Deformation, crystal preferred orientations, and seismic anisotropy in the Earth's D '' layer

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Deformation, crystal preferred orientations, and seismic

anisotropy in the Earth’s D ” layer

Andrea Tommasi, Alexandra Goryaeva, Philippe Carrez, Patrick Cordier,

David Mainprice

To cite this version:

Andrea Tommasi, Alexandra Goryaeva, Philippe Carrez, Patrick Cordier, David Mainprice.

Defor-mation, crystal preferred orientations, and seismic anisotropy in the Earth’s D ” layer. Earth and

Planetary Science Letters, Elsevier, 2018, 492, pp.35-46. �10.1016/j.epsl.2018.03.032�. �hal-01851859�

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Contents lists available atScienceDirect

Earth

and

Planetary

Science

Letters

www.elsevier.com/locate/epsl

Deformation,

crystal

preferred

orientations,

and

seismic

anisotropy

in

the

Earth’s

D

layer

Andréa Tommasi

a

,

∗

,

Alexandra Goryaeva

b

,

Philippe Carrez

b

,

Patrick Cordier

b

,

David Mainprice

a

a_Geosciences_Montpellier,_CNRS_&_Université_de_Montpellier,_F-34095_Montpellier_cedex_5,_France

b_Univ._Lille,_CNRS,_INRA,_ENSCL,_UMR₈₂₀₇_–_UMET_–_Unité_Matériaux_et_{Transformations,}_F-59000_Lille,_France

a

r

t

i

c

l

e

i

n

f

o

a

b

s

t

r

a

c

t

Articlehistory:

Received27November2017 Receivedinrevisedform2March2018 Accepted16March2018

Availableonline10April2018 Editor:J.Brodholt Keywords: mantleconvection Dlayer post-perovskite ferropericlase deformationmodeling seismicanisotropy

We use a forward multiscale model that couples atomistic modeling of intracrystalline plasticity mechanisms (dislocation glide ± twinning) in MgSiO3 post-perovskite (PPv) and periclase (MgO) at

lowermantlepressuresandtemperaturestopolycrystalplasticitysimulationstopredictcrystalpreferred orientations(CPO)developmentandseismicanisotropyinD.WemodeltheCPOevolutioninaggregates of70%PPvand30%MgOsubmittedtosimpleshear,axialshortening,andalongcorner-flowstreamlines, which simulate changes in flow orientation similar to those expected at the transition between a downwellingandflowparalleltothecore–mantleboundary(CMB)withinDorbetweenCMB-parallel flow and upwelling at the borders of the large low shear wave velocity provinces (LLSVP) in the lowermostmantle.AxialshorteningresultsinalignmentofPPv[010]axeswiththeshorteningdirection. Simple shearproduces PPvCPO withamonoclinic symmetrythatrapidly rotatestowardsparallelism between the dominant [100](010) slip system and the macroscopic shear. These predictions differ fromMgSiO3post-perovskitetexturesformedindiamond-anvilcellexperiments,butagreewiththose

obtained insimple shearand compressionexperiments usingCaIrO3 post-perovskite.Developmentof

CPOinPPvandMgOresultsinseismicanisotropyinD.ForshearparalleltotheCMB,atlowstrain,the inclinationofScS,Sdiff,andSKKSfastpolarizationsanddelaytimesvarydependingonthepropagation direction.Atmoderateandhighshearstrains,allS-wavesarepolarizednearlyhorizontally.Downwelling ﬂowproducesSdiff,ScS,andSKKS fastpolarizationdirectionsand birefringencethatvarygraduallyas afunctionoftheback-azimuthfromnearlyparalleltoinclinedbyupto70◦toCMBand fromnull to

∼5%.Change intheﬂowto shearparalleltothe CMBresults indispersionoftheCPO,weakeningof the anisotropy,and strong azimuthalvariationofthe S-wavesplittingup to250kmfromthe corner. TransitionfromhorizontalsheartoupwellingalsoproducesweakeningoftheCPOandcomplexseismic anisotropypatterns,withdominantlyinclinedfastScSandSKKSpolarizations,overmostoftheupwelling path. Modelsthat take intoaccounttwinning inPPvexplain mostobservations ofseismicanisotropy inD,butheterogeneityoftheﬂow atscales <1000kmis neededto complywith theseismological evidenceforlowapparentbirefringenceinD.

1. Introduction

ThethinshelloftheEarth’smantlejustabovethecore,named D byBullen (1949),isanessentialfeatureofthemantle convec-tionsystem.Itformsitslowerthermalboundarylayer,controlling thethermal,chemical, andmechanicalinteractions withthe core. D isexpectedtobemainlycomposedof(Mg,Fe)SiO3 (

∼

70%)and

(Mg,Fe)O – ferropericlase (Hirose et al., 2015). Experimental

re-*

Correspondingauthor.

E-mailaddress:andrea.tommasi@umontpellier.fr(A. Tommasi).

sults,atomisticmodeling,andseismologicalobservationsconverge to(Mg,Fe)SiO3 beingpresentasbridgmanite,withan

orthorhom-bic perovskite (Pv) structure in hot zones of D, but acquiring a post-perovskite (PPv) structure in colder regions (cf. review in Hiroseetal.,2015).

Seismicvelocities inD show stronglateralvariations atboth smallandlargewavelengths,indicatingthermalandchemical het-erogeneity (e.g., Lay et al., 1998; van der Hilst et al., 2007). Seismological observations also point to changes in D thickness from

<

100 km to

>

350 km, which may occur over short lat-eral distances (e.g., Thomas and Kendall, 2002; van der Hilst et al., 2007). Last but not least, D is characterized by spatially

https://doi.org/10.1016/j.epsl.2018.03.032

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Fig. 1. (a)Slipsystemsand(b)twinninginMgSiO3 PPvand(c)slipmodesinMgO.Notethatduetothecubicsymmetryofferropericlasethe3slipmodesdisplayedin

Fig.1cresultin24slipsystems.

heterogeneous seismic anisotropy, which hasbeen measured us-ing a variety of techniques, such as the analysis of: (i) wave-formsanomalies(e.g.,LayandYoung,1991; Maupin,1994; Cottaar andRomanowicz, 2013), (ii) splittingof shear wavestraveling at low incidence angles through D (e.g., Kendall and Silver, 1996; Nowacki et al., 2010), (iii) differences between horizontally and verticallypolarizedshearwavesinglobaltomographymodels(e.g., PanningandRomanowicz,2006),(iv)thediscrepancyinthe resid-ualsplitting,aftercorrectionsforuppermantleanisotropy,ofcore shear waves (SKS and SKKS, e.g., Restivo and Helffrich, 2006; Long, 2009), and(v) changes in polarity of P-waves reﬂected at the top ofD (e.g., Thomas etal., 2011). These datacarry infor-mation on the convective ﬂow in D, but their exploitation de-pendsonourabilitytorelate theseismicanisotropyobservations todeformation-inducedcompositionallayeringorcrystalpreferred orientationsofthemainrock-formingmineralsinD:bridgmanite, post-perovskite,andferropericlase.Thisled to alarge number of forwardmodelsofdevelopmentofseismicanisotropyinD based on mantle circulation orconvection models, which tested differ-enthypothesesonthe(Mg,Fe)SiO3post-perovskitedeformationor

phasetransitionmechanisms(e.g.,Wenketal.,2006,2011;Walker etal.,2011,2017;Nowackietal.,2013).

Inthisarticle,wealsouseaforwardmulti-scalemodeling ap-proachforexploringthecontributionofdeformation-induced crys-talpreferred orientations(CPO) ofPPvandferropericlaseto seis-micanisotropy intheD layer.We couplethemostrecent atom-isticmodelsofintracrystallineviscoplasticdeformationinMgSiO3

PPvandMgO(thepureMgend-memberofbothsolidsolutions)at Dconditions(Amodeoetal.,2011; Cordieretal.,2012;Goryaeva etal.,2015a,2015b,2016,2017;Carrezetal.,2017)topolycrystal plasticity simulations of simple, end-member ﬂow patterns. Po-tentialeffects of thisCPO-induced anisotropy on P- andS-waves reﬂectedatthetopofDareanalyzedinacompanionarticle (Pis-contietal.,inpreparation).

2. ViscoplasticdeformationofPPvandMgOatDconditions

Numerical modeling of the dislocation structures and glide properties in MgSiO3 PPv and MgO at lowermost mantle strain

rates,temperatures,andpressures(Amodeoetal.,2011; Cordieret al.,2012;Goryaeva etal., 2015b,2016,2017) constraintheactive

slipsystemsinthetwomineralsandtheirrelativestrengthsunder D conditions(Fig.1 andTable 1).Thesemodels predictthat the easiest slipsystems for both minerals, namely[100](010)PPv and

[001](010)PPv and1/2

110

{

110

}

MgOand1/2

110

{

100

}

MgO,have

extremelylowlatticefrictionsunderlowermostmantleconditions, implying low strengths for mantle ﬂow by dislocation creep in domains with high volume fractions of PPV in D. In contrast, similarmodelsforbridgmanitepredictextremelyhighlattice fric-tionsforallstudiedslipsystems,implyingthatdislocationglideis not an effective deformation process for this phase in thelower mantle(Kraychetal., 2016).Dislocationdynamicsmodelspredict that bridgmanite should rather deform by pure climb (Boioli et al., 2017)and,hence,notdevelopstrongCPOunderlowermantle conditions.ThecorollaryofthesemodelsisthatPPv-richdomains in D should develop strong CPOofboth PPv andferropericlase, leading to a marked anisotropy of physical properties, whereas bridgmanite-rich onesshouldhavemuch loweranisotropies, only controlledbytheCPOofferropericlase.

In PPv, if onlydislocation glide isactive, no strain parallel to the[100],[010],or[001]crystalaxescanbeaccommodated. How-ever,atomic-scalemodelsforPPvalsopredictthedevelopmentof 1/2

110

{

110

}

deformationtwins(Carrezetal.,2017).{110} twin-ningshould playa signiﬁcantrole intheevolution oftheCPOin PPv, since it adds additional degreesof freedom fordeformation (it mayaccommodatestrain parallelto[100]and[010]),reducing strainincompatibilityproblems.

3. Modelingstrain-inducedCPOevolutionandassociatedseismic

anisotropyinD

Development of CPO in PPv and MgO polycrystals deformed under D conditions is modeled by a viscoplastic self-consistent (VPSC) approach (Molinari et al., 1987; Lebensohn and Tomé,

1993), whichconsiderseach grain asa viscoplasticinclusion em-bedded in and interacting with a viscoplastic effective medium thatrepresentstheaveragebehaviorofthepolycrystal.Eachgrain deforms by dislocation glide only (MgO) or by dislocation glide and twinning (PPv); these processes allow for shear in a ﬁnite setofcrystallographicplanesanddirections(Fig.1).Diffusive pro-cessesareonlyimplementedinanimplicitway.First,byassuming thattheycontributetorecoverymechanisms,suchasclimb,which

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Table 1

Slipsystemsandtwinningdatausedinthedifferentsimulations.CriticalResolvedShearStresses(CRSS)forthe differentsystemswerederivedbasedonatomicscalemodelsofintracrystallinedeformationinMgSiO3

post-perovskiteandMgO(afulldescriptionoftheprocedureispresentedintheonlinesupplementarymaterial). Slip/twinning systems’ CRSS Model

Referencemodel: Twin-1

NoTwin-1 Twin-2 NoTwin-2

MgSiO3PPV [100](010) 1 1 1 1 [001](010) 1 1 3 3 [100]{011} 10 10 10 10 [100](001) 20 20 20 20 1/2110{110¯ } 3 – 3 – 110{111}a ₅₀ ₅₀ ₅₀ ₅₀ 011{111}a MgO 1/2110{110¯ } 1 1 1 1 1/2110{100} 1 1 1 1 1/2110{111} 5 5 5 5

a _Mark_auxiliary_systems_(not_predicted_by_atomistic_models),_which_are_included_in_the_calculations_for

nu-mericalstability;theirhighCRSSensurethattheyneveraccommodate>2%oftheaggregatestrain.Differences inCPOevolutionbetweenmodelsTwin-1(NoTwin-1)andTwin-2(NoTwin-2)areonlysigniﬁcantatshearstrains higherthan5.ThecomparisonoftheCPOintensityevolutioninthefourmodelsisshowninFig.4;fullCPO patternsformodelTwin-2arepresentedintheonlinesupplementarymaterial.

avoid hardening but do not produce strain in the present mod-els.Second,byassumingthattheycontributetoaccommodatethe straincomponentsthatcannotbeproducedbytheknownslip sys-temsortwinninginPPv,whichinthemodelsare accommodated by“auxiliary slipsystems”,not predictedby atomic-scalemodels butimposedtoclosetheyieldsurfaceofthePPvcrystal.

CPOevolution is controlled by the imposed deformation, the initialtexture,andtheactiveslipandtwinningsystems,which de-pendon the mineral structure, butalso on the temperatureand pressureconditions,whichcontrol their relativestrength or criti-calresolvedshearstrength(CRSS).Here,weuseCRSSderivedfrom theatomicscalemodelsofdislocationstructuresandglide proper-tiesinPPvandMgOatD strainrates,temperatures,andpressures discussedinthe previous section(Table 1; thefull descriptionof theprocedureusedforestablishingthe differentCRSS setstested inthepresentstudyispresentedintheonlinesupplementary ma-terial).High CRSS(50, Table1) areimposed tothe “auxiliaryslip systems”inPPv.Thisensuresthatthey neveraccommodatemore than2%ofthetotalviscoplasticstrain anddonotsigniﬁcantly af-fecttheCPOevolution.

Actualstress-strainraterelationsforPPvarenotknown. How-ever, recent dislocation dynamics simulations for MgO suggest a typicaldislocation creep regime inD (Reali etal., 2017). In this regime,mostofthe deformation isaccommodated by dislocation glide,butstrainratesarecontrolled byrecoverybyclimb,leading to a steadystate behavior described by a power lawwith stress exponent

(

n

)

valuesaround3.Giventhehightemperatures consid-eredinthepresentsimulations,wesupposethatPPvhasasimilar behavior. Thussimulations forboth PPv andMgO were runwith n

=

3 forallslipandtwinningsystemsandnohardening.

Twinning inPPv is modeled using the PredominantTwin Re-orientation Scheme proposed by Tomé et al. (1991). Similarly to dislocation glide, twinning is described as a shear deformation ona givenplane anddirection(forPPv, 1

/

2

110

{

110

¯

}

,Fig.1b). Its activation is controlled by a CRSS (Table 1). Twinning differs neverthelessfromslipbyitsuniquesenseofshear,whichis mod-eled by activating twinning only if the resolved shear stress has the samesign as the slipdirection. The total crystalviscoplastic strain is thesum ofthe shear on all slipand twinsystems. The effectoftwinning on theCPO evolutionis modeled ina statisti-calwaybychangingtheorientationoftheentirecrystalwhenthe twinnedvolumeinthegrainishigherthanathreshold(50%inthe present models). Different values for the parameters controlling theevolutionofthetwinnedvolumeinthegrainweretested;the

resultsarepresentedintheonlinesupplementary material. Hard-eningassociatedwiththeformationoftwinsisneglected,because themodels aresetforhightemperatures.We alsorunmodels in whichtwinningwassuppressed(NoTwin-1andNoTwin-2models, Table1).

WeﬁrstinvestigatetheevolutionofCPOinaggregatesof1000 crystals witha random initial preferredorientation composed of

70% PPv and30% MgO submitted to two end-member

deforma-tion regimes: axial shortening (for comparison with experimen-tal data) and simpleshear. Simple shear models were run up to a shear strain of 10; this would correspond to a horizontal dis-placement of 2500 km in a 250 km thick D layer if the strain was homogeneously distributed. Actual flow inD ismost likely three-dimensional, but regions submitted to large deformations probably display a strong shear component, whose orientation relatively to the CMB will depend on the large-scale convection pattern. Changes inCPOevolution in transpression and transten-sion relative to simple shear are analyzed in the online supple-mentary material. Finally, we modeled the CPO evolution along two 2D corner-flow streamlines inan isoviscousNewtonian fluid (Batchelor,1967).Thesestreamlines arenot representativeofany actual flow in D, but allow studying the effect of changes in flow direction, such asthose expected at the transitionbetween adownwellingslabandflowparalleltotheCMBwithinD or be-tweenshearparalleltotheCMBandupwellingatthebordersofa LLSVP,onCPOpatternsandseismicanisotropyinD.Thevelocity gradientsalong themodeledstreamlinesarepresentedinthe on-linesupplementary material(Table S1);theassociatedstrain rates are

∼

10−15s−1.

Totest forthe effectofthe linearizationscheme,tangent and secondorderVPSCmodels(LebensohnandTomé,1993; Lebensohn et al., 2005) were run. The effect of changing the linearization scheme is found to be minor. The CPO patterns are similar, al-though the CPO evolves slightly slower in second order models. Thuswe presentonlythemoreaccurate secondorderVPSC mod-els.

Seismic properties for 70% PPv – 30% ferropericlase aggre-gates were calculated using the modeled CPOs and elastic con-stant data of Wu et al. (2013) for ferropericlase and Zhang et al. (2016) for PPv using the MTEX Matlab toolbox (Mainprice et al., 2011). The calculations were performed for compositions of (Mg0.75Fe0.25)SiO3 and (Mg0.8125Fe0.1875)O, temperatures of

2000 K, and pressures of 125 GPa. It is important to note that changes inFe andAl contents inPPv, aswell asinpressure and

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Fig. 2. PPvandMgOCPOafter20%ofaxialshorteningformodelsinwhichtwinningisactive(top)orsuppressed(bottom).(a)PolefiguresofthePPvCPO;stereographic projections,contoursat0.5multiplesofuniformdistribution(m.u.d).(b)Inversepolefigure(IPF)oftheshorteningdirectionforPPvandMgO(similarforthetwomodels). Insertonthetopleftindicatesthereferenceframeofthepolefigures,withtheblackcirclemarkingtheshorteningdirection.(Forinterpretationofthecolorsinthefigure(s), thereaderisreferredtothewebversionofthisarticle.)

temperatureintherangesexpectedtooccurinD produceminor variations of the anisotropy patterns and intensity (Zhang et al.,

2016andonlinesupplementaryFig. S3),whichdonotchangethe conclusionsofthepresentstudy.

4. Results

4.1. CPOevolutioninaxialcompression

Axialcompressionproducesaﬁber-[010]PPvCPOcharacterized byamaximumof[010]PPVatlowangletothecompression

direc-tion(blackdotinthecenterofpoleﬁgure)andgirdlesof[100]PPV

and[001]PPVathighangletoit(Fig.2).ThisCPO,althoughweak,is

alreadywelldevelopedat20%shortening.Suppressionoftwinning leadstostrongeralignmentof[010]PPV withtheshortening

direc-tionandfasterconcentrationoftheCPOasafunctionofstrain. MgOalsodevelopsanaxisymmetricCPOcharacterizedby align-ment of [101]MgO parallel to the compression direction (Fig. 2).

With increasing strain, the PPv CPO becomes stronger, but the patternremainsconstant.Incontrast,MgOdevelopsastrong align-mentof[001]MgOparalleltothecompressiondirectioninaddition

totheinitial[101]MgOmaximum,whichbecomesasecondary

ori-entationcomponent.

4.2. CPOevolutionanddevelopmentofseismicanisotropyinsimple

shear

Simpleshearresultsindevelopment ofamonoclinic PPvCPO, whichprogressivelyrotatestowardsparallelismbetweenthe dom-inant[100](010)PPvslipsystemandthemacroscopicshear(Fig.3).

The [010]PPv axis displays the strongest concentration, which

tends, for shear strains greater than 2, to align normal to the shear plane. [100]PPv and [001]PPv axes form girdles at low

an-gle to the shear plane, with a weak [100]PPv maximum aligned

withthesheardirectionand,athighstrains,a[001]PPv maximum

normaltoit.Rotationofthetwinnedfractionsby34.5◦aroundthe [001]axis(Fig.1b)producesdispersionof[100]PPvandof[010]PPv

ontheXZplane,thatis,inaplane normaltotheshearplanebut containingthesheardirection.

Inthepresentstudy,PPvandMgOaremodeledashaving sim-ilar viscoplasticstrengths (Table 1). Byconsequence, strain tends to be evenly partitioned between the two phases. However, the highnumber ofavailable slipsystems in MgO (the 3slip modes listedin Table1provide 24slipsystemsdueto thecubic crystal

symmetry) results in weaker CPO relative to PPv (Fig. 3). Maxi-mum concentrations are

≤

2 multiples of a uniform distribution, evenatashearstrainof10.BoththeintensityandCPOpatternsof MgOvaryinaperiodicmannerwithincreasingshearstrain, with-out attaininga stableorientation (asalsoobservedinlargestrain shearingofhalite,whichisisostructuralwithMgObyWenketal.,

2009).Well-developedMgOCPOareneverthelesscharacterizedby concentrationof

100

MgOnormaltotheshearplaneandaweaker

concentrationof

110

MgOparalleltothesheardirection.

ThesePPv andMgOCPOresultin markedanisotropy forboth P- andS-wavespropagatingthroughD.ThePPvCPOcontrolsthe seismicanisotropy,buttheMgOcontributionresultsinlower max-imumP- andS-waveanisotropiesthana100%PPvaggregatewith the same CPO. Similarly to the PPv CPO, fast P-waves propaga-tiondirectionsandfastS-wavespolarizationplanesrotatetowards parallelism withthe shear directionwith increasing shear strain (Fig. 3). Both P- and S-waves maximum propagation and polar-ization anisotropies increase non-linearly with increasing strain: quicklyuptoshearstrainsof2,slowerthereafter(Fig.4).

P-wave propagationanisotropypatterns havean orthorhombic symmetry(Fig.3).Atlowstrains,thehighestP-wavevelocity cor-respondstopropagationparalleltothelineation(maximum elon-gationdirection),whichisat

∼

20◦ anticlockwisetotheshear di-rection,andthelowest,topropagationalongthemaximum short-eningdirection.Withincreasingstrain,thepatternevolvestowards transverseisotropywithaslowsymmetryaxisnormaltotheshear plane andhigh P-wavevelocitiesfor mostpropagationdirections intheshearplane.

Shear wave polarization anisotropy patterns alsochange with increasing strain(Fig.3).At ashearstrainof1,highbirefringence isobserved inthefoliationplane (planenormalto themaximum ﬁniteshorteningdirection),whichisat

∼

20◦ anticlockwisetothe shearplane,witha90◦periodicity:thehighestbirefringenceis ob-servedforS-wavespropagatingparallelornormaltothelineation (maximum ﬁniteelongation direction).Weakbirefringenceis pre-dictedforS-wavespropagatingintheXZplaneat

≥

30◦tothe lin-eation.Atshearstrainof2,signiﬁcantbirefringence(

≥

2.5%)is pre-dictedforallpropagationdirectionsathighangletotheshear di-rection,withthehighestanisotropy(4.7%)forS-wavespropagating normaltothesheardirectionintheshearplane.Apparentisotropy ispredictedforS-wavespropagating intheXZplane obliquelyto thesheardirection.Atshearstrains

≥

5,mostS-wavespropagating obliquelytotheshearplanesamplehighbirefringence(

≥

3%).

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Fig. 3. EvolutionofPPvandMgOcrystalpreferredorientationsandseismicanisotropywithincreasingshearstrainforthereferencemodel(Twin-1).Lowerhemisphere stereographicprojections.Contoursat1multipleofuniformdistribution(m.u.d)forPPvandat0.2m.u.dforMgO.Insertonthetopleftshowsthestructuralreferenceframe andtheoneinthetopright,thedirectionssampledbydifferentS-wavestraveling inDiftheshearplaneisparalleltotheCMB.

Fig. 4. EvolutionofthemaximumP-wavepropagation(gray)andS-wave polariza-tionanisotropy(black)withincreasingshearstrainformodelswithandwithout twinning.CRSSvaluesforthedifferentmodelsarepresentedinTable1.

Fig.5 displays the birefringence of S-waveswith different in-cidence angles in D predicted for shearing parallel to the CMB based on the models shown in Fig. 3. At low shear strains, all S-waves show a strong variability of both the direction of fast-polarization(inFig.5isdisplayedtheinclinationofthefast polar-izationdirectionrelativelytothehorizontal,whichiswhatcanbe measuredseismologically,cf.Fig. 6inWookeyandKendall,2008) andoftheintensityofthebirefringenceasafunctionofthe

prop-agationdirection.Sdiffwavesdisplaystrongbirefringencefor fast-polarizationsinclined by25–50◦ tothehorizontalandlower bire-fringenceforsubhorizontalfastpolarizations.ScSandSKKSwaves show astrong variationof theorientation offastpolarization di-rections,whichrangeforSKKSfromnearhorizontaltoinclinedby

>

50◦, asa function ofthe propagationdirection. SKSwaves dis-play lower birefringence and lower maximum inclination angles for the fast polarization direction (

>

30◦). With increasing shear strain, the azimuthal variabilityin the birefringence is preserved orevenenhanced,butthemaximuminclinationanglesofthefast polarizationdirectionsdecrease.MaximumScSfast-polarization di-rectioninclinations,forinstance,areof25◦ forashearstrainof2 andof15◦ forashearstrain of5.Higher inclinations(upto30◦) areobserved forshear strainsof10,butthey areassociatedwith lowbirefringence.

Suppressionof twinninginPPv (modelNoTwin-1, Table1) re-sultsinaCPOwithaclearorthorhombicsymmetry, which inten-sityevolvesfasterthaninthereferencemodel(Fig.6).Italsoleads toslowerrotationoftheCPOtowardsparallelismbetweentheeasy [100](010)slipsystemandtheimposedmacroscopicshear,which isnotfullyattainedevenata shearstrainof10.Forhighstrains, suppressionoftwinningresultsinpoint distributionsforall three axes:[100],[010],and[001],butthelatterhasalower concentra-tion.Seismicanisotropypatternsaresimilartothoseinthemodels withtwinning,butanisotropiesatanygivenﬁnitestrainarehigher (Fig.4).Inaddition,seismicanisotropypatternsareslightlyoblique to theshearreferenceframe evenata shearstrain of10, dueto the slower rotation of the CPO towards parallelism between the dominant slip system and the macroscopic shear in the models weretwinningissuppressed(Fig.6).

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Fig. 5. BirefringenceofS-waveswithdifferentincidenceanglesinD(cf.insert)as afunctionofthepropagationdirection(measuredrelativelytothesheardirection), predictedforthemodelsdisplayedinFig.3consideringthattheshearplaneis par-alleltotheCMB(consideredlocallyashorizontal).Thebirefringenceisexpressedby boththeinclinationofthedirectionoffast-polarizationrelativelytothehorizontal andtheintensityoftheanisotropy(sizeofthesymbols).

4.3. CPOandseismicanisotropyevolutioninresponsetoachangein

ﬂowdirection

ThePPvCPOevolutionalongadownwellingflow,startingfrom randomorientationsat300kmabove theCMB(based onthe hy-pothesisthat bridgmanitedeformsdominantlyby climbanddoes not develop CPO, Boioli et al., 2017), is characterized by a slow rotationof[100]towardsthevertical,whichisnot completed be-forethe downwellingimpactsthe CMBandthe flowevolvesinto dominantshearingparallel totheCMB(Fig.7).At thecorner,the change inflow patternleads to progressive evolutionof theCPO towards one better orientedto accommodatethe imposed shear-ingparalleltotheCMB.Thisresults,first,inweakeningoftheCPO (Fig. 7). Newmaxima of [100] parallel to the flow directionand [010]normaltotheshearplane developandareprogressively re-inforced,whereas thoseformedinthedownwellingpathdecrease inintensity.TypicalhorizontalshearingCPOareobservedat

>

300 kmfromthedownwelling(Fig.7).

Thedownwellingpathischaracterizedbypredominanceoffast S-wavepolarizationsinclinedrelativelytotheCMB(Fig.7).The in-tensityoftheanisotropyincreaseswithdepth.Boththeanisotropy intensity and the inclination angle of the fast polarization vary markedly as a function of propagation direction. At the end of the downwelling path, they range from null to 4.7% and from subhorizontalto

>

50◦,respectively.ScSandSdiffwaves propagat-ing parallelto the“slab” trendsample thehighestbirefringences, which, at the end of the downwellingpath, are associated with fast-polarizations inclined by upto 50◦ to thehorizontal(Fig. 7). Core shear waves (SKS and SKKS) sample weaker birefringences along their paths in D in the vicinity of a downwelling. Close tothecorner,depending ontheback-azimuth,SKKSmight never-theless sampleupto3%ofbirefringence.Formostback-azimuths, SKS sample lower birefringences and show lower inclinations of thefastpolarizationdirectionthanSKKS(Fig.7).

The weakening of both PPv andMgO CPOin response to the change in ﬂow direction results in reduction of the anisotropy andrathercomplexS-wavesplittingpatternsup to300kmaway fromthedownwelling(Fig.7).Inthisinterval,Sdiff,ScS,andSKKS waves display fast polarizations, which change sharply from in-clined toparallel to the CMB, andhighly variable delay timesas a functionofthe back-azimuth(Fig. 7).ScS andSKKSwavesmay displayfast-polarizationdirectionsinclinedby

>

50◦fromthe hor-izontal. SKS display a lower back-azimuthal variability, with fast polarization directionsinclinedby

≤

30◦fromthehorizontal.Sdiff only show strongbirefringence forpropagation directions within

±

30◦ of the ﬂow direction and have in this case, subhorizontal fast-polarizationdirections(Fig.7).

At

>

300 km fromthe downwelling (Fig. 7), fast S-waves po-larizationsforall incidenceangles andpropagationdirections are dominantlysubhorizontal(

<

20◦).Delaytimesstilldependonthe propagation direction. Sdiff, ScS, SKKS, andSKS waves propagat-ing athighangletotheﬂowdirectionsample highbirefringences (

>

3.5%). For other propagation directions, Sdiff and SKS sample low birefringence (0–2%).In contrast, ScS andSKKS waves prop-agatingintheplanethatcontainstheﬂowdirectionsamplerather highbirefringence(

≥

3%).

Despite the contrast in initial CPO (the upwelling calculation wasinitializedwiththeCPOpredictedforahorizontalshearstrain of 10 in Fig. 3), the change from shear parallel to the CMB to upwelling, which might occur, forinstance, at the boundariesof LLSVPs, alsoproduces weakening of the PPv CPOand of the as-sociated seismicanisotropy inmost ofthe upwelling path in D (Fig. 8). Even early in the upwelling path (within

<

100 km of thecorner,Fig.8),ScS,SKKS,SKSwavesshowdominantlyinclined fast-polarizations.Thelattervaryasa functionofthepropagation directionbetween30◦and65◦forScSwavesandbetween40◦and

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Fig. 6. EvolutionofPPvcrystalpreferredorientationsatshearstrainsof1and10andseismicanisotropyatashearstrainof10forModelNoTwin-1(twinningsuppressed). Lowerhemispherestereographicprojections,contoursat2multipleofuniformdistribution(m.u.d).NotethatthemaximumintensityofthescalebarintheCPOstereoplots istwicetheoneinFig.3.Insertonthetopleftshowsthestructuralreferenceframe.

60◦forSKKS,withthehigherinclinations,butlowerbirefringence observedforwavespropagatinginplanesthatareeitheratlowor highangle totheX-direction (Fig.8). SKSwavesshowalmost no back-azimuthalvariabilityintheinclinationofthefast-polarization direction, which is

∼

30◦. Sdiff waves, in contrast,display nearly horizontalfast-polarizations andstrongbirefringenceforall prop-agationdirections,exceptthoseathighangletoX,whichare char-acterized by inclined fast-polarizations andlow birefringence. At

>

200kmfromthecorner,aclearverticalshearingCPOdevelops. Itresults instrongly inclined (65–90◦) fast-polarizations forSdiff

wavesandinstrongazimuthalvariabilityintheinclinationofthe fast-polarizationforScSandSKKSwaves(from0◦to65◦andfrom 0◦ to50◦,respectively).SKSwavesshowlowermaximum inclina-tions of thefast-polarizations (

≤

25◦). All S-waves show a strong variabilityoftheintensityofthebirefringenceasafunctionofthe propagationdirection(Fig.8).

Actual flow patterns in D are certainly more complex then thetwocornerflowlinesstudiedhere.Geodynamicmodelsshow time-dependent flowpatternswithfrequentbucklingoftheslabs when impinging upon the CMB (McNamara et al., 2002).

Com-Fig. 7. EvolutionofthePPvCPOandoftheS-wavespolarizationanisotropypredictedforthe70%PPv+30%MgOaggregatealongacornerflowlinesimulatingthechangein flowdirectionassociatedwiththetransitionfromadownwellingtoshearingparalleltotheCMB(cf.sketchatthebottomleftofthefigure).Lowerhemispherestereographic projections.AllCPOpolefiguresusethesamecoloringrange,between0and5multiplesofauniformdistribution,foreasyvisualizationofthechangesinCPOintensity. S-wavepolarizationanisotropyplotsarecoloredindependentlyfromeachother,thelocalmaximumbirefringence(whitesquare)isindicatedatthetoprightofeachpole figure.Plotsatthetoprightshowthevariationoftheanglebetweenthefastpolarizationdirectionandthehorizontal(equatedlocallytotheCMB)asafunctionofthe propagationdirectionmeasuredrelativelytoXforS-wavesthatsampleDwithdifferentincidenceangles(cf.insertattopright)at3selectedlocationsalongtheflow line(reddots).CPOcalculationswereperformedusingTwin-1CRSSset(Table1).ThevelocitygradientevolutionimposedalongtheflowlineispresentedintheOnline SupplementaryMaterial.

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Fig. 8. EvolutionofthePPvCPOandoftheS-wavespolarizationanisotropypredictedforthe70%PPv+30%MgOaggregatealongacornerflowlinesimulatingthechange inflowdirectionassociatedwiththetransitionfromshearingparalleltotheCMBtoupwellingattheborderofaLLSVP(cf.sketchatthebottomrightofthefigure).Lower hemispherestereographicprojections.AllCPOpolefiguresusethesamecoloringrange,between0and10multiplesofauniformdistribution,foreasyvisualizationofthe changesinCPOintensity.S-wavepolarizationanisotropyplotsarecoloredindependentlyfromeachother,thelocalmaximumbirefringence(whitesquare)isindicatedat thetoprightofeachpolefigure.PlotsatthetopleftshowthevariationoftheanglebetweenthefastpolarizationdirectionandtheCMBasafunctionofthepropagation directionmeasuredrelativelytoXforS-wavesthatsampleDwithdifferentincidenceangles(cf.insertattopleft)at3selectedlocationsalongtheflowline(reddots).CPO calculationswereperformedusingTwin-1CRSSset(Table1).ThevelocitygradientevolutionimposedalongtheflowlineispresentedintheOnlineSupplementaryMaterial.

positionally stratified slabs may also rotate, so that the denser crustallayer facesdown (Tackley,2011).In addition,plumesmay formattheedgesandsidesoftheslabs,disruptingthehorizontal slab spreading atop the CMB (Tackley, 2011). The present mod-elsgive,nevertheless,afirstorderunderstandingonhowtheCPO evolution and seismic anisotropy will respond to such changes in flow patterns: CPO and seismic anisotropy patterns do reori-ent in response to the changing flow field, but with a delay, which maycorrespond spatially to up to 300 km foran average strain rate of 10−15 _s−1_, _which _is _the _one _used _in _the _present

models. Faster strain rates will result in faster strain accumula-tion and hence in faster reorientation of the CPO and seismic anisotropy patterns; the opposite is also true. In most cases, as thosemodeled here, sharpchangesin ﬂowdirectionresultin lo-cal weakening of the CPOand, hence, limit the strengthening of the anisotropy. Yet, this weakening may not occur if the preex-istingCPOiswell orientedtoaccommodatethenewdeformation ﬁeld.

5. Discussion

5.1. ComparisontoexperimentaldataonPPvdeformation

ExperimentaldataonCPOdevelopment inPPvcomprise mod-erate temperature and pressure compression and simple shear experiments on CaIrO3 PPv (Yamazaki etal., 2006; Miyagi etal.,

2008; Niwa et al., 2012), which maintains the post-perovskite

structure at ambient conditions, allowing therefore post-mortem analysis of the deformation microstructures, and laser-heated diamond-anvil cell (DAC) compression experiments on MgGeO3

and(Mg,Fe)SiO3 PPv.The latterexperimentsbetter reproduce

ac-tualDcompositionsandpressureandtemperatureconditions,but they havepoorly controlledboundaryconditions,involvemultiple phase transformationsandvery highstresses (

>

GPa),andcannot bequenched.

Despite signiﬁcant differences in bond strengths and elastic properties between MgSiO3 and CaIrO3 post-perovskites (Metsue

et al., 2009), CPO evolutions predicted in the present study are in excellent agreement with those observed in experimental de-formation of CaIrO3 PPv in both compression and simple shear

(Yamazaki et al., 2006; Miyagi et al., 2008; Niwa et al., 2012).

{

110

}

twinswerealsoobservedbyTEMindeformedCaIrO3

post-perovskite(Niwaetal.,2012).

The modeled CPO (Fig. 2) are nevertheless at odds withCPO developed in laser-heated diamond-anvil cell (DAC) experiments on (Mg,Fe)SiO3 PPv and on MgGeO3 PPV, which are

character-ized by a concentration of (102), (100), or (001) normal to the compression direction (Merkel et al., 2007; Miyagi et al., 2010; Wuetal.,2017).Thereisnostraightforwardexplanationforthese CPO, which are not supported by our current understanding of themicrophysicsofviscoplasticdeformationinPPv.Theymightbe duetopre-texturingofPPvduetoviscoplasticdeformationofthe precursor phases andinheritance upon phase transition, as pro-posedtoexplain(100)and(102)textures(Miyagietal.,2010),or

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tothehighdifferentialstressesatplayintheexperiments,which mayallowthe activationofslipsystems withhighCRSS, such as [100](001)PPv (Table 1). The latter behavior has indeed been

ob-servedduringcoldcompressionofwadsleyite(ThurelandCordier,

2003).

5.2.ComparisontoobservationsofseismicanisotropyinD

SeismicmeasurementsofanisotropyinDareessentiallybased ontheanalysisofthebirefringenceofS-waveswithdifferent inci-denceanglesandpathsinD.Despitethecommonuseof ‘trans-verseisotropic’modelswithdifferentorientationsofthesymmetry axistointerpretseismicanisotropyobservationsinD,thepresent models, independently of the choice of input parameters (CRSS of the different slip systems and activation of twinning or not), implythat seismic anisotropy patternsin D should have an or-thorhombicsymmetry, withbothradial andazimuthal anisotropy components.The modelsalsoshowthat theS-wavebirefringence (orientationofthefast-polarizationandintensityoftheanisotropy) dependsontheorientation ofthepropagationdirectionrelatively totheﬂow.Formonotonicsimpleshearortranspression,atshear strains higher than 2, although the intensity of the anisotropy variesasa functionofthe propagationdirection,the polarization of fast S-waves is dominantly at low angle (

>

20◦) to the shear direction (Fig. 3 and Supplementary Material Figs. S1 and S2). However,atlowshearstrains,intranstension,orsubsequentlytoa changeinflowdirection,fastS-wavepolarizationsmightbehighly obliquetothelocalflowdirection(Figs.3,5,7,8and Supplemen-taryMaterialFigs. S1andS2). Themaximumbirefringence varies from3% at a shearstrain of1 to 6% ata shear strain of 10. In-creasingpressure and temperatureto 3500 K and 150GPa does notsignificantlychangetheabovepredictions(Online Supplemen-taryMaterialFig. S3).

In the next paragraphs, we compare these predictions to ob-servationsofseismicanisotropyinD.Theseobservationsdepend on multiple corrections to isolate the lowermost mantle signal andmaybebiasedbyeffectsarisingfromcomplexityinthe low-ermost mantle structure or noise (cf. Komatitsch et al., 2010; MonteillerandChevrot, 2010; Panningetal., 2010; Chang et al.,

2014;Borgeaudetal.,2016).Thesepossiblebiaseswillbeignored inthefollowingdiscussion.Moreimportantly,observationsof seis-micanisotropyinD integratetheanisotropicsignalnotonlyover longpaths,whichrangefroma300–400kmforSKSandSKKSto 1000–3000kmforScS andSdiff,butalso,duetoﬁnite-frequency effects,over large volumes (banana-doughnut sensitivitykernels) aroundthepath(FavierandChevrot,2003;Sieminskietal.,2009). The present models do not allow testing the effect of the in-tegration of a spatially variable anisotropy signal, since we only calculate the CPO and seismic anisotropy evolution in response to a few simple strain histories. However, they allow to discuss whichﬂowpatternsmayproducetheobservedseismicanisotropy. In addition, by considering that the different anisotropic contri-butions (ponderated by the local anisotropic kernel sensitivity) add up if the orientation of the fast polarization is similar or combine in a more complex manner if the orientation of the anisotropyvaries, producingingenerallower delay timesand in-termediateorientationsofthefastaxes(FavierandChevrot,2003; NowackiandWookey,2016),wetrytodiscusstheeffectsof inte-gratingaspatiallyvariablesignal.

5.2.1. Danisotropyinglobaltomographymodels

Mostglobal anisotropic tomography models show up to

±

2% ofanisotropy

ξ

= (

V2

SH

/

VSV2

)

≤

1

.

02 inthelowermostmantle

(Pan-ningandRomanowicz,2006;Kustowskietal.,2008;Panningetal.,

2010; Changetal., 2014; DeWit andTrampert,2015).The exact

spatialdistributionoftheanisotropicdomainvariesbetween mod-els,butthetransverse (SH)componentoftheS-velocity is domi-nantlyfasterthantheradial(SV)componentindomains character-izedbyfasterthanaveragevelocitiesandSHisdominantlyslower thanSVwithinorinthevicinityoftheLLSVPs.Thepresent mod-elsshowthatSHfasterthanSVwhenaveragingoveralargerange ofpropagationdirectionsandincidenceanglesisonlyachievedfor ﬂow nearly parallel to the CMBandshear strains

>

2 (Figs.3, 5,

7, 8). SH faster than SV in fast velocity domains may therefore correspond to lateral spreading of slab material at the base of themantle.Evenmoreconstraining,althoughfastpolarizations in-clinedrelativelytothehorizontalareproducedinmanymodels,SV fasterthanSHfordataaveragedoveralargerangeofpropagation directionsandincidenceangles(consideringthatsuch an average signal resultsfrompredominanceoffastpolarizationsinclinedby

>

45◦tothehorizontal)isonlyachievedforverticalflowafter sig-nificantstrain,suchasatthebaseofadownwelling(Fig. 7)orat the top ofan upwelling (Fig. 8).Thus SV fasterthan SH are sur-roundedby areaswithSH fasterthan SV,asimagedbyChang et al. (2014) inthelowermostmantlebeneaththecircum-Pacific sub-ductionrim, maybeconsistent withtransitionfromdownwelling to shear parallel to the CMBas the slabs impact upon the CMB (Fig.7). Themeasuredvalues

ξ

= (

V2

SH

/

VSV2

)

≤

1

.

02 arefully

con-sistentwiththosepredictedinthepresentmodelsforsimpleshear paralleltotheCMBIndeed,

ξ

,calculatedbyimposingtotheactual elastic tensor of the aggregate a VTI symmetry (we average the tensorcomponentsoverarotationaroundthenormaltotheshear plane),is1.03forashearstrainof10.

5.2.2. SdiffandScSwavessplitting

The largest dataset investigating D anisotropy concerns re-gional studies using shear waves with grazing incidence paths. These studies have analyzed anomalies in the amplitude of the SV component of the core diffracted phase Sdiff (e.g., Vinnik et al., 1989; Lay and Young, 1991; Maupin, 1994; Cottar and Ro-manowicz, 2013) or performed splitting measurements on Sdiff andon S-wavesreﬂected atthe CMB(ScS), measuringthe polar-ization anisotropy alonglow anglepaths within D (e.g.,Kendall andSilver,1996; WookeyandKendall,2008; Nowackietal.,2010). In the following discussion, we focus on observations in regions withhigherthanaveragevelocities,possiblyassociatedwithlower temperature, in which CPO of PPv may be the dominant factor producingseismicanisotropy.Althoughlesscommon,evidencefor seismicanisotropyhasalsobeenreportedinlowermostmantle do-mains withlower thanaverage seismicvelocities,liketherootof the Hawaii hotspot (e.g.,Fouch et al., 2001), but, in these cases, other sources forthe anisotropy,such asalignedmelt inclusions, shouldprobablybeinvoked.

Most early studies based on Sdiff and ScS interpreted D anisotropy asvertically transverse isotropic (VTI). SH faster than SVwasdetectedinD beneathAlaska,theCaribbean, Centraland NorthernPaciﬁc, and Indianoceans. Measured delay times range from3 to 9s;these delay timescorrespond, ifthe anisotropy is homogeneous throughoutthe1000–2800 kmlong paths,to bire-fringencesof0.5–3.0%(e.g.,Kendall andSilver,1996; Garneroand Lay, 1997; Fouch etal., 2001; Garnero and Lay, 2003). Such fast polarization data would be consistent with dominant horizontal ﬂowinD,butpredicteddelaytimesshouldbehigherthanthose measured,unlessallstudies sampledby chancelowbirefringence propagation directions (Fig. 3). Very low anisotropy (

<

0.25%) or isotropywasdetected fora varietyofNNE–NEorientedpaths be-neaththeCentralAtlantic(Garneroetal.,2004).Thiswouldimply extremelylowstrainsinthisregion,sincethereisenoughvariation in the orientation of the paths to ensure that not all will sam-ple an apparent isotropydirection. Alternate explanationsfor the observed apparentisotropy and/or low delaytimes wouldbe the

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activationofaprocess,likedynamicrecrystallization,whichwould limit CPOconcentration (Signorelli and Tommasi, 2015), or spa-tialvariationinthe orientationof theCPOdueto changesinthe flowpattern,leadingtodestructiveinterferenceandlowintegrated anisotropy along the path (or around it,since sensitivitykernels forSdiffandScSare wideinthelowermost mantle;Sieminskiet al., 2009). We favorthe second hypothesis, sincerecrystallization disperses, but does not randomize the CPO, and only an almost isotropicCPOwouldproducesuch lowbirefringence foravariety ofpropagationdirections.Thesamereasoningmayexplainthelow “average”birefringence sampledintheother studies.The NE–SW changeinSHfasterthanSVtoSV fasterthenSHobservedinthe southern Pacific(Ford etal., 2006) isconsistent witha transition fromflowparalleltotheCMBtoupwelling(Fig.8)attheboundary ofthePacificLLSVP.

Morerecent studies show that: (i) thefast polarization direc-tion of ScS waves in D is often inclined relative to the CMB and(ii) waves withdifferent propagationazimuths samplingthe same region in D display markedly differentanisotropy signals. Azimuthalvariationsinanisotropy(bothorientationofthefast po-larizationanddelaytime)and/orinclinedfastS-wavepolarizations were reported,for instance,below the Caribbean(Garnero etal.,

2004; Maupinetal.,2005; Nowacki etal., 2010),Siberia(Wookey and Kendall, 2008), the Northern Paciﬁc (Wookey et al., 2005), thesouthernedgeoftheAfricanLLSVP(Cottaar andRomanowicz,

2013),andthenorthernedgeofthePermlowS-waveanomaly be-neath Russia(LongandLynner, 2015). Theseresultsindicate that anisotropy in D does not have VTI symmetry, consistently with the present model predictions (Figs. 3, 5, 7, 8). They also con-strainthemaximumaveragebirefringenceinDto

<

2%ingeneral, thoughupto4%ofbirefringenceisneededtoexplainthe observa-tionsatthesouthernedgeoftheAfricanLLSVP.

Strong variations in the intensity of the S-waves polariza-tion anisotropy as a function ofthe propagation direction (back-azimuth)are predictedinall models (Figs.3,5,6,7, 8). FastScS polarizationsinclined by

>

25◦ to thehorizontal arepredicted in horizontal shearing models at low shear strains (

<

2, Fig. 5), in 3D flowregimes inwhichhorizontalshearing is accompaniedby extension in the vertical direction(transtension, Fig. S2), andin downwellingorupwelling flows (Figs.7 and8). InclinedScS fast polarizations are also observed in the horizontalsegment ofthe downwellingcornerflowstreamlineupto200kmaway fromthe change in flow direction(Fig. 7). In thesedomains, both the in-clinationofthefastpolarization andtheintensityofthe birefrin-genceshowsharpchangesasafunctionoftheback-azimuth,with bothnearhorizontalandinclinedfastpolarizationsassociatedwith eitherhighorlowbirefringence.

FastScS polarizations inclined by 46◦ fromthe transverse di-rectionand 4% anisotropy measured atthe southern edge ofthe AfricanLLSVP are consistent withthe anisotropy modeled foran upwelling ﬂow (Fig. 8), if propagation directions are at low an-gle to the limit of the LLSVP as inthe Cottaar and Romanowicz (2013) study,sincethisresultsinsamplingoftheupwelling struc-turealongalargesegmentofthepathwithpropagationdirections thatproducefastScSpolarizationsinclined by40–50◦ tothe hor-izontal. A path sampling at low angle the transition between a downwelling and shear parallel to the CMB (Fig. 7) might also explain the inclined polarizations detected beneath the northern Paciﬁc(Wookeyetal.,2005).

Aspatiallyvaryingﬂowpattern,withpaths samplingthe tran-sition between downwelling ﬂows and shearing parallel to the CMBindifferentdirectionsandpositionsand,hence,fordifferent lengths(Fig.7)mightexplainthechangesininclinationofthefast polarization fromsubhorizontal toup to45◦ asa functionofthe back-azimuthoftheScS wavesbeneathSiberiaandtheCaribbean (WookeyandKendall,2008; Nowackietal.,2010).

Thelocalbirefringencepredictedbythemodelsformany prop-agationdirections,inparticularforpropagationparalleltotheslab strike(

>

4%),shouldneverthelessproducedelaytimessigniﬁcantly higher then those measured. As discussed in the previous sec-tion, thelower delay timesmeasured inthe seismicstudies may by explainedby the fact that long-periodScS waves average the anisotropy over a large volume (the anisotropic sensitivity ker-nels width encompasses most of the thickness of D, Sieminski etal.,2009).Variationsinthedeformationpatternbothalongand aroundthepathwillresultinalowerintegratedsplitting.Forward models of ScS splitting performed usingboth ray-theory and3D generally-anisotropic simulations ofScS wavesat thefrequencies of the observations, but with no anisotropy outside the lower-mostmantleshow indeedthat even forhomogeneous anisotropy in150 km-thicklayerinD,ﬁnite-frequencymodelspredictdelay times on average 1.5 times lower than ray-theory (Nowackiand Wookey,2016).

5.2.3. DiscrepancybetweenSKSandSKKSsplitting

Discrepancy in splitting for SKS-SKKS records for the same earthquake-stationpairhasbeenusedtoprobeseismicanisotropy in D, since these waves have similar paths in the upper man-tle, butdifferentones inD (piercing points ofSKSandSKKS at the CMBareseparated by

∼

1000kmandincidenceangles differ by

>

20◦).AnalysisofthemodeledS-wavepolarizationanisotropy for horizontal simple shear (Fig. 5) shows that for shear strains

>

2 fastpolarization directionsin D for both SKSandSKKS are similar, being mainly close to horizontal. However, at low shear strains, for vertical ﬂow, and in the vicinity of changes in ﬂow direction, the fast polarization direction of SKS andSKKS waves differby

>

20◦forawiderangeofpropagationdirections(Figs.5,

7,8).Inmostcases,whenadiscrepancyinbirefringencebetween the two waves is present, SKKS shows a higher inclination of thefastpolarization relativelytothe horizontalthan SKS(Figs.5,

7,8),butindownwellingflows,somepropagationdirectionsresult in more inclined SKS fast polarizations than SKKS ones (Fig. 7). Most models also show significant variations in the intensity of theanisotropysampledbythetwowaves.Thusthepresent mod-els suggestthatevenhomogeneousdeformation fieldsmight pro-duce discordant SKS–SKKS splittingin D. However, noneof the presentmodelsproducesresultsequivalent totheobservationsin theeasternPacific,inthevicinityofthePermanomaly,orbeneath SE Asia where strong SKKS splitting with inclined fast polariza-tions is accompanied by almost null SKS splitting (Long, 2009; Long andLynner, 2015; Roy et al., 2014) and very few propaga-tiondirectionsinaupwellingflowdoresultinnullSKKSsplitting butsignificantSKSsplittingasalsoobservedinthevicinityofthe Perm anomaly (Longand Lynner,2015). Suchobservations might be explainedby changesintheflow patternbetweentheregions sampledbythetwowaves,thatisatascale

<

1000km.

However, the present modelsbring a series ofquestions con-cerning theinterpretationofSKSandSKKSdataintermsof seis-mic anisotropyinD.First,themodelspredictthatSKKSandSKS should, formostflow configurationsandwavepropagation direc-tions, sample significant anisotropy in D. Yet observational evi-dence for such anisotropy is rare.Splitting in D should deviate SKSandSKKSinitialpolarizationsfromthesource-receiverplane. Indeed,analysisofalargeglobalSKS–SKKSdatasethighlightsthe existence of such deviations, which are in general stronger for SKKSthanSKSandmostlyobservedforwaveswithpiercingpoints at CMBin higherthan average velocity domains, suggestingthat they may result from anisotropy in D due to PPv CPO, as the one modeled here (Restivo and Helffrich, 2006). Yet, this study also showed that such deviations characterize not morethan 5% of the analyzed dataset and that discrepancy between SKS and SKKS splitting is even more rare. Moreover, all studies describe

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a few discrepant SKS–SKKS pairs associated with a large num-ber of coherent pairs with paths sampling nearby regions in D (e.g., Restivo and Helffrich, 2006; Long, 2009; Roy et al., 2014; LongandLynner,2015.Altogether,theseobservationssuggestthat inmostcasesD anisotropyisnoteffectivelysampledbySKSand SKKS phases. Apossible explanation maycomefrom the consid-eration offinite-frequency effects. Calculationof anisotropic sen-sitivitykernels for SKS andSKKS shows that they have a strong sensitivityina50–200 kmwideconicdomainintheupper man-tle,but a weak sensitivitydistributed overa 600–1000 km wide domainin D (Favier and Chevrot,2003; Sieminskiet al., 2009). Thisimpliesthat,eveniflocallythebirefringencesampledbythese wavesis strong(up to 7–8%,Fig. 3), SKSandSKKS will only ac-cumulatesignificant splitting in D if the anisotropy is coherent withinmostofthis600–1000kmwide zone.Lateralvariationsin flowpatternatthesescalesmightalsoaccount fortheratherlow delay times measured for the discordant SKS–SKKS pairs, which imply that the maximum anisotropy levels sampled by S-waves withsteeplydippingpathsinD are

<

2%.

6. Conclusion

ForwardmodelsofCPOandseismicanisotropydevelopmentin aD layercomposedby70%ofPPvand30%ofMgObasedonthe mostrecent atomic scale models of the viscoplastic deformation ofthesetwophasespredictseismic anisotropyinD withan or-thorhombicsymmetry, whichproduces simultaneously radialand azimuthalanisotropy components.Independentlyofthe choiceof inputparametersforthePPvdeformation(twinningactive ornot, difference in CRSS for [100] and [001] glide on the (010) plane ornot), the present models indicatethat thepolarization offast S-waves is often subparallel to the direction of flow in D, but that this relation is lost at low finite strains and in the vicinity ofchanges intheflowpattern. TheintensityoftheS-waves bire-fringencevariesstronglyasafunctionofthepropagationdirection, evenforaconstantincidenceanglerelativelytotheflowplane.For steadysimpleshear,themaximumbirefringenceincreasesfrom3% atashearstrainof1to6%atashearstrainof10.Suppressionof twinninginthe modelsresultsinfasterstrenghtening ofthePPv CPOwithincreasingstrainand,hence,inhighermaximumseismic anisotropiesatanygivenfinitestrain.

The present models with twinning may explain most obser-vations of seismic anisotropy in D, in particular ScS splitting dataindicating inclined (relativelytothe CMB)fastpolarizations, which may be produced by either vertical flows (down- or up-wellings), weak horizontal shearing, transtension, or within the horizontalsegmentofthedownwellingcornerflowstreamlineup to200 kmaway fromthechangein flowdirection. Althoughthe fast-polarizationorientations observedusing a wide varietyof S-waves maybe explained by simple flow patterns as the models presentedhere,theobservedlowapparentbirefringence(

<

2%)for S-waves propagating at both low and highangle to CMB cannot be reconciled with the presentmodel predictions (and withany CPO-inducedanisotropymodel,independentlyoftheslipsystems strengths used), unless ﬁnite-frequency effects and variations in the ﬂow patterns along and around the waves paths, that is, at scales

1000 km, are considered. Both effects also need to be invokedto explain whyonly in rarecases SKSand SKKS sample signiﬁcantanisotropyinD.

Yet, in presence of spatially varying ﬂow directions in D at scales below or equivalent to the path lengths in D, which is probably the most common situation on Earth, as suggested by mantlecirculation andconvection models (e.g.,McNamara et al.,

2002; Tackley, 2011; Nowacki et al., 2013, Nowacki andWookey,

2016),S-wavesplittingmeasurementsdonotrecordasimpleway theﬂowdirectionsinD.ForwardmodelingoftheCPOandelastic

anisotropyfieldsproducedbydifferentflowpatternsinthemantle followed by finite-frequencycalculations of the resulting seismic anisotropy seemthus anessential tool foradvancingtowards the ultimategoalofusingseismicanisotropydatatomapdeformation in thedeep Earth. The models presented hereare a first step in thisdirection,astheyconstraintherelationbetweenthe deforma-tion historyand the evolutionof elastic anisotropy of amaterial volumeofaPPv-richD layer.

Acknowledgements

We thankRicardoLebensohnandCarlosTomé formakingthe codeVPSC7c,whichincludesmostofthelastdevelopmentsin vis-coplastic self-consistent modeling, freely available, S. Stackhouse forassistance indeﬁning elasticconstants offerropericlase based onWuetal. (2013) work,S.Zhangforprovidingelasticconstants for PPvas a function of composition, pressure, andtemperature, and S. Chevrot for discussions on ﬁnite-frequency and noise ef-fectsonthemeasurementofseismicanisotropyinD.Twohelpful andthroughoutreviewsare alsoacknowledged.WorkinLillewas supported by fundingfromthe European ResearchCouncil under theSeventh FrameworkProgramme (FP7), ERCgrant N◦290424 – RheoMan.

Appendix A. Supplementarymaterial

Supplementarymaterialrelatedtothisarticlecanbefound on-lineathttps://doi.org/10.1016/j.epsl.2018.03.032.

References

Amodeo,J.,Carrez,P.,Devincre,B.,Cordier,P.,2011.MultiscalemodellingofMgO plasticity.ActaMater. 59,2291–2301.

Batchelor, G.K.,1967.An IntroductiontoFluidDynamics. CambridgeUniv.Press, NewYork.

Boioli,F.,Carrez,P.,Cordier,P.,Devincre,B.,Gouriet,K.,Hirel,P.,Kraich,A.,Ritterbex, S.,2017.PureclimbcreepmechanismdrivesﬂowinEarth’slowermantle.Sci. Adv. 3,e1601958.

Borgeaud,A.F.,Konishi,K.,Kawai,K.,Geller,R.J.,2016.Finitefrequencyeffectson apparentS-wavesplittingintheDlayer:comparisonbetweenraytheoryand full-wavesynthetics.Geophys.J.Int. 207,12–28.

Bullen, K.E., 1949. Compressibility–pressure hypothesis and the Earth’s interior. Mon.Not.R.Astron.Soc. 5,355–368.

Carrez,P.,Goryaeva,A.,Cordier,P.,2017.Predictionofmechanicaltwinningin mag-nesium silicate post-perovskite.Sci.Rep.https://doi.org/10.1038/s41598-017 -18018-1.

Chang,S.J.,Ferreira,A.M.,Ritsema,J.,vanHeijst,H.J.,Woodhouse,J.H.,2014.Global radiallyanisotropicmantlestructurefrommultipledatasets:areview,current challenges,andoutlook.Tectonophysics 617,1–19.

Cordier,P.,Amodeo,J.,Carrez,P.,2012.ModellingtherheologyofMgOunderEarth’s mantlepressure,temperatureandstrainrates.Nature 481,177–180.

Cottaar,S., Romanowicz,B.,2013.Observationsofchanginganisotropyacrossthe southernmarginoftheAfricanLLSVP.Geophys.J.Int. 195,1184–1195. DeWit,R.W.L.,Trampert,J.,2015.Robustconstraintsonaverageradiallower

man-tleanisotropyandconsequencesforcompositionandtexture.EarthPlanet.Sci. Lett. 429,101–109.

Favier,N.,Chevrot,S.,2003.Sensitivitykernelsforshearwavesplittingintransverse isotropicmedia.Geophys.J.Int. 153,213–228.

Ford,S.R.,Garnero,E.J.,McNamara,A.,2006.Astronglateralshearvelocitygradient andanisotropyinthelowermostmantlebeneaththesouthernPaciﬁc.J. Geo-phys.Res. 111,B03306.

Fouch,M.J.,Fischer,K.M.,Wysession,M.E.,2001.Lowermostmantleanisotropy be-neaththePaciﬁc:imagingthesourceoftheHawaiianplume.EarthPlanet.Sci. Lett. 190,167–180.

Garnero, E.J., Lay, T., 1997. Lateral variations in lowermost mantle shear wave anisotropy beneath the North Paciﬁc and Alaska. J. Geophys. Res. 102, 8121–8135.

Garnero,E.J.,Lay,T.,2003.Dshearvelocityheterogeneity,anisotropyand disconti-nuitystructurebeneaththeCaribbeanandCentralAmerica.Phys.EarthPlanet. Inter. 140,219–242.

Garnero,E.J.,Moore,M.M.,Lay,T.,Fouch,M.J.,2004.Isotropyorweakvertical trans-verseisotropyinDbeneaththeAtlanticOcean.J.Geophys.Res. 109,B08308. Goryaeva, A.M., Carrez, P., Cordier, P., 2015a. Modeling defects and plasticity

in MgSiO3 post-perovskite: Part 1—generalized stacking faults.Phys. Chem.

(13)

Goryaeva, A.M.,Carrez, P., Cordier,P., 2015b.Modeling defectsand plasticity in MgSiO3post-perovskite:Part2—screwandedge[100]dislocations.Phys.Chem.

Miner. 42,793–803.

Goryaeva, A.M.,Carrez, P., Cordier, P.,2016. Low viscosityand high attenuation inMgSiO3post-perovskiteinferredfromatomic-scalecalculations.Sci.Rep. 6,

34771.

Goryaeva, A.M., Carrez, P., Cordier, P., 2017. Modeling defects and plasticity in MgSiO3post-perovskite:Part3—screwandedge[001]dislocations.Phys.Chem.

Miner. 44,521–533.

Hirose,K.,Wentzcovitch,R.,Yuen,D.A.,Lay,T.,2015.Mineralogyofthedeep man-tle–thepost-perovskitephaseanditsgeophysicalsigniﬁcance.In:Treatiseon Geophysics,pp. 85–115.

Kendall,J.M.,Silver,P.G.,1996.Constraintsfromseismicanisotropyonthenatureof thelowermostmantle.Nature 381,409.

Komatitsch,D.,Vinnik,L.P.,Chevrot,S.,2010.SHdiff–SVdiffsplittinginanisotropic Earth.J.Geophys.Res. 115,B07312.

Kraych,A.,Carrez,P.,Cordier,P.,2016.OndislocationglideinMgSiO3bridgmanite

athigh-pressureandhigh-temperature.EarthPlanet.Sci.Lett. 452,60–68. Kustowski,B.,Ekström,G.,Dziewo ´nski,A.M.,2008.Anisotropicshear-wavevelocity

structureoftheEarth’smantle:aglobalmodel.J.Geophys.Res. 113,B06306. Lay,T.,Young,C.J.,1991.AnalysisofseismicSVwavesinthecore’spenumbra.

Geo-phys.Res.Lett. 18,1373–1376.

Lay,T.,Williams,Q.,Garnero,E.J.,1998.Thecore–mantleboundarylayeranddeep Earthdynamics.Nature 392,461.

Lebensohn,R.A.,Tomé,C.N., 1993.A self-consistentanisotropicapproachforthe simulationofplasticdeformationandtexturedevelopmentofpolycrystals– ap-plicationtozirconiumalloys.ActaMetall.Mater. 41,2611–2624.

Lebensohn,R.A.,Tomé,C.N.,PonteCastañeda,P.,2005.Improvingtheself-consistent predictionsoftexturedevelopmentofpolycrystalsincorporatingintragranular ﬁeldﬂuctuations.Mater.Sci.Forum 495–497,955–964.

Long,M.D.,2009.ComplexanisotropyinDbeneaththeeasternPaciﬁcfromSKS– SKKSsplittingdiscrepancies.EarthPlanet.Sci.Lett. 283,181–189.

Long,M.D.,Lynner,C.,2015.Seismicanisotropyinthelowermostmantlenearthe PermAnomaly.Geophys.Res.Lett. 42,7073–7080.

Mainprice,D., Hielscher, R., Schaeben,H., 2011. Calculating anisotropic physical propertiesfromtexturedatausingthe MTEXopensourcepackage.In:Prior, D.J.,Rutter,E.H., Tatham,D.J.(Eds.), DeformationMechanisms,Rheologyand Tectonics:Microstructures,MechanicsandAnisotropy.Geol.Soc.(Lond.)Spec. Publ. 360,175–192.

Maupin,V.,1994.OnthepossibilityofanisotropyintheDlayerasinferredfrom thepolarizationofdiffractedSwaves.Phys.EarthPlanet.Inter. 87,1–32. Maupin,V.,Garnero,E.J.,Lay,T.,Fouch,M.J.,2005.AzimuthalanisotropyintheD

layerbeneaththeCaribbean.J.Geophys.Res. 110,B08301.

McNamara,A.K., van Keken,P.E.,Karato, S.-i.,2002. Developmentof anisotropic structureinthe Earth’s lowermantleby solid-stateconvection.Nature 416, 310–314.

Merkel,S.,McNamara,A.K.,Kubo,A.,Speziale,S.,Miyagi,L.,Meng,Y.,Wenk,H.R., 2007. Deformationof(Mg, Fe) SiO3 post-perovskite and D anisotropy.

Sci-ence 316,1729–1732.

Metsue,A.,Carrez,Ph.,Mainprice,D.,Cordier,P.,2009.Numericalmodelingof dis-locationsanddeformationmechanismsinCaIrO3andMgGeO3post-perovskites

– comparison with MgSiO3 post-perovskite. Phys. Earth Planet. Inter. 174,

165–173.

Miyagi,L.,Nishiyama,N.,Wang,Y.,Kubo,A.,West,D.V.,Cava,R.J.,Duff,T.S.,Wenk, H.R.,2008. Deformation and texture developmentin CaIrO3 post-perovskite

phaseupto6GPaand1300K.EarthPlanet.Sci.Lett. 268,515–525. Miyagi,L.,Kanitpanyacharoen,W.,Kaercher,P.,Lee,K.K.,Wenk,H.R.,2010.Slip

sys-temsinMgSiO3post-perovskite:implications forD anisotropy.Science 329, 1639–1641.

Molinari,A.,Canova,G.R.,Ahzi,S.,1987.Aself-consistentapproachofthelarge de-formationpolycrystalviscoplasticity.ActaMetall. 35,2983–2994.

Monteiller,V.,Chevrot,S., 2010.Howtomakerobustsplittingmeasurementsfor single-station analysisand three-dimensional imagingof seismicanisotropy. Geophys.J.Int. 182,311–328.

Niwa,K.,Miyajima,N.,Seto,Y.,Ohgushi,K.,Gotou,H.,Yagi,T.,2012.Insitu obser-vationofshearstress-inducedperovskitetopost-perovskitephasetransitionin CaIrO3andthedevelopmentofitsdeformationtextureinadiamond-anvilcell

upto30 GPa.Phys.EarthPlanet.Inter. 194,10–17.

Nowacki,A.,Wookey,J.,Kendall,J.M.,2010.Deformationofthelowermostmantle fromseismicanisotropy.Nature 467,1091–1094.

Nowacki,A.,Walker,A.M.,Wookey,J.,Kendall,J.M.,2013.Evaluatingpost-perovskite asacauseofDanisotropyinregionsofpaleosubduction.Geophys.J.Int. 192, 1085–1090.

Nowacki, A., Wookey, J., 2016. The limits ofray theorywhen measuring shear wavesplittinginthelowermostmantlewithScSwaves.Geophys.J.Int. 207, 1573–1583.

Panning,M.,Romanowicz,B.,2006.Three-dimensionalradiallyanisotropicmodelof shearvelocityinthewholemantle.Geophys.J.Int. 167,361–379.

Panning,M.P.,Leki ´c,V.,Romanowicz,B.A.,2010.Importanceofcrustalcorrections inthe developmentofanew globalmodelofradialanisotropy. J.Geophys. Res. 115,B12325.

Reali,R.,Boioli,F.,Gouriet, K.,Carrez,P.,Devincre,B.,Cordier,P.,2017. Modeling plasticityofMgOby2.5Ddislocationdynamicssimulations.Mater.Sci.Eng. A 690,52–61.

Restivo,A.,Helffrich,G.,2006.Core–mantleboundarystructureinvestigatedusing SKSandSKKSpolarizationanomalies.Geophys.J.Int. 165,288–302.

Roy,S.K.,Kumar,R.,Srinagesh,D.,2014.Upperandlowermantleanisotropyinferred fromcomprehensiveSKS andSKKSsplittingmeasurementsfromIndia.Earth Planet.Sci.Lett. 392,192–206.

Sieminski, A., Trampert, J., Tromp, J., 2009. Principal component analysis of anisotropicﬁnite-frequencykernels.Geophys.J.Int. 179,1186–1198. Signorelli,J., Tommasi,A.,2015.Modelingtheeffectofsubgrainrotation

recrys-tallizationontheevolutionofolivinecrystalpreferredorientationsinsimple shear.EarthPlanet.Sci.Lett. 430,356–366.

Tackley,P.,2011.Livingdeadslabsin3-D:thedynamicsofcompositionally-stratiﬁed slabsenteringa“slabgraveyarDabovethecore–mantleboundary.Phys.Earth Planet.Inter. 188,150–162.

Thomas,C.,Kendall,J.-M.,2002.ThelowermostmantlebeneathnorthernAsia—II. Evidenceforlower-mantleanisotropy.Geophys.J.Int. 151,296–308.

Thomas,C.,Wookey,J.,Brodholt,J.,Fieseler,T.,2011.Anisotropyascauseforpolarity reversalsofDreﬂections.EarthPlanet.Sci.Lett. 307,369–376.

Thurel,E.,Cordier,P.,2003.Plasticdeformationofwadsleyite:I.High-pressure de-formationincompression.Phys.Chem.Miner. 30,256–266.

Tomé, C.N., Lebensohn,R.A., Kocks,U.F.,1991. A modelfortexturedevelopment dominatedbydeformationtwinning:applicationtozirconiumalloys.Acta Met-all.Mater. 39,2667.

vanderHilst,R.D.,deHoop,M.V.,Wang,P.,Shim,S.-H.,Ma,P.,Tenorio,L.,2007. Earth’score–mantleboundaryregionseismostratigraphyandthermalstructure. Science 315,813–816.

Vinnik,L.P.,Farra,V.,Romanowicz,B.,1989.ObservationalevidencefordiffractedSV intheshadowoftheEarth’score.Geophys.Res.Lett. 16,519–522.

Walker, A.M., Forte, A.M., Wookey, J., Nowacki, A., Kendall, J.-M., 2011. Elastic anisotropyofD predictedfromglobalmodelsofmantleﬂow.Geochem. Geo-phys.Geosyst. 12,1–22.

Walker,A.M.,Dobson,D.P.,Wookey,J.,Nowacki,A.,Forte,A.M.,2017.Theanisotropic signaloftopotaxyduringphasetransitionsinD.Phys.EarthPlanet.Inter. 276, 159–171.

Wenk,H.-R.,Speziale,S.,McNamara,A.K.,Garnero,E.J.,2006.Modelinglower man-tle anisotropydevelopmentinasubductingslab.EarthPlanet.Sci.Lett. 245, 302–314.

Wenk,H.-R.,Armann,M., Burlini,L.,Kunze, K.,Bortolotti,M., 2009.Largestrain shearingofhalite:experimentalandtheoreticalevidencefordynamictexture changes.EarthPlanet.Sci.Lett. 280,205–210.

Wenk,H.-R.,Cottaar,S.,Tomé,C.N.,McNamara,A.,Romanowicz,B.,2011. Deforma-tioninthelowermostmantle:frompolycrystalplasticitytoseismicanisotropy. EarthPlanet.Sci.Lett. 306,33–45.

Wookey,J.,Kendall,J.M.,Rümpker,G.,2005.Lowermostmantleanisotropybeneath theNorthPaciﬁcfromdifferentialS-ScSsplitting.Geophys.J.Int. 161,829–838. Wookey, J.,Kendall,J.M.,2008. Constraintsonlowermostmantlemineralogyand fabric beneath Siberia from seismic anisotropy. Earth Planet. Sci.Lett. 275, 32–42.

Wu,Z.,Justo,J.F.,Wentzcovitch,R.M.,2013.Elasticanomaliesinaspin-crossover system:ferropericlaseatlowermantleconditions.Phys.Rev.Lett. 110,228501. Wu,X.,Lin,J.F.,Kaercher,P.,Mao,Z.,Liu,J.,Wenk,H.R.,Prakapenka,V.B.,2017.

Seis-micanisotropyoftheDlayerinducedby(001)deformationofpost-perovskite. Nat.Commun. 8,14669.

Yamazaki,D.,Yoshino,T.,Ohfuji,H.,Ando,J.I.,Yoneda,A.,2006.Originofseismic anisotropyinthe D layerinferred fromshear deformationexperiments on post-perovskitephase.EarthPlanet.Sci.Lett. 252,372–378.

Zhang,S.,Cottaar,S.,Liu,T.,Stackhouse,S.,Militzer,B.,2016.High-pressure, temper-atureelasticityofFe- andAl-bearingMgSiO3:implicationsfortheEarthslower