[PDF] Inner core differential rotation inferred from antipodal seismic - HIGP

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PhysicsoftheEarth andPlan etaryInterio rs

journalhomepage:www.elsevier.com/locate/pepi

Innercoredi

ff erentialrotationinferred fromantipodalseismicobservat ions

SeijiTsuboi

a, ⁎ ,Rhet tButler b a

CenterforEarthI nformationS cienceandTechno logy,JapanAgencyforMarine-EarthSciencean dTechnology, Yokohama236-0001, Japan

b HawaiiInstitut eofGeophysicsandPlanetology,Univ ersityofHawa iiatManoa,Hono lulu,HI96822,USA

ABSTRACT

TheEart h'sInnerCoremayrot ateatadi

ff

erentspeedtha nEarth'sc rust-mantle. Weuseobservations forantipodalearthquakeandstationpairs toex aminethe

arrivaltimeshiftoft hewhispering-g allerywav ewhichpropag atesta ngentiallyalongthetopoftheInnerC ore.Observation softhese wavesforearthquakeswhich

occurredatthesamelo cationrev ealthatt raveltimesvary by ≥

0.2soverthe past 20years.Wepropo sethat thesetimeshiftsa recaused bytheinteractiono faz ero

rigiditypatch(la teralheterogeneity)at theInnerCoresurfacewiththe InnerCoredi ff erentialrotation. Thesimplestinterpretationinfersarotation rate of0.05°/

year,whichison eorderof magn itudesmaller thanthoserepo rtedbypreviou sstudies.Ourresultmayalso giveconstrainttothe provenanceo fazerorigiditypatch

attheInn erCores urface.TheFresnelz onecoverage ofwhispering-galleryPKIIKP+...an tipod almeasurementsben eaththeInnerCore boundaryextendover~60%

ofthebou ndarysu rface,incontrasttoPKiKP-PKPpaths whichindividuallymeasure specu larreflections(~1Hz)fromthetopo ftheICBo ver Fresnelzoneseac h

encompassing0.002%oftheInner-Out erCoreboundary.

1.Introduc tion

Thedi

ff erentialrotationo ftheEarth'sInnerCorewithrespect tothe Mantlehasbeencontroversia lsinceit sdis covery(SongandRichards ,

1996;Suetal. ,1 996;Creager,1997;LaskeandMasters ,1999;Vidale

etal .,2000;Zhangetal., 200 5;Wen,2006 ;Caoetal.,2 007 ;Waszek etal .,2011;Tkalčićetal .,2013).Observa tionsapparentlycontra- dictorytodi ff erentialICrotationha vebeen raisedbyMäkinenaand Deuss(2011)andYaoetal.( 201 9).Theq uest ionofinnercorerotation isimport antforunderstanding thegrowt handstructureoftheICover time(e.g. ,Loper,1983;LoperandRobert s,1981;ListerandBuffett,

1995;Huguetetal.,20 18),conv ectionintheOuterCore,andthe

geodynamoresponsibleforEarth'smag neticfield(e.g.,Gubbins,1977,

1981;Loper,1978;GlatzmaierandRoberts,1995;Aubertand

Dumberry,2011).

Hereweex tend ourantipodalobs ervationsof thewhispering-gal- lerywave( ButlerandTsuboi,201 0andSupplement) andreportonthe timeshiftof thiswaveo verthepas t20yea rs.Thesimplestint er- pretationforourobservedt imeshiftisbyt heInnerCored i ff erential rotationwitha0.05°/year rotation rate, whichdiscloseslateralhet- erogeneityatthetopof theIC.Non etheless,o therexplanat ionsare considered.Sincethewhispering-gall erywavepropagatesa tthetop of theInnerC ore(seeFig.1) - tangentialtotheverticalradialando vera raysurfac eencompassingnearly60 %oftheInnerCore - itprovides corroborationofInnerCorerotationan dlatera lheterogeneityin- dependentofpreviousobserva tionsof PKiKP,andPKP BC .

2.Antipodalo bservations

Antipodalobservationshavethepo tentialtoilluminatestructurein theInnera ndOuterCo reregionoftheEa rth(Rial,1979;Rialand Cormier,1980;Butler,1986;Niuan dChen,2008 ).In201 0wefo unda pairofeart hquakes( adoublet)inTonga,recordeda tTAM,Ta - manrasset,Algeria(seeButlerandTsuboi,20 10,Su pplementalmate- rial).Thesubstant iala mplificationandphaseshiftforPKP AB withre- specttoPKIKPsho wnintheses eismog ramsdemonstrat estheir close proximitytotheant ipode.Bot heventsex hibitthesamePKP AB -PKIKP di ff erentialtimeof113. 2stowit hin0.1s, indicatingthesameant i- podaldistance. Thecross-correlationmeasurementofg ood nessoffit r 12 =0. 97overa130swin dowextending fromPKIKP andthrough PKP AB. Inthis observedwav eform,PKIIKP(asinglereflec tionwithin theInnerC oreattheInner- OuterCoreB oundary ,IOCB)c omesabout

32safter PKIKP( asdeterminedbyta u-P method(Crotwelletal.,1999 )

forPREMan dIASPEI91 ),whichrepresentsa "whisperinggallery"of energypropagat ingalongtheboundary(Fig.1).After8 yearsfrom discovery,wehavecheckedifathirdeven thad occurredinthes ame region,conferringat ripletofantipodalobserva tion s.Weactua llyfoun d thattherewasa neventin2 011,which occurreda tthesameregio n withalmos tthesamemagnitude( Supplementa ryTableS1). Thisthird eventalsosho wssubstantialan tipodalamplifi cationforPKP AB with respecttoPKIKP,appropria tePKP AB phaseshifts,iden ticalPKP AB - PKIKPtimin gof113.2s ,andco rrelationwiththedoublet (Fig.2). Wemod eledthedatainFig.2byus ingthespectral-el ementmethod (SEM)asare fer ence( KomatitschandVilotte,1998;Komatitschetal., https://doi.org/10.1016/j.pepi.2020.106451 Received12September20 19;Receiv edinrevisedform21 February2020;Accepted2 2February2020 ⁎

Correspondingauthor.

E-mailaddress:tsuboi@jamstec.go.jp(S.Tsuboi).

2002;Tsuboietal.,20 03;Komatitschetal.,2005)tocomputesynthetic

seismogramsaccurateupto3.5s.Theiniti almodeluse dincor porate sa simplePREMmodel( DziewonskiandAndersonDziewonskiandAnderson,

1981).Th esyntheticseismogr amshowsarrivalofPK IIKPatantipodal

stationwith smalleramplitudethan observation,which maysuggestthat theIOCBre gionisnotm odeledwellwiththesi mplePRE Mmode l.

3.Times hiftofwhispe ring-gallerywave

Forthean tipodal( ~180°)TAMtripletinFig.2,wec alc ulatecross- correlationofPKIKParrivalsforeach eventpair,( i.e., 1992-2001,

1992-2011,and2001-2011)andshift thetimeseriestoa lignPKIKP

phases.Thenwereadtimes hiftso farriv alsofPKIIKP manuall y,which

Fig.1. Principalantipodal raysurfacesareshownin

crosssection.PKIKP (black)travelsaraypathal ong the diametralaxisbetweenearthqu akeandseismics tation, butisnot ant ipodallyfocu sed.PKP-AB(blue)traverses theD"regio natthe baseoftheMa ntlean dtheupper

OuterCore.PKP-C

di ff (red)di ff ractsaroundtheIn ner Coreatthebas eofthe OuterCo re.PKIIKP(green)enters theInnerC oreandreflectso ncebeneatht hetopofthe InnerCore.Thewhis pering-gallerya rrival s(...PKIIIKP +PKIIIIP+...)tra velbetweenPKIIKPandPKP-C di ff ray surfaces.(Forinterpretationo fthereferencestoc olorin thisfigure legend,thereaderisreferred tothewebver- sionofthisart icle.)

Fig.2. (A)Broadba ndverticalseismogramsfortriplet

events,TAM-2011(bl ue),TAM-2001(red)andTAM-

1992(black),are plotted.Eachvelocityseis mogramis

alignedtothearrivalof PKIKPphase.ThePKIIKP phaseis highlightedwithindottedwindo w.Synt heticvelocity seismogramofPREMmodelforevent TAM-19 92isals o plotted(green).Timeisexpres sedrelativetoearthquake origintimealign edtoPKIKPpeak. (B)Detailofantipod al tripletsforTAMarepl ottedfor velocity .Arrivalt imesof

PKIIKPphas e(firsttrou ghwithindottedwindo w)are

readataro und32 safterthePKIKParrival.(For inter- pretationofthereferencestoc olorint hisfigure legend, thereaderis referredtothewebvers iono fthis article.)

S.Tsuboi andR.Butler

areasso ciatedwiththewhispering-gallerywavesatt heveryto pofthe InnerCore.Wesho wcloseupPKIKPa ndPKIIKP arrivalsinFig.2b (detail).Between1992and2001 thetimeshiftis+0 .25sandbetween

1992and2011 thetimeshiftis+0. 2s.Becauseitisd i

ffi culttodes- ignatewhereexactlythePKIIKP wave startsandendsasawhispering gallery,tobeveryconservat ivewemeas uredt hefirstarriv alsofPKIIKP waves(veloc ity)showninFig.2attheinit ialfirstmo tion(trough) followingthePREMtime(32s) forPKIIKPat1 80°.Non etheless, awider spreadofdi ff erentialtimesandphase correlat ionsarealso apparent laterintothePKIIKP+PKIIIKP+...wa vetrain,whichd onotco nfo rm withasimple linea rtrend. Ifthe topICB structureisl aterally homogeneous,thentherewould beno timeshiftinPKIIKP. Hence,both lateral heterog eneity andro- tationarenecessaryto seeany"ro tation"e ff ectsinPKIIKP.Ifthere isno rotation,thenthelateralheterogen eitymustbe timedependen tto produceachangingtime shift. Hence,the~0.2stemporalanomal yisa minimumestimate - e.g .,ButlerandTsuboi(2 010)estimatedan anomalyof+0.5s,basedo ndisplac ementdata.As showninButlerand Tsuboi(2010),the antipod alannularray-surfaceforPKIIKPfo rthe Algeria-Tongaaxisencompassnearly60%o ftheICB.Beca usethear- rivalsofPKP AB relativetoPKIKPatTAMdon otshowt het imeshifts seeninthePKIIKP phas e,wemayas sume thatthesetempora lc hanges ofPKIIKParriva ls over20yearsarisesfromso metemporalchang esat theICB.

4.InnerCo redi

ff erentialrotationandh eterogeneityatthe IC surface Herewepro pos ethatthistemporalcha ngeinPKIIKPphasema y arisefromthedi ff erentialrotationo ftheInnerCorerelativetothe mantle.Itisgenerallytho ught that theInnerCoresurfacereveals quasi- hemisphericalstructure( TanakaandHamagu chi,1997;Niuan dWen,

2001).Wemaya ss umethatd uetotheeasterndirection ofinner-core

di ff erentialrotation, theannularPKIIKPpropagationpath atthesu rface oftheInn erCoreisl aterallyheterog eneous-e.g., PKiKP-PKIKPd i ff er- entialtimesarefast erinthequ asi-east ernhemisphere(40°E-180° E, surfacelongitudepro jectedtoICB)andslowerinthequas i-western hemisphere(180 °W-40°E),withrespecttothePREMmodel.Recentlyit alsohasbeenshowntha tsomeport ions ofthesurfac eoftheInnerC ore mayexhibital mostzero rigidity(Cormier,2015).Thislow rigid ity featureatthesurfac eoftheIn nerCore isalsoshownbystackedt races ofourstudy (Fig.3).Wehave su bstantially augmentedtheantipodal datasetintroduc edbyourprev iousstudy(ButlerandTsuboi,20 10), comprisingdiametralaxesbetween earthquakeandantipod alreceiving station(i.e.,Tonga-Algeria )from8earthquakest o39inthedistance range Δ >17 9°.Thishasenableddata sta ckingtoimpro vethesignal- to-noiseoftheinnercorearriva ls.Sta ckedantipo daldatafo rtheTon- ga-Algeriadiametralaxisares howninFig.3.Wemo delt hedatain Fig.3byus ingSEMforPREMand modifiedmod elVp4.Theworkin g modelVp4incorpora tesa liquid-liquidIOCB(Cormier,2015),anda liquid-soliddiscontinuityataradius of1100km,or~120kmbelowthe IOCB.Anunknown innercore arrivalinFig.3isfeat uredinVp4butnot PREM,whichsug geststha ttheremayexistaregionofveryslow, shear wavevelocity atthetopoftheInnerCore. Ifthe rigidityisz erointheselowshear velo cityregion s,t henwe mayassu methatthePwavespeedbecomes almost6.1 %slower,c on- sistentwiththePREMvelo citydecrea sebetweenthe Inneran dOuter Core(Cormier,2015).Theobserv ed0 .2sdelayofPKIIKPphas emaybe interpretedthattheP-wa vevelocitya longso meportionofPKIIKPray pathsurface becomes~6.1%sloweratthe ICB.Wemayass umethis portionisabout22km, whichis theraypathlengt hoverwhich a6. 1% P-wavevelocityred uction(solidtoliquid)res ultsina0.2sslower traveltimecomparedwit haP-wave velocityof11km/s. Becaus ethe diametralaxisbetweenTonga- TAMisnearlyeq uatorial ,a22kmpor- tionofPKIIKPraypa thcorrespo nds to~1°ro tationatthe surfaceofthe InnerCore.Chan gesinPKIIKPraypath (1992)projectedatt hesu rface oftheInn erCorea reshowninFig.4.Thus ,a1°rotatio nof theInner Coreover2dec adesisequiva lent toa0.05°/yrrate,which isa lmost6 to20times smaller rotation ratesthanreportedbypreviouss tudies (SongandRichard s,1996;Creager,1997;Zhangetal., 200 5).Since PKIIKPpropa gatesatthetopoftheInn erCore - tan gential tothever- ticalradialando veraraysurfaceen compassingmuc hoftheInner Core,itprovides corro borationofInnerCo rerotationindependentof PKP BC -PKIKPandPKiKP- PKIKPobservation s.

5.Discuss ion

Recently,WangandSo ng(2019)hasclaimed thatthedoublet earthquakesweobservedin2010a reno tlocatedatant ipod eofTAM andthatthePKIIKP phaseweobservedwa sgenerat edbys catteringof strongheterogeneitiesinthema ntlewedgeabovethesubdu ctin gTonga slabnearFiji.Theyu sedISCepicentersfo rourdo ublet andtheepi- centraldistancefor theseearthquakesfromstationTAMisl essthan

179.6°.InButlerandTsuboi(20 10),weha vec arefullyselect ed20

station-eventpairswithgoodsignal-to-no iseinthea ntipodal distance range179-180°ba sedonNEICorISCdistances.Wehav eshownthat thedoubl etreportedinButlerandTsuboi(20 10Supplement)exhibits substantialamplificationforPKP AB andotherphases withrespectto PKIKP(whic hisnotfocu sed) andshowthec haracteristic,additional π /

4phas eshiftpredictedfo rPKP

AB .Wea lso havecalculated thecorre- lationcoe ffi cientoftrac esaligned onPKIKPandPKP AB (r 12 =0.97) andconfirmedt hatthetwoeventscanbe regardedasdou bletevent.

WangandSo ng(2019)doesnotco nsiderPKP

AB amplificationand waveformsimilaritiesand rejectsthepossibilityof antipodallo cationof thedoubl et,whichisnotadecisiveargu ment.Thuswe su pposethatour statementofdoubletidentific ationa tantipodestillholds andwemay assumethatthelargea mplitudearriva lisreally PKIIKPphase. Althoughwehavediscussedasc at teringoriginoft hisphaseinthe SupplementalmaterialofButlerandTsuboi(20 10)weco nsiderthe possibilitiesofgeneratingalarg eamplitu dephasebyscatteringnear thesubdu ctedTongaslabtotheantipod eatTAM.WangandSo ng's (2019)scattererislocatedat(1 8.7 °S,179.1°W)atadeptho f450km nearFiji,andis basedso lelyontiming. However, thisdoesnot account forgeometric spreadingassociat edwiththescatteringint eraction(see bistaticradarequatio n4-1,Ishimaru,1978),whenthera ypara meteris reset(i.e., notaspecularreflec tion).LetR 0 =26371kmforantipod al

PKIKP,R

1 ~800km(dista nce toscattererfromearthquake)and R 2 =26371-450km(PKIKPd ista ncefromsca tterer toTAM). For

PKIKPgeo metricspreadingisproportio nalto(1/R

0 )whereas forthe scattererpath,geometricspreading isproportional to ()RR 1 12 (Ishimaru,

1978).PKIKPspread inge ffectisproport ion alto7.8×10

-5 whereas forthesc atteredpat hthee ff ectis1.0 ×10 -7 .Henc e,energeticall ythe scatteredwavearrivalis0.1% oftheamplitu deofPKIKP.Thisdoesnot takeintoac counttheac tualconversionlossesinthes cattering inter- action(bothwiththeTo nganslabandbel owFiji),whic hwillfurt her diminishtheamplitude ofthepropo sedscatteredarrivalatTAM. Fi- nally,thetimingoftheS- to-Psc atteredarrivalrel ativet oPKIKPis ~114safterPKIKP,whic hisl aterthanthe~3 2s timeofPKIIKP.G iven theobserva tions(Fig.3)of PKIIKP+PKIIIKP+...withana mplitu de comparabletoPKIKPandatthetheo reticalt imeof PKIIKP,thescatterer proposedbyWangandSon g(2019)isan insufficientalternat iveto

PKIIKPobs ervedatTAM.

ButlerandTsuboi(20 10)consideredascattererdirectly beneat hthe doubletscorrespondingtoS 300PKIKP,whichnominallyhastiming nearPKIIKP.Since both SVandSHmotions arenormalto PKIKP,the

S300-to-PKIKPtransmissioncoe

ffi cientiszerofort herad iallysy m- metricearth.To haveanon- zeroc oe ffi cient,theremustbeas ubstant ial dippinginterface at300km.TheTongaslab isabout4 00kmwest, dipping12°west ward.Therefore,PKIKPorS travelingvertically downwardmisstheTongans ubductio nheterogen eity.RecentP-wave tomographicimagingoftheTonga subductionsys tem(Fukaoand

S.Tsuboi andR.Butler

Obayashi,2013)sho wvelocityan omaliesof<1%beneaththeTAM antipodenearthe300kmdept h,butnoclear evidenceo fascatterin g structure.Althoughacontribu tionfromS-to-PKIKPcannotberefut ed, neitheristhereeviden ce.S incethePKIIKP isaregularseismicphase,it hasprovena nceoveranill-definedscatt eringsurfaceor body. RecentworkbyYaoetal.( 201 9)carefullyexaminedinnercore di ff erentialrotationreport edinpreviousworksandclaimedtha tob- servedPKIKPandPKiKPc hang esmaybeexplain edbyt emporal changesoftheICsurfac erathertha nrotatio n.O neofthreeassertions involvedscatterersattheIC B.ToexplaincodaobservedinPKIKPa nd PKiKParriv alsfroma1993earthqua ke,Yaoetal.( 201 9)proposea scattererattheICBbeneathno rthernBraz il,o ff set~10°E laterallyfrom thegreatc irclebetweenarrays inAlaskaandCa nadaan dSouth SandwichIslands(SSI)d oubletearthquakes.Sincethiss cattererisnot observedtorotate withtheInn erCoreintothefieldofv iewofthe observingarrays - andevent uallydisappearsby2003 - Yaoetal. (2019)concludethatdifferentialrotationof theICis"implausible." Nonetheless,asthescatterer'slo cationis derivedfromt imingandback azimuthmeasures,weinvoke Ishimaru(1978) tocons idergeometric spreadinge ff ects.Forapathlen gthR 0 betweenSSIea rthquakesand Alaskaarrays,thesc attererparsesthepathleng thinsec tionsofabout R 1 =R 0 /3an dR 2 =2R 0 /3.Forthe directpat h,thegeomet ric spreading~1/R 0 andfortheco mbinedpathsea rthquake→scatterer& scatterer→array,thegeometrics preadingampl itudefollows: == () {}{} RRR R 11

4.5/ .

RR 12 3 2 3 9 2 0 2 0 2 00 Althoughasimpleexample,thisillu stra testhattheampl itudeofthe scatteredpathdiminishesas4.5 /R 0 2 .Giv entheextremegeo metricloss rateforthes catteredpa th,theappa rentlackofrotationale ff ectsandits disappearance,arenotunexpected. AlthoughtheobservationofPKIIKPa tantipod alstationsisnot discussedinYaoetal.(2 019 ),tempo ralchangesofthe ICsurfaceatthe PKIIKPreflect ionpointwith1kminc reaseinradius( Yaoetal., 201 9) mayexplain 0.2schangeofPKIIKP phaseover20 years .However, PKIIKPreflect ionshouldoccur intheannularregions urroundingtheIC surface,whichiscontrad ictoryto thes uggestedlocalizedchangeatthe ICsu rfacewithinatimescaleof daysor mont hs,asproposedinYao etal .(2019).Thus ,thesimplestex clamatio nforthetemporalchan geof PKIIKPov er20yearsisby innercore rotationwith0 .05 °/y ear. Arecen tstudyfor theamplificationofant ipodalPKIIKPwa ves (Cormier,2015)propo sesaregionintheequa toria lquasi-eas tern hemisphereatt hesurface ofInnerC orewherethereexistsanomal ously lowornear-z eroshearmod ulusina20to40kmt hicklayerbeneat hthe ICB,alsorepo rtedbyAttanayakeetal.(2018)andTkalcicandPham (2018).Al thoughthepatchsizeofthisano malous regionisnotcertain, itispro pos edthatthispatchisbes texplainedbyfreezin grathert han melting(Cormier,2015).Thisano mal ouspatchintheequatorialquasi- easternhemispheremayresult intemporalev olutio nofthePKIIKP arrival.Ifweassumethe east wardd i ff erentialrotationo ftheInner Core,thefract ionofthe slowregionalongthera ypatho fPKIIKPwave mayincreas eatthemarginofPKIIKPrayan nulus ataroun d50°E.It alsoshouldben otedthatthereisapossibilit ytha tthetimeshiftof PKIIKParriv albecomeszeroornega tive,ifthissl owpatch regionis entirelycoveredbythePKIIKP annulusasthe resul toftheIn nerC ore di ff erentialrotation.This mayimplythatthePKIIKParrivaltimeshift maygivec onstraintst othesizeofslowpatchifwemayassumet he di ff erentialrotationra te.Theremaybeapossibilitythatthe slowpatch regionmaya ff ectthewav eformofPKIKPpha se.However,asthe thicknessofslowpatch isthinand thevelocityperturba tionissmall,it isno tlikelythatitis seeninPKIKPwaveform.ButlerandTsuboi(2 010) showadditio nalantipodalpairswhereinthePKIKPwaveformsmay passthrought hisslowpatch,butdoesn otshow suchfeatures.

Asanal ternative explanationtodi

ff erentialrotation,t hetimeshift ofPKIIKParriva lmay arisefromlateralex pansiono rcontractio nof near-zeroshearmodulus patchesovertime. However,thesechanges wouldnotberestric tedtotheedge oft hePKIIKPFresnelzone,but wouldencompasst heintegratedcontributionover thewhole ICray surfaceofthewhisperinggal leryphase( Fig.4).Decad alchangesin

PKiKP-PKIKP(~1 Hz)di

ff erentialtimesmaybemodel edby1-km changesinICtopography,n otd uet orotation(Wen,2006 ).However, theheatof fusionreq uiredtofreeze ormeltthismass(2. 4E+15kg)is substantial.FortheCore,Nimmo(2 015)andHuguetetal.(201 8)

Fig.3. (left)StackedTAM displacementdataareco mparedwithPREM andInnerCoremodelVp4.ThePKIIKParrival timeinaqua,preceded byanunkn ownInner

Corearrival(? )inyellow,arefeat uredinVp4(bluea rrows) butnotPREM.(right)Inn erCorevel ocityprofiles,Vp4, forP- waves (green)andS-waves (blue).Dotted

redind icatesmodificationfromPREMmod el.

S.Tsuboi andR.Butler

estimatetheheatoffusio nat750 kj/kg,and specificheat capacityat

785±75j/kg° .Thus ,theheato ffusionassocia tedwiththismass

(2.4E+15kg)requires1.8E+18kj ,whichisabo ut1000-fol dlarger thanitsheatc apacity( compareice, wheretheratioisabout80).Ov era decadethepowerrequiredisabo ut5.8G W.Thisisafa irlylarge numberforafairly smallfeat ure.In contrast, the"shadow"di ff erential rotationcaneasilyexposeo rhidesuchs tructures,thatmay beformed overmuchlo ngertimescal es.Withoutdi ff erentialrotationt hePKIIKP +...ray surface mustintegrateoverproces sescovering60 %oftheICB, dynamicallyactingoveradecade,topro ducetravel-timefluctu a- tions>0.2s. Wereco gnizethatthe20yearsaret ooshortanint ervalto clearly resolvetheinnercorerot ationrat eandtheco ncomitantvel ocityhet- erogeneityoftheInnerCore. Overthese twodeca des,wehaveobs erved minimumtimeshifts of+0.2s .Thus,weadmitt hattheinn ercore di ff erentialrotationweo bservedforPKIIKPtimeshiftsfortheeart h- quaketripletisnoty etstronglyres ol ved.Weneedtoha veaddit ional earthquakesforthesameregion. Observatio nsforac enturymightbe necessarytoconfirmtheinn ercorerot ationratethroughseis mologica l observation.Nonetheless,becausethet emporalinhomogeneityob- servedforPKIIKPhas beenchangin gfor past20y ears, itmaybe promisingtousethes eobservat ionsfortheest imationofinn ercore rotationrateandInnerCore structure.We maywaituntilt henext earthquaketocompriseaquart etforcheckin gthetimeshiftforPKIIKP. Searchingforotherantipo dalpairst oobtainPKIIKPphase observations mightbeneces sary .

6.Conclusio ns

Wehav eusedobserva tionsforant ipodalearthquakeandstation pairsandfo undthatthereex istsatimeshiftoft hewhispering-gall ery wavewhichpropag atesalo ngthetopofInnerCore.Wepropo sethat thesetimeshiftsa recaused bytheinteract ionofaz erorigiditypatchat theInnerC oresurfacewit htheInnerCore di ff erentialrotation.O ur interpretationisconsistentwiththe rota tionrateis0.05°/year,whichis oneorderofma gnitudesmal lerthan thosereportedbypreviousstudies. Supplementarydatatothisarticle canbefoundonlin eathttps:// doi.org/10.1016/j.pepi.2020.106451.

Acknowledgmentsanddata

Datawereobtainedfro mGEO SCOPE.Weusedthecomputer pro- gram(SPECFEM3D )forSpectral-ElementMethod.All thecomput ations areperformedus ingtheEart hSimulatoratt heEarthSimu latorCenter ofJAMS TEC.Centroidmomenttensorso lutions(GCMT)areu sedfor syntheticmodels.Theauthorswo uldliketothankVernon Cormier and anonymousreviewersforvaluablecomment swhichgreat lyimproved themanus cript.SOESTcontributionnumber10 915.

CRediTauthorshipc ontributionstatement

SeijiTsuboi: Conceptualization,Methodology,Writing-original draft.RhettButler:Methodology,Investigation,Writing-review& editing,Visualization .

Declarationofcompetinginte rest

Thereare noconflic tsofint eresttodeclare.

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