurface waveswaves RMS from DKP2005  AzimuthalAzimuthal :: RayleighRayleigh SV1SV1 fasterfaster thanthan SV2SV2 PREM radial average

Radial average from S362WMANI model depth depth [km]

(V /V )2 SH SV

core mantle

e.g. Dziewonski & Anderson (1981); Debayle et al. (2005); Panning & Romanowicz (2006); Kustowski et al. (2008) 17/51 AzimuthalAzimuthal anisotropyanisotropy patternspatterns

 SVSV (Rayleigh)(Rayleigh) anomaliesanomalies atat ~75~75 kmkm depthdepth

e.g. Tanimoto & Anderson (1984); Montagner & Nataf (1986); Ekström (2001); Debayle et al. (2005) 18/51 LatticeLattice preferredpreferred orientationorientation texturestextures

Lower hemisphere projection of the alignment concentration of crystallographic axes

fast

 MantleMantle mineralsminerals (olivine)(olivine) intrinsicallyintrinsically (single(single crystal)crystal) anisotropicanisotropic  MultiMulti graingrain assembliesassemblies formform anisotropicanisotropic texturestextures underunder dislocationdislocation creepcreep  SeismicSeismic anisotropyanisotropy isis aa recordrecord ofof tectonictectonic strainstrain andand flowflow

Zhang & Karato (1995) 19/51 AnisotropyAnisotropy andand mantlemantle convectionconvection

Montagner (1998)

e.g McKenzie (1981); Tanimoto & Anderson (1984); Ribe (1989) 20/51 NewNew developmentsdevelopments I:I: OlivineOlivine alphabetalphabet

dry wet stress

0 Water content 300 ppm wt

Karato et al. (2007) 21/51 NewNew developmentsdevelopments II:II: EfficientEfficient mineralmineral physicsphysics theoriestheories ofof texturingtexturing

Zhang & Karato Kaminski & Ribe (1995) lab (2001) theory  IncludeInclude simple recrystallizationrecrystallization shear effectseffects  WeWe useuse KaminskiKaminski etet al.al. ((2004)2004) DREXDREX implementation,implementation, uniaxial tunedtuned toto lablab resultsresults compression  LinkLink flow,flow, strain,strain, texture,texture, andand seismicseismic anisotropyanisotropy quantitativelyquantitatively Kaminski & Ribe (2001) 22/51 NewNew developmentsdevelopments III:III: SphericalSpherical modelsmodels withwith laterallateral viscosityviscosity variationsvariations

 WithWith largelarge scalescale computing,computing, wewe cancan nownow solvesolve thermo-thermo- chemicalchemical convectionconvection problemproblem inin spheresphere  WillWill focusfocus onon instantaneousinstantaneous solutionssolutions withwith temperature,temperature, stress,stress, andand depth-depth- dependentdependent visco-visco- plasticplastic rheologiesrheologies

e.g. Tackley (1994); Bunge et al. (1996);Zhong et al. (2000); Tackley (2000a,b) 23/51 QuantitativeQuantitative modelsmodels ofof upperupper mantlemantle flowflow andand anisotropyanisotropy

ComputeCompute globalglobal flowflow withwith dislocation/diffusiondislocation/diffusion creepcreep ComputeCompute globalglobal anisotropyanisotropy usingusing mineralmineral physicsphysics forfor upperupper mantlemantle DeriveDerive seismicseismic propertiesproperties andand comparecompare withwith observationsobservations 24/51

CirculationCirculation modelmodel

 UseUse geologicgeologic informationinformation (stiff(stiff cratonscratons andand seafloorseafloor ages)ages) forfor lithospherelithosphere  InferInfer temperaturetemperature anomaliesanomalies inin mantlemantle fromfrom seismicseismic tomographytomography (SMEAN)(SMEAN)  ComputeCompute 3-D,3-D, sphericalspherical mantlemantle flowflow  SolveSolve withwith CitcomSCitcomS (Zhong(Zhong etet al.al. 2000)2000)  EitherEither – PrescribePrescribe velocityvelocity (histories)(histories) atat surfacesurface – PrescribePrescribe weakweak zoneszones andand solvesolve forfor velocitiesvelocities 25/51 RealisticRealistic olivineolivine rheologyrheology fromfrom lablab

η η disl diff

 TwoTwo creepcreep mechanismsmechanisms activeactive – DiffusionDiffusion creepcreep -- graingrain sizesize dependentdependent – DislocationDislocation -- stressstress dependentdependent  BothBoth viscositiesviscosities temperaturetemperature andand pressurepressure (depth)(depth) dependentdependent  PartitioningPartitioning betweenbetween thethe twotwo willwill determinedetermine texturetexture formationformation

e.g. Ashby & Verral (1975); Hirth & Kohlstedt (2003); McNamara et al. (2003) 26/51 PowerPower lawlaw flow:flow: FreeFree surfacesurface withwith weakweak zoneszones viscosity varies only radially  Shown:Shown: – flowflow atat 250250 kmkm depth,depth, colorcolor == speedspeed – viscosityviscosity variationsvariations coloredcolored inin backgroundbackground

dry olivine creep law  SurfaceSurface velocitiesvelocities matchmatch observedobserved plateplate motionsmotions  Sub-oceanicSub-oceanic asthenosphereasthenosphere weakerweaker byby highhigh strain-ratesstrain-rates andand temperaturestemperatures  OceanicOceanic platesplates movemove fasterfaster Becker (2006) 27/51 PowerPower lawlaw flow:flow: AverageAverage viscositiesviscosities

region of sub- LPO formation continental

sub­oceanic asthenosphere

 DryDry olivine,olivine, graingrain sizesize ~5~5 mm,mm, viscosityviscosity broadlybroadly consistentconsistent withwith geoidgeoid andand post-glacialpost-glacial reboundrebound  DepthDepth rangerange ofof dislocationdislocation creepcreep consistentconsistent withwith anisotropyanisotropy observationsobservations

Cadek & Fleitout (2003); McNamara et al. (2003); Podolevsky et al. (2005); Becker (2006) 28/51 FitFit toto observedobserved netnet rotationsrotations

 ModelsModels withwith stiffstiff continentalcontinental keelskeels induceinduce netnet rotationsrotations ofof thethe wholewhole lithospherelithosphere withwith respectrespect toto thethe lowerlower mantlemantle  ThisThis isis seenseen inin hotspothotspot referencereference framesframes;; polespoles ofof HS2/HS3HS2/HS3 matchedmatched well,well, amplitudeamplitude tootoo lowlow

Net rotation Euler poles, circle size indicates amplitude

Ricard et al. (1991); Zhong (2001); Steinberger et al. (2004); Becker (2006) 29/51 LateralLateral viscosityviscosity variationsvariations duedue toto olivineolivine rheologyrheology (power(power law)law)

FocusingFocusing ofof shearingshearing withinwithin sub-oceanicsub-oceanic asthenosphereasthenosphere PlatePlate tectonictectonic likenesslikeness ofof surfacesurface velocitiesvelocities betterbetter thanthan withoutwithout laterallateral viscosityviscosity variationsvariations Ocean/continentOcean/continent velocityvelocity ratiosratios dependdepend stronglystrongly onon laterallateral viscosityviscosity variationsvariations GlobalGlobal flowflow modelsmodels consistentconsistent withwith texturetexture formationformation underunder dislocationdislocation creepcreep inin upperupper ~350~350 kmkm ofof mantlemantle PredictedPredicted netnet rotationrotation consistentconsistent withwith sense,sense, butbut notnot amplitude,amplitude, ofof somesome hot-spothot-spot referencereference modelsmodels 30/51 QuantitativeQuantitative modelsmodels ofof upperupper mantlemantle flowflow andand anisotropyanisotropy

ComputeCompute globalglobal flowflow withwith dislocation/diffusiondislocation/diffusion creepcreep ComputeCompute globalglobal anisotropyanisotropy usingusing mineralmineral physicsphysics forfor upperupper mantlemantle DeriveDerive seismicseismic propertiesproperties andand comparecompare withwith observationsobservations 31/51 3) Anisotropy prediction

2) Texturing

1) Mantle flow

 ComputeCompute globalglobal (here:(here: steady)steady) flowflow  FollowFollow tracerstracers untiluntil saturationsaturation strainstrain isis reachedreached  ComputeCompute texturetexture forfor olivine-enstatiteolivine-enstatite mixmix  VoigtVoigt averageaverage ofof single-crystalsingle-crystal elasticelastic tensorstensors

Becker et al. (2006a) 32/51 3) Anisotropy prediction

2) Texturing model synthetics S wave splitting

1) Mantle flow  LabLab basedbased texturingtexturing theorytheory producesproduces realisticrealistic mantle xenolith S wave splitting heterogeneityheterogeneity inin globalglobal flowflow

Becker et al. (2006a) 33/51 StrainingStraining relationshipsrelationships existexist andand matchmatch naturalnatural samplessamples

simple shear straining trend ellipticity single crystal single crystal S anisotropy S

P anisotropy P anisotropy  MostMost anisotropyanisotropy hexagonal;hexagonal; cancan useuse scalingscaling relationshiprelationship forfor seismologicalseismological inversionsinversions andand asas strainstrain gaugegauge Montagner & Anderson (1988); Becker et al. (2006a); Becker et al. (2008) 34/51 GlobalGlobal matchmatch toto azimuthalazimuthal anisotropyanisotropy

 GoodGood fitfit inin oceanicoceanic regionsregions  Continents:Continents: notnot soso muchmuch  MantleMantle flowflow betterbetter thanthan plateplate shearshear (absolute(absolute plateplate motionmotion model)model)  ActiveActive upwellingsupwellings requiredrequired good bad  TextureTexture derivedderived predictionprediction similarsimilar Angular misfit between data and model toto finitefinite strainstrain

Gaboret et al. (2003); Becker et al. (2003, 2007a); Behn et al. (2004); Conrad et al. (2007) 35/51 TheThe effecteffect ofof netnet rotationsrotations onon azimuthalazimuthal anisotropyanisotropy predictionspredictions No net rotation Large net rotation (HS3)

 SystematicSystematic decreasedecrease inin correlationcorrelation forfor largelarge netnet rotations,rotations, independentindependent ofof seismologicalseismological oror flowflow modelmodel

Becker (2008) 36/51

GlobalGlobal azimuthalazimuthal anisotropyanisotropy

 RealisticRealistic texturestextures predictedpredicted byby flowflow modelsmodels  ScalingScaling lawslaws provideprovide aa prioripriori informationinformation forfor seismologyseismology  AzimuthalAzimuthal anisotropyanisotropy matchedmatched betterbetter forfor activeactive flowflow thanthan onlyonly plateplate shearshear  ActiveActive continentalcontinental andand oceanicoceanic regionsregions fitfit betterbetter thanthan oldold continentscontinents  OnlyOnly moderatemoderate amountsamounts ofof netnet rotationrotation (~30%(~30% ofof HotHot SpotSpot 33 model)model) compatiblecompatible withwith azimuthalazimuthal anisotropyanisotropy 37/51

ShearShear wavewave (SKS)(SKS) splittingsplitting

garnero.edu

Complex signature in old continental regions – simpler in active and oceanic regions Fouch et al. ASU compilation; ISC database; Becker et al. (2007b) 38/51 SplittingSplitting sortedsorted intointo tectonictectonic regionsregions

Correlation length Roughness orogenic zones platforms

Fouch et al. ASU compilation; ISC database; Becker et al. (2007b) ContinentalContinental splittingsplitting 39/51

correlationcorrelation lengthslengths Angular match between splits Angular between match (2007b) et al. al. et Becker Becker CorrelationCorrelation CorrelationCorrelation lengthlength ~~ 600600 kmkm lengthlength ~~ 15001500 kmkm 40/51

SplittingSplitting correlationcorrelation lengthslengths

 OlderOlder continentalcontinental regionsregions appearappear longerlonger wavelengthwavelength thanthan moremore recentlyrecently deformingdeforming crustcrust  LateralLateral viscosityviscosity variationsvariations inin flowflow cannotcannot explainexplain thesethese discrepanciesdiscrepancies  Interpretation:Interpretation: OldOld continentalcontinental regionsregions reflectreflect pastpast (>(> 100100 Ma),Ma), large-scalelarge-scale deformationdeformation suchsuch asas continentcontinent –– continentcontinent collisionscollisions YoungYoung continentalcontinental regionsregions moremore affectedaffected byby moremore recentrecent (<(< 3030 Ma,Ma, smaller-scale)smaller-scale) convectiveconvective flowflow 41/51 RadialRadial anisotropyanisotropy averagesaverages

V > V SH SV  OnlyOnly radialradial viscosityviscosity variations,variations, texturetexture formsforms isotropy everywhereeverywhere

Becker et al. (2008) 42/51 RadialRadial anisotropyanisotropy averagesaverages

V > V SH SV  DryDry olivineolivine flow,flow, texturetexture formsforms inin dislocationdislocation creepcreep isotropy  RadialRadial anisotropyanisotropy averageaverage matchedmatched belowbelow lithospherelithosphere  CorrelationsCorrelations ofof radialradial patternspatterns alsoalso improvedimproved

Becker et al. (2008) 43/51 RadialRadial anisotropyanisotropy patternspatterns

 5050 km:km: RadialRadial averageaverage under-under- predicted,predicted, patternpattern matchmatch poorpoor

 150150 km:km: RadialRadial averageaverage andand patternpattern matchmatch good,good, azimuthalazimuthal patternspatterns goodgood (correlation(correlation ~~ 0.5,0.5, likelike slabs)slabs)

 250250 km:km: RadialRadial averageaverage andand patternpattern matchmatch OKOK

= (V /V )2  SH SV V fast V fast SV SH Becker et al. (2008) 44/51 ExploringExploring differencesdifferences fromfrom thethe geodynamicgeodynamic referencereference modelmodel lithosphere 45/51 ResidualResidual anisotropyanisotropy atat 5050 kmkm Model discrepancy for two seismological models stochastic model in old continents

residual (V /V )2 SH SV over-predicted under-predicted

Frozen-in, old texture in continental shields and cratons missing from geodynamic model (< 50 Ma)

Nettles & Dziewonski (2008); Kustowski et al. (2008); Becker et al. (2007b); Becker et al. (2008) 46/51 ExploringExploring differencesdifferences fromfrom thethe geodynamicgeodynamic referencereference modelmodel

asthenosphere

Becker et al. (2008) 47/51 DryDry texturetexture modelmodel atat dry asthenosphericasthenospheric depthsdepths

seismology geodynamics

= (V /V )2  SH SV

Origin of low velocity, high attenuation asthenosphere may be related to volatile variations, melt, or both – can we probe for this?

Becker et al. (2008) 48/51 Best-fitBest-fit modelmodel forfor mixingmixing dry

ofof twotwo texturetexture typestypes wet

seismology geodynamics

= (V /V )2  SH SV

Addition of texture due to wet type of slip-system reduces discrepancies. Correlation ~ 0.8

Becker et al. (2008) 49/51 VolatileVolatile contentcontent wet

 Inferred volatile content moderate  Possibly related to plumes in Pacific dry

Becker et al. (2008); Karato et al. (2008) 50/51 ConclusionsConclusions

 GeodynamicGeodynamic referencereference modelmodel forfor convection-convection- inducedinduced texture,texture, fromfrom graingrain toto plateplate scales,scales, explainsexplains azimuthalazimuthal andand radialradial anisotropyanisotropy  OnlyOnly moderatemoderate netnet rotationsrotations areare compatiblecompatible withwith azimuthalazimuthal anisotropyanisotropy  ObservationsObservations constrainconstrain laterallateral viscosityviscosity variationsvariations andand variationsvariations inin couplingcoupling  SignatureSignature ofof recentrecent convectionconvection inin oceanicoceanic plates,plates, frozen-infrozen-in structurestructure inin oldold continentscontinents  CanCan imageimage volatilevolatile contentcontent ofof asthenosphereasthenosphere 51/51 CollaboratorsCollaborators andand supportsupport  Donna Blackman, UC San Diego  Lapo Boschi, ETH Zürich  Jules Browaeys, UT Austin  Sebastien Chevrot, CNRS Toulouse  Göran Ekström, LDEO Palisades NY  Tom Jordan, USC, Los Angeles  Jamie Kellogg, Cate School, Santa Barbara  Bogdan Kustowski, Chevron  Rick O'Connell, Harvard, Cambridge MA  Vera Schulte-Pelkum, CU Boulder  Special Thanks To: – Edouard Kaminski (DREX); Shijie Zhong, Eh Tan, & Louis Moresi (CitcomS); seismic tomographers sharing their models; Matt Fouch and the ISC for their SKS splitting database – Funding agencies: National Science Foundation, DAAD – Additional support from USC's High Performance Computing Center 52/51 ReferencesReferences

 Becker, T. W.: Azimuthal seismic anisotropy  Kaminski, E., Ribe, N. M. and Browaeys, J. constrains net rotation of the lithosphere.35, L0530 T.: D-Rex, a program for calculation of GRL, 35, L05303, 2008. seismic anisotropy due to crystal lattice preferred orientation in the convective upper  Becker, T. W., Kustowski, B., Ekström, G.: Radial seismic anisotropy as a constraint for mantle. GJI, 158, 2004. upper mantle rheology. EPSL, 267, 2008.  Qin, P. SPICE benchmark pour méthodes tomographiques globaux et test des modèles  Becker, T. W., Ekström, G., Boschi, L., and tomographiques globaux et test des modèles Woodhouse, J.: Length scales, patterns, and tomographiques globaux. PhD thesis, IPGP, origin of azimuthal seismic anisotropy in the Paris, 2007. upper mantle as mapped by Rayleigh waves.  Steinberger, B. and M. Antretter: Conduit GJI, 171, 2007a. diameter and buoyant rising speed of mantle plumes: Implications for the motion of  Becker, T. W., Browaeys, J. T., and Jordan, T. H.: Stochastic analysis of shear wave hotspots and shape of plume conduits, G3, splitting length scales. EPSL, 259, 2007b. 7(1), 2006.  Zhong, S.J., M. T. Zuber, L. Moresi, and M.  Becker, T. W.: On the effect of temperature and strain-rate viscosity on global mantle Gurnis, Role of temperature-dependent flow, net rotation, and driving forces. GJI, viscosity and surface plates in spherical shell 167, 2006a. models of mantle convection, JGR, 105, 2000.  Becker, T. W., Chevrot, S., Schulte-Pelkum,  V., and Blackman, D. K.: Statistical Zhong, S.J., Role of ocean-continent contrast properties of seismic anisotropy predicted by and continental keels on Plate motion, net upper mantle geodynamic models. JGR rotation of lithosphere and the geoid, JGR, 111, B08309, 2006b. 106, 2001.