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Article:

Frost, DA, Garnero, EJ and Rost, S orcid.org/0000-0003-0218-247X (2018) Dynamical links between small- and large-scale mantle heterogeneity: seismological evidence. Earth and Planetary Science Letters, 482. pp. 135-146. ISSN 0012-821X

https://doi.org/10.1016/j.epsl.2017.10.058

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Title: Dynamical links between small- and large-scale mantle heterogeneity:1seismologicalevidence23

Authors:DanielA.Frost1*,EdwardJ.Garnero2,andSebastianRost34

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Affiliations:6

1Earth&PlanetaryScience,UniversityofCalifornia,Berkeley,California,USA7

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2SchoolofEarthandSpaceExploration,ArizonaStateUniversity,Tempe,Arizona,9

USA10

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3InstituteofGeophysicsandTectonics,SchoolofEarthandEnvironment,University12

ofLeeds,Leeds,UK13

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*Correspondenceto:dafrost@berkeley.edu15

Abstract1617We identify PKP�PKP scattered waves (also known as P′�P′) from earthquakes18

recordedatsmall-apertureseismicarraysatdistances less than65°. P′�P′energy19

travelsasaPKPwavethroughthecore,upintothemantle,thenscattersbackdown20

throughthecoretothereceiverasasecondPKP.P′�P′wavesareuniqueinthatthey21

allowscatteringheterogeneitiesthroughoutthemantletobeimaged.Weusearray-22

processing methods to amplify low amplitude, coherent scattered energy signals23

and resolve their incoming direction. We deterministically map scattering24

heterogeneity locations from the core-mantle boundary to the surface.Weuse an25

2

extensive dataset with sensitivity to a large volume of the mantle and a location26

methodallowingustoresolveandmapmoreheterogeneitiesthanhavepreviously27

been possible, representing a significant increase in our understanding of small-28

scalestructurewithin themantle.Ourresultsdemonstrate that thedistributionof29

scattering heterogeneities varies both radially and laterally. Scattering is most30

abundant in the uppermost and lowermost mantle, and a minimum in the mid-31

mantle,resemblingtheradialdistributionoftomographicallyderivedwhole-mantle32

velocity heterogeneity. We investigate the spatial correlation of scattering33

heterogeneities with large-scale tomographic velocities, lateral velocity gradients,34

the locationsofdeep-seatedhotspotsandsubductedslabs. Inthe lowermost150035

kmofthemantle,small-scaleheterogeneitiescorrelatewithregionsoflowseismic36

velocity,highlateralseismicgradient,andproximitytohotspots.Intheupper100037

km of the mantle there is no significant correlation between scattering38

heterogeneity location and subducted slabs. Between 600 and 900 km depth,39

scatteringheterogeneitiesaremorecommonintheregionsmostremotefromslabs,40

andclosetohotspots.Scatteringheterogeneitiesshowanaffinity forregionsclose41

to slabs within the upper 200 km of the mantle. The similarity between the42

distribution of large-scale and small-scale mantle structures suggests a dynamic43

connection across scales, whereby mantle heterogeneities of all sizes may be44

directedinsimilarwaysbylarge-scaleconvectivecurrents.45

Keywords:seismology;deepEarth;scattering;mantlestructure;mantledynamics;46seismicarrays47481.Introduction49

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The high frequency (~1 Hz) seismic wavefield provides evidence of50

kilometre scale structure within the Earth [Cleary and Haddon, 1972]. Seismic51

energy that is not explained by wave propagation in smoothly varying velocity52

modelsof theEarthhasbeenattributedtoreflectionsandscattering fromsharply53

contrasting volumetric heterogeneities and roughness on interfaces [Chang and54

Cleary,1981].Theinteractionofthewavefieldwithdiscrete,small-scalevariations55

inelasticpropertiesand/ordensitycandivertseismicenergyontonewpaths,often56

generatingprecursorsorpostcursors(coda)tothemainseismicphasesthattravel57

inthegreatcircleplane.Thesizeofthescatterersthatcanbeimagedisdependent58

upon the wavelength that is analysed; for the teleseismic high-frequency P-59

wavefieldabove1Hztheyaretypicallyontheorderof1to10km.60

Global imaging of Earth’s small-scale heterogeneities is difficult due to the61

uneven distribution of earthquake sources and seismic receivers, and the low62

amplitudeof the scatteredsignals involved. Scattering canbe studiedusing single63

stations,butwiththisapproachthelocationofthescatteringheterogeneitycanbe64

ambiguous[Wen,2000].Alternatively,seismicarrays,i.e.,3ormorecloselylocated65

sensors,canresolvetheincomingdirectionofscatteredwaves,thusitispossibleto66

deterministicallylocateheterogeneities[Thomasetal.,1999;RostandEarle,2010;67

Frost et al., 2013]. In the last few decades a number of studies have started to68

unravelthedistributionofsmall-scaleheterogeneitiesofEarth’smantle.Hedlinetal.69

[1997], and later Mancinelli and Shearer [2013, 2016] studied the depth70

distribution of heterogeneity within the mantle through analysis of PKP pre- and71

postcursorsrecordedatsinglestations.UsingastochasticRayleigh-Bornscattering72

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approach, Mancinelli and Shearer [2013, 2016] developed a global model of73

scattering heterogeneity containing 0.1% root-mean-square velocity variations in74

thedeepest1200kmofthemantlewithheterogeneityscalesizesrangingfrom2to75

30km.76

Thisworkiscomplementedbystudiesthatdeterministicallymapsmall-scale77

scattering heterogeneity within the upper and lower mantle. These studies have78

noted lateral variations in heterogeneity distribution, as well as variations in79

amplitudesofscatteredwaves.ScatteredP-to-P(P�P,wherethe“�“representsthe80

locationofscattering)andP-to-S(P�S)wavesaresensitivetoheterogeneitiesinthe81

upperhalfofEarth’smantle;theyhavebeenusedtomapscatteringheterogeneityin82

regionsinfluencedbyrecentsubduction[KaneshimaandHelffrich,1998;Bentham83

andRost,2014].Scatteringinthelowermostmantlehasalsobeenobservedtovary84

laterally [Waszek et al., 2015]. Strong scattering has been observed in regions85

beneathmantlehotspots [Wen,2000],nearsmall, regionalultra-lowvelocityzone86

(ULVZ)structures[YaoandWen,2014],beneathsubductionzones[MillerandNiu,87

2008], and near the edges of LLSVPs [Frost et al., 2013]. A near-global study of88

PK�KP–aPKPwavethatisback-scatteredinthelowermantleontoasecondPKP89

path – suggests a spatial correlation between scattering and LLSVP edges in the90

lowermost300kmofthemantle[RostandEarle,2010;Frostetal.,2017].91

The volume of the mantle that can be investigated for scattering92

heterogeneityiscontrolledbythespecificsoftheseismicprobe.PK�KPcanbeused93

toinvestigatethelowermantleclosetotheCMB[ChangandCleary,1981;Rostand94

Earle, 2010; Frost et al., 2017]. ThedirectwavePKPPKP (also calledP′P′) results95

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from a PKP wave (P′) reflecting from the underside of the surface, back into the96

Earth as a secondPKPwave, along the great-circlepath (GCP).Thisphase canbe97

precededbyscatteredenergycalledPKP�PKP(P′�P′),causedbyback-scatteringof98

PKPatanydepthinthemantle[Rostetal.,2015].LikePK�KP,P′�P′hasanunusual99

scatteringgeometry(Fig.1)andcanscatter from locationsoff theGCP,and theP′100

segmentsneednotbesymmetric toeachother.P′�P′ is thecontinuationofPK�KP101

towardsthesurface,thusthisphaseisabletosamplethewholemantlefromCMBto102

crust(Fig.2).Weextendourearlierworkandinvestigatethemantleupwardsfrom103

theCMBtothesurfacetodeterministicallymaptheverticalandlateraldistribution104

ofscatteringheterogeneitiesthroughoutthemantle.Incontrasttootherscattering105

probes, the unusual (and versatile) raypath geometry of P′�P′ allows the study of106

previouslyunsampledregionsoftheEarth.107

TheinternalstructureoftheEarthandthenatureofmantleconvectionare108

inherently connected across scales [e.g. Tackley 2015]. The distribution of large-109

scale mantle structure as imaged by seismic tomography has been investigated110

usingthermo-chemicalgeodynamicmodels,whichindicatethatdownwellingofcold,111

dense slabs at subduction zones moves and shapes the hot, convecting piles of112

seismically slow material at the CMB, forming the Large Low Shear Velocity113

Provinces (LLSVPs) [McNamara and Zhong, 2005; Li et al., 2014; Domeier et al,114

2016]. The LLSVPs, if compositionally distinct, may modulate mantle dynamics115

through thermal instabilities that result in mantle plumes that rise up causing116

hotspot volcanism [Thorne et al., 2004; French and Romanowicz, 2015].117

Furthermore, calculations suggest thatmantle plumesmaybe spatially correlated118

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with the LLSVPs [Thorne et al., 2004; Doubrovine et al., 2016]. Geodynamic119

modelling of thermo-chemical structures in the deep mantle indicates that small-120

scaleheterogeneities(assmallaskilometre-sized)canbepassively transported in121

thelarge-scaleflow[BrandenburgandvanKeken,2007;Lietal.,2014,Mulyukova122

et al., 2015]. Furthermore, geochemical analysis of intraplate volcanism suggests123

thatheterogeneitiessituatedinthedeepEarthmaybetransportedtothesurfaceby124

entrainment in mantle convection [Williams et al., 2015]. Therefore, there is125

compelling evidence that the distribution of small-scale seismic structure in the126

mantleislinkedtothelarge-scalestructures.127

Hereweuseaglobalcollectionofearthquakesrecordedatseismicarraysto128

identifyP′�P′ anddeterministically locate thepositionof the causativevolumetric129

scatteringheterogeneitywithinthemantle.Weinvestigatetherelationshipbetween130

scatteringheterogeneityandotherseismologicallyimagedstructuresinthemantle.131

We use our observations to understand the distribution of small-scale132

heterogeneities throughout the whole of the mantle, and the connection with133

dynamicprocesses.134

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135Figure1:PKP�PKP(P′�P′)examplepath.(a)AP′�P′pathfromthesource(star)to136

a scattering point in the mantle (circle) and then to the receiver (triangle). P′�P′137

travelsalongtwogreat-circlepaths(solidlines)toandfromthescatteringpoint,off138

thegreat-circlepathbetweenthesourceandreceiver(dashedline).PKPraypaths139

from(b)sourcetoscatterer(PKPab)and(c)scatterertoreceiver(PKPbc).Thetwo140

PKPlegsmaybesymmetricorasymmetric(asinthiscase)andcanscatterfromany141

depthinthemantlefromtheCMBtothesurface.Raysobservedatthesurfacearrive142

fromaspecificdirectionknownastheback-azimuth,ȟ,measuredrelativetoNorth,143

ortherelativeback-azimuthmeasuredfromtheGCP,andfromaverticalincidence144

angle,referredtoastheslowness,u.145

[SINGLEOR1.5COLUMNFIGURE]146

147148149150151

c Scatterer to Receiver

!

b Source to Scatterer

a

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152Figure2:Travel-timecurvedisplayingP′�P′andotherscatteredphasesinthehigh-153

frequencyseismicwavefield.BlacklinesmarkmajorP-wavephases.Theblueregion154

marks the time and distance region investigated for P′�P′ waves in this study.155

HatchedregionmarkstimeanddistanceregioninvestigatedforPK�KPinFrostetal.,156

[2017]. Grey and pink lines mark the P- and S-waves, respectively, that may157

contaminatetheP′�P′studyregion.OtherP-andS-wavesarenotshownforclarity.158

Differently shaded grey regions denote time and distance regions previously159

investigatedforotherscatteredwaves.AdaptedfromRostetal.,[2015].160

[SINGLECOLUMNFIGURE]161

1622.Data163164

We collect data from 643 earthquakes at any depth with magnitudes M≥6165

recordedatupto12smallandmediumaperturearrayswithin65°ofanyevent(Fig.166

3).Thearrayscontainamixtureofshortperiodandbroadbandinstruments;weuse167

onlythemostcommoninstrumenttypeineacharray.Thesearraysweredesigned168

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to determine the directivity of short-period P-waves thus are ideally suited for169

analysis of high-frequency scattered waves. The aperture of an array controls its170

directivityresolution,thusweselectonlyarrayswithaperturesof10kmto30kmto171

ensurethatweareabletoresolvewelltheincomingdirectionofwaves.172

Eachevent-arraypairhasaspecificgeographicalvolumeofthemantlefrom173

whichpossibleP′�P′scatteredwavescanbedetected(Fig.3).Thesizeandshapeof174

thesamplingregionatanygivenscatteringdepthisdependentontheevent-array175

distance. Using estimations of the potential scattering volumes combined for all176

source-arraypairs,wedevelopa“potentialsamplingdensitymap”ofourdatasetfor177

differentdepths,whichrepresents theabundanceof scattererswewoulddetect if178

the actual distribution of scattering in the Earth distribution were uniform. The179

potentialscatterersamplingdistributionofthedatasetisuneven,butincontrastto180

otherprobes,thesouthernhemisphereiswellcoveredthroughoutthedepthofthe181

mantle, allowing investigation of the relationship between scattering182

heterogeneities and the South and Central American subduction zones, and the183

AfricanandPacificLLSVPs. 184

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185Figure 3: Earthquakes (dots) and arrays (triangles) in our dataset and resultant186

potential P′�P′ scattering sampling. The 643 events and up to 12 arrays yielded187

1715 event-array pairs. Global sampling distributions are constructed by188

summationofthepotentialscatteringsamplingforallsource-arraypairsat:(a)the189

surface(0kmdepth);(b)transitionzone(600kmdepth);(c)mid-mantle(1200km190

depth);and(d)theCore-MantleBoundary(2889kmdepth).Samplingisdensestin191

themid-mantle andmost geographically extensive in the lowermostmantle. Grey192

wedge in (a) displays an example of the potential scattering regions for a single193

event-arraypair.194

[2COLUMNFIGURE]195

196

1973.Methods198199

We investigate energy associatedwithmantle scattering in a timewindow200

from the firstpossible arrival of P′�P′ at~1700safter theearthquakeorigin time201

(for a surface focus event) corresponding to scattering at theCMB, up to the first202

Z=0 kma Z=600 kmb

d Z=2889 kmc Z=1200 km

0 325 650 975 1300Potential sampling

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possiblearrivalofthedirectwaveP′�P′dfat~2400s,whichistheearliestP′�P′GCP203

phase, reflecting from the underside of the surface on the antipodal side (Fig. 2).204

P′�P′ scattering related to interactions with small-scale mantle heterogeneity is205

feasibleforanytimeanddistanceinthiswindow(blueshadedregioninFig.2).206

Wede-trend the data and discard any discontinuous traces i.e. gaps in the207

recording.Theremainingtracesarefilteredwitha2ndorderbandpassbetween0.5208

and2Hztoenhancethefrequenciesmostassociatedwithsmall-scalescatteringin209

paststudiesthatinvestigatedfrequencycontent[Mancinellietal.,2016;Frostetal.,210

2017]. Wesearchforscatteredsignalswithinthewavefielddatausingfk-analysis211

(frequency-wavenumber), which performs a grid-search over incoming directions212

to maximise coherence (the similarity of two or more signals in the frequency213

domain)ofthesignalstackedacrossthearray,calculatedinthefrequencydomain214

[Capon, et al., 1967]. We search over slownesses from 0 to 8 sec/deg and back-215

azimuthsbetween -180° to180° relative to theGCP.By selecting signalswith the216

highestcoherencewedeterminethebestfittingslownessvector(acombinationof217

theback-azimuth,θ,andthehorizontalslowness,u)oftheincomingsignals inthe218

scattering search time-window (1700s to 2400s after earthquake origin). To219

improve the resolution of the slowness vector of incoming signals, as well as to220

furtherincreasetheprominenceofsignalsabovethenoise,weapplytheF-statistic221

to the fk-analysis (Fig.4) [Blandford,1974;Selby,2011].TheF-statisticcalculates222

theratiooftheamplitudeofthestackedsignaltothesumofthedifferencesbetween223

the stack and each trace used to form the stack. The F-trace has the effect of224

penalising stacks that differ from individual input traces i.e. signals that are225

12

incoherentacrossthearray.Thus,thebestfittingslownessandback-azimuthfrom226

the grid-search are those that produce the most representative stack of the227

individual array traces.Byperforming these calculations in the frequencydomain228

weincreaseefficiencybyreducingthenumberoftransformationsrequiredbetween229

thetimeandfrequencydomains.However,thefkapproachreturnsasinglevalueof230

coherencefromeachslownessvectoraveragedacrossthewholetimewindow,thus231

collapsingthetimeaxis.CombiningtheF-statisticwithtraditionalfk-analysisresults232

in much-improved slowness vector resolution, even for the small-aperture arrays233

usedhere[Frostetal.,2013].Thustheoriginofthescatteredenergycanbemore234

preciselyestimated.235

We measure the slowness and back-azimuth of the most coherent signals236

receivedatthearrayinconsecutive50s longtimewindows(Fig.4).Thiswindow237

length gives depth resolution comparable to that obtained in global tomography238

models, and is sufficient to identify broad-scale trends in scattering distribution,239

both laterally and with depth. We assume the arrival time of a signal to be the240

middleofthe50stimewindow,andgiventhatscatteringofP′�P′fromarangeof241

depthscanarriveatthearraywithsimilartravel-times,each50stimewindowthat242

weinvestigateissensitivetoscatteringfroma50to200kmthicknessofthemantle.243

The thickness of the scattering region that each time window is sensitive to244

decreases with scattering depth hence, at shallower depths, there is overlap in245

depth sensitivity between windows – adjacent time windows can contain energy246

scatteredfromthesamedepth(albeitfromdifferentlocations).247

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Mantle scattered P′�P′ waves are expected to arrive with slownesses248

between2.1and4.4s/deg.TherangeofdirectionsfromwhichP′�P′wavescanbe249

observed is dependent upon the event-array distance and scattering depth. Array250

analysespermitrecognitionandomissionofcontaminatingwavesbydetermination251

oftheincomingdirectionofenergy,comparedwiththedirectionspossibleforP′�P′.252

We compute the expected arrival times for possible contaminating waves: direct253

phases, depthphases, andmultiple reflectionsof bothP- andS-waves.Wedonot254

calculate multiples reflecting off upper mantle discontinuities (i.e. a downgoing255

wave reflecting off the 660 km discontinuity, then reflecting back down from the256

410 km discontinuity). Contaminating waves would likely be detected along the257

GCP (we take both minor and major arc arrivals into account). In contrast, P′�P′258

scatteredenergymostcommonlyarrivesofftheGCP,allowingclearidentificationof259

thescatteredarrivals.However,atshortevent-arraydistancesitispossibleforP′�P′260

toarrivealongtheGCP;thesesituationscanbepredictedandextracareistakento261

exclude contaminatingphases.As there are fewphases that can arrivewithin the262

P′�P′window (Fig 2),wewould expect few timewindows to be contaminatedby263

other seismic phases. Nonetheless, we discard any time window where we both264

observeasignalwithin20degreesoftheGCP(inmajororminorarcdirections)and265

anyknownseismicwaveispredictedtoarriveinthesametimewindowandalong266

the same backazimuth (i.e. minor or major great-circle path) (e.g Fig. 4d). Of all267

identified signals, only 2% match the time and direction predicted for known268

seismicphases,andthusarediscarded.269

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Thewavefieldmayalsobecontaminatedbyforeshocksoraftershockstothe270

analysedevents,thusweexcludefromfurtheranalysisanyscatteredsignalswhere271

any magnitude ≥6 earthquake occurs within two hours of the origin time of the272

studied earthquake (11% of identified scattered signals). As a further test we273

removeany scattered signal that couldbe contaminatedbyamagnitude≥5event274

butfindnosystematicdifferenceinthedistributionofscatteringheterogeneity.Our275

focusoncorewavearrivalswithslownessesfrom2.1to4.4s/deghelpstoexclude276

contaminationfromsmaller,closerevents,whichhavehigherslownessesassociated277

with more horizontal incoming energy (and the discarding of GCP signals further278

minimizes energy from small local events contributing to data we analyse).279

Therefore,wearecertainthatourdataselectionpreventsanycontaminationofthe280

results by local and regional events. Lithospheric scattering directly beneath the281

arraymayredirecthighslownesscontaminatingenergytolowerslownessestypical282

ofmantlescatteringthatweconsiderhere.However,thedirectcontaminatingwave283

would arrive in the same time window as the lithospheric scattered energy, and284

would likely be more coherent with an obviously inappropriate slowness. This285

allows a straightforward identification (and removal) of energy scattered from286

lithosphericstructure.287

Aftercontaminatedtimewindowshavebeenremoved,scatteredsignalsare288

identified. We pick time windows containing energy prominently above the289

backgroundnoise level in f-k spaceandconsistentwith thedirectivity criteria for290

P′�P′ scattering (e.g. Fig. 4b). We identify the slowness and back-azimuth of the291

scattered signal, and select the time at the middle of the 50 s long window as292

15

scattered travel time; therefore, we only identify one scattered signal per 50 s293

window.IfmultipleP′�P′signalsareobservedinthesametimewindowweretain294

the signal with the highest coherence, as this will be the best spatially resolved.295

Multiplewavesarrivingat a similar time, either scatteredordirect,may interfere296

causing the apparent arrival direction of energy at the array to be incorrect. The297

apparentsignalwould likelyappearblurredacrossdirections, thusweonlyselect298

signalswithtightlyresolvedslownessandback-azimuth(withinthecapabilitiesof299

thearray).300

Theback-azimuth,slowness,andtimeinformationforeachscatteredsignal301

are used to calculate a scattering location in the mantle. The back-azimuth of a302

signal indicates thehorizontal direction alongwhich thewave travelledwhile the303

slownessdefinesadiscretepathfora1DEarthmodel,andthetravel-timerelatesto304

the scattering depth (Fig. S1). Thus there is a trade-off between the distance and305

depth of a scattered path, hence we attempt to fit both slowness and travel-time306

simultaneouslywithagridsearch.Weraytracebackwardsfromthearrayalongthe307

observedback-azimuthtoarangeofpossiblescatteringdepthsanddistances,and308

then ray-trace from these scattering locations to the source. Possible scattering309

locationsarespacedevery0.01° indistancebetween theminimumandmaximum310

possiblepath lengthsofPKPalongtheresolvedback-azimuthand50kmindepth311

from theCMB to the surface.Wemodel the scattering locationbyminimising the312

misfit between the calculated slowness and time for each potential scattering313

location and the observed values. Mapped scattering heterogeneity locations are314

discarded if traced rays to the solution location do not well fit the observed315

16

slownessandtime:ifthesquaredslownessmisfit(observedminuspredicted)plus316

twicethesquaredtimemisfitisgreaterthan10,i.e.aweightingfactorof2isused317

fortraveltimemisfitandthereforewefavourfittingscatteringlocationswithsmall318

travel-time misfits. The misfit value selected fits signals within the slowness319

resolution limit of the arrays. Overall, of the original 4319 identified scattered320

signals, we discard signals contaminated by other events (11% of the original321

population),otherphases(2%),andpoorlyfitsignals(44%),leaving1876mapped322

scatteringheterogeneities.323

Duetotheuncertaintyintravel-time(fromusingthemiddleofthe50stime324

window)andtheuncertaintyinslowness(duetotheabilityofthearraystoresolve325

theincomingdirection)wedeterminethedimensionsoftheregionthatcontainsthe326

heterogeneity based on these limitations. We calculate scattering locations for327

signals arriving at the start and end of the 50s time window, and with slowness328

variationof±0.3s/degrelative to thatmeasuredat thearray(estimated fromthe329

slowness spacingof thegrid-search).Thisdefinesa regionaround thebest fitting330

heterogeneitylocationthatis,onaverage,±100kmlaterallyandvertically.Formid-331

mantle scattering at high slowness values (~1000-1800 km depth), the error332

regionscanoccasionallygrowtovaluesaslargeas±800kmlaterallyand±500km333

vertically but this larger misfit is only relevant for around 5% of the solution334

scatteringlocations,thusthemajorityofthescatteringheterogeneitiesidentifiedin335

ourdatasetarelocatedtowithin±100kmverticallyandlaterally.336

Sub-surface structurebeneath themajorityof thearraysused in this study337

hasbeendemonstratedtohaveaninsignificanteffectontheresolvedslownessand338

17

back-azimuth (Bondar et al., 1999). Nevertheless, removing scattering339

heterogeneitiesobservedatChiangMaiarray,whichismostaffectedbysub-surface340

structure, dominantly reduces scattering in the upper 200 km of the mantle and341

causes no significant change in our conclusions on the relationship with lower342

mantlestructure.343

344

345

346Figure4:Arraydataareshownfor(aandb)amagnitude6.5event,24kmdepth,347

52°awayfromYellowknifearray,and(candd)amagnitude7.8event,0kmdepth,348

37°awayfromWarramungaarray.(a)ThetimewindowforP′�P′scattering(1700-349

2450secforthisevent,blueregioninFig.2).Thepredictedtimeofthedirectphase,350

P′P′df,isshownbytheverticalline,markingtheendofthescatteringwindowused351

here. Data are filtered between 0.5 and 2.0 Hz. The grey shaded time window352

18

corresponds to information shown in (b). (b) f-k processing of the 50 sec time353

windowshowngreyin(a),displayedintermsofback-azimuth(ȟ,azimuthalaxis)354

andslowness(u,radialaxisoutwardsfrom0to8s/degwithringsmarking2to6355

s/deg). Back-azimuth is measured relative to the great-circle path (vertical blue356

line).Thewhitestarshowsthemaximumcoherenceinthef-kanalysis,arrivingwith357

relative back azimuth = -106° (blue dashed line). The 90% coherence contour is358

roughly ±10° wide in back-azimuth and ±0.5 s/deg in slowness around the359

maximum. The green regions show the range of possible slownesses and back-360

azimuths for P′�P′ waves scattering at this distance and the median depth of361

scatteringforthistimewindow(fromtheshapeofthepotentialscatteringregions,362

greyregions inFig.3).(c) f-kprocessingofatimewindowshowingnoclearP′�P′363

waves.(d)f-kprocessingofatimewindowthatislikelycontaminatedbythedirect364

phasePKKKP (predicted slownessandback-azimuthmarkedbypurplediamond).365

Timewindows(c)and(d)arenotpickedforfurtherprocessing.366

[2COLUMNFIGURE]367

3683693704.Results371372

Themappedlocationsofscatteringheterogeneitiesareunevenlydistributed373

in themantle,both laterallyandwithdepth.This isnotunexpectedgiventhat the374

potentialsamplingcapacityofourdatasetalsovariesinlocationanddepth(Fig.3).375

Wedividethenumberofmappedscatterersbythepotentialsamplingdensity(Fig.376

3) in order to compare relative scattering density for different regions. This377

normalised scattering population shows that heterogeneities are distributed378

throughout the mantle, but more abundant scattering heterogeneity is present in379

theuppermostandlowermostmantle(Fig.5).Theradialscattererdistributionalso380

showsasmallincreaseinscatteringheterogeneitybetween600and900kmdepth,381

19

justbelowthetransitionzone,andaminimuminthemid-mantlebetween1400to382

1800kmdepth.383

We find that the radial abundance of small-scale scattering heterogeneity384

matchestheRMSamplitudeoflarge-scaletomographicvelocities(Fig.5):scattering385

ismostcommonand theRMSvariationof tomographicvelocities ishighest in the386

uppermost and lowermost mantle. This correlation holds roughly for all387

tomographicmodels(Fig.S2).388

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0.0 0.2 0.4 0.6 0.8 1.0

0 1 2 3 4

dVs RMS (SEMUCB-WM1)

Depth

(km

)

Normalised

scattering/sampling

20

Figure 5: Normalised scattering heterogeneity density with depth (number of392

scatterers divided by number of samples in each 100 km thick layer) for the393

completedataset(black,lowerx-axis)andRMSoftheshearvelocityperturbations394

fromtheglobaltomographicmodelSEMUCB-WM1(greyanddashed,upperx-axis)395

[French and Romanowicz, 2014]. The depth distribution of small-scale scattering396

heterogeneity roughly correlates with the RMS of long-wavelength dVs397

perturbations.Bothlinesarescaledtofitthesameaxis.398

[SINGLECOLUMNFIGURE]399

400401

Weinvestigatepossiblespatialcorrelationbetweentheresolvedscattering402

heterogeneities and large-scale mantle features, which may be interpreted as403

proxiesfordynamicprocesses,asinFrostetal.,[2017].Wecomparethelocationof404

scatteringheterogeneitytogeographicalregionsbeneathhotspots,subductedslabs,405

regionsofhighandlowtomographicvelocities,andregionsofhighandlowlateral406

tomographic velocity gradients. The high/low velocities and gradients from407

tomographicmodelslikelyrelatetothelocationsofLLSVPsandsubductedslabsin408

the mantle. The spatial locations of scattering heterogeneities are shown,409

normalisedbysampling,intheSupplementaryMaterial,whiletheabsolutelatitude,410

longitude, and depth information for each scattering heterogeneity is shown in411

SupplementaryTable1412

413

414

4.1Relationshipbetweenscatteringheterogeneitiesandmantlestructure415

We compare the distribution of scattering heterogeneity with S-wave416

tomographicmodels,bothbecausetheyarethebasisforthedefinitionoftheLarge417

21

LowShearVelocityProvinces,andalsoshowconsistencybetweenmodels[Garnero418

etal.,2016].Weuseseveral tomographicmodels:GyPSuM[Simmonsetal.,2010],419

SEMUCB-WM1[FrenchandRomanowicz,2014],S40RTS[Ritsemaetal.,2011],and420

TX2011 [Grand,2002].Additional comparisonswithP-wavemodels are shown in421

thesupplementarymaterial(Figs.S7-9).Wecalculatelateralvelocitygradientsfrom422

tomographic models, revealing abrupt changes in mantle structure, which thus423

serveasaproxy forboundariesof theLLSVPs [Thorneetal.,2004,Garneroetal.,424

2016].Wecalculategradientsoveradistanceof10°astheresultinggradientswell425

replicatethemarginsoftheLLSVPsfoundinforwardmodellingstudies[Garneroet426

al.,2016andreferencestherein].427

We use hotspots from the study of Courtillot et al. [2003]. French and428

Romanowicz [2015] analysed the tomographic model SEMUCB-WM1 [French and429

Romanowicz, 2014] and characterised hotspots based on associated tomographic430

velocityanomalies.Weusethe20hotspotsthatwerelabelledaseither“primary”or431

“clear”meaningthatthehotspotoverliesacolumnoflowvelocitiesfromtheCMBto432

1000kmdepthwithdVslessthan-1.5%orlessthan-0.5%,respectively.433

We use slab locations from the Regionalized Upper Mantle (RUM) model,434

which locates slabs at depth using intra-slab seismicity [Gudmundsson and435

Sambridge,1998].Whencomparingwithscatteringheterogeneitylocationsweuse436

slablocationsatthesurface(zerodepth).Slabsmoveonlyasmallamountlaterally437

astheysubduct(ӊ5°relativetotheplateboundaryatthesurface[Steinbergeretal.,438

2012]),whichisunlikelytostronglyinfluenceourcorrelations.439

22

To account for differences in themagnitude, range, andpattern of velocity440

anomalies and velocity anomaly gradients between tomographic models, and441

differencesinthenumberoflocationsinofmapsofhotspotandslablocations,we442

convertmapsoftomographicvelocitiestomapsofpercentagecumulativeareaona443

spheresortedbydecreasingvelocityanomaly(fromfasttoslow).Forexample,the444

20%area corresponds to the area of the 20%highest tomography velocities of a445

givendepthshell(Fig.6).Weonlyconsidertheregionsofthetomographicmodels446

thatmatchtheregionssampledbytheP′�P′datasetateachdepth.Inthisway,the447

highest and lowest velocities in several tomographic models with inherently448

differing amplitudes of velocity variation can be directly compared. We establish449

geographical area percentages associated with the locations of hotspots and450

subductedslabsbycomputingthecumulativeareasurroundingthefeatureswithin451

specific distances from them (within the area sampled by the P′�P′ dataset). For452

example,thefirst20%areaforslabscorrespondstotheregionclosesttoslabsthat453

addsupto20%oftheEarth’ssurfacearea;converselythelast20%areaindicates454

thatamountofsurfaceareafurthestfromslabs.455

To estimate correlations between the abundance of small-scale scattering456

and subducted slabs, hotspots, tomographic velocities and gradients, we compare457

the location of these features to the distribution of scattering heterogeneity. For458

each 100 km depth shell, we count scattering heterogeneities in each 20% area459

division from the feature of interest. To account for the variability in sampling460

coverage of our dataset (Fig. 3), we count our estimation of potential scatterers461

(afforded by our event-array distributions) in the same 20% area regions, and462

23

calculate the ratio of the number of observed-to-potential heterogeneities. This463

allowsus to construct amapof normalised scatteringprevalence, thus effectively464

removingthebiasofourunevensampling.465

ThefirstsetofcomparisonsisdisplayedinFig.7asacumulativehistogram466

asafunctionofdepth.Intheupper200kmofthemantle,scatteringheterogeneities467

are most common in regions of high velocity (Fig. 7a), which is evident from the468

horizontalwidthofthelightanddarkblueshadingbeinggreaterthanthewidthof469

the light and dark red shading over the same depth range. In the lower mantle,470

especially in the deepest 500 km or so, the opposite is true: scattering471

heterogeneitiesaremoreabundantinlowvelocityregions(asevidentbywiderred472

shading). Regions of the lowermost mantle with high seismic velocities show473

virtuallynocorrelationwith scatteringheterogeneities.Scattering is slightlymore474

commoninregionsofhighseismicvelocitybetween600and900kmdepth.475

In the deepest 200 km of the mantle, scattering heterogeneities are more476

common inregionsofhigh lateralseismicvelocitygradients(Fig.7b: thewidthof477

theblackanddarkblueshadingissignificantlygreaterthanthelightgreencolors).478

In the lowest ~1000 km of the mantle, scattering heterogeneities are in greater479

abundance in the20%areaaroundhotspots than inanyotherbin; there isalsoa480

slight increase in mapped heterogeneities beneath hotspots in the mid-mantle481

between600-900kmdepth(seethewideredcolorsshading,Fig.7c).Ourmapped482

scattering heterogeneities show little correlation with regions surrounding the483

surface location of slabs, except in areas furthest from slabs in the 600-900 km484

depth range (indicated by the wide orange-yellow shading, Fig. 7d). In the upper485

24

200kmofthemantle,scatteringstronglycorrelateswithhighseismicvelocitiesand486

proximitytoslabs(Figs.7aand7d,blueandyellowshading,respectively),which,at487

theseshallowdepthsismostcloselyrelatedtothelocationofcontinents.Whilethe488

precise locations of the heterogeneities is different, the heterogeneities resolved489

withP′�P′showaverysimilardistributioninthelowermost300kmofthemantle490

tothoseheterogeneitiesresolvedwithPK�KPinanearlierstudy[Frostetal.,2017].491

Totesttherobustnessofthesecorrelationswedeterminehowlikelytheyare492

tohavebeenproducedby chance.We rotate the tomographicmodels (of velocity493

and lateral gradient), and hotspot and slab locations by a random angle about a494

randomlylocatedpoleofrotation.Wethenrecomputethecorrelationsbetweenthe495

rotated geographical features and the distribution of the unrotated scattering496

heterogeneities. The random rotation is repeated 200 times for each tomography497

model,aswellasforthehotspotandslablocations,tocalculatetherangeofpossible498

correlations.Themeanandstandarddeviationoftherangeofcorrelationsateach499

depthiscomputed,assumingGaussianstatistics.Wecomparethiswiththeoriginal,500

unrotateddatainFig.8,andconsideranycorrelationtobestatisticallysignificantif501

thecorrelationvaluebetweenscatterersandregionsof theunrotatedphenomena502

plots outside one standard deviation from the mean correlation of the rotated503

phenomena (demonstrating that at least 84% of the random correlations are a504

lower value). When we do not assume a distribution and instead calculate the505

proportionofsamplesaboveandbelowonestandarddeviationofthedata,wefind506

very similar patterns of significant observations. Using this metric, we define the507

followingcorrelationsassignificantandunlikelytheproductofchance:508

25

(1) Anincreasedcorrelationwithscatterersinregionsoflowvelocityatdepths509

greaterthan1800km(solidredlineintheleftpanelofFig.8a)510

(2) An increased abundance of scattering heterogeneities in regions of high511

velocity gradient in thedeepest fewhundredkmof themantle, aswell as512

between1600-2000kmdepth(solidredlineintherightpanelofFig.8b).513

(3) Anincreasedabundanceofheterogeneitiesclosetosurfacehotspotlocations514

atdepthsgreaterthan2100kmdepth(solidredlineinleftpanelofFig.8c).515

(4) Adecreasedabundanceofheterogeneitiesfarfromsurfacehotspotlocations516

atalmostalldepthsgreaterthan800kmdepth(solidredlineinrightpanel517

ofFig.8c).518

There is no significant correlation seen between scatterer locations and slab519

locations, except an increase in correlation between heterogeneities and large520

distancesfromslabsbetween600and900kmdepth,whichmatchesthedepth521

rangeoftheincreasedcorrelationwithlowvelocitygradients(solidredlinesin522

leftpanelofFig.8bandrightpanelof8d),andanincreasedcorrelationbetween523

heterogeneities and large distances from slabs throughout much of the lower524

mantle(whichiswhatoneexpectsifcorrelationsarestrongforlowvelocities).525

526

4.2Dependenceuponchoiceofmodel527When comparing small-scale scattering locations with tomographically528

derived high or low velocities, the results may depend upon the choice of the529

tomography model. In our previous analysis, we compared the distribution of530

scattering heterogeneities to tomography model SEMUCB-WM1 [French and531

Romanowicz,2014].Wefurtherexploretherelationshipbetweenourmappedfine-532

26

scale scattering heterogeneities with large-scale structures in other tomography533

models:GyPSuM,S40RTS,andTX2011(Figs.S4-6andS7-9forP-wavemodels).We534

find small differences in precise depths and magnitudes of correlations with535

differentmodels,butthecorrelationbetweenscatteringandlowvelocitiesatdepths536

below1600km,andwithhighvelocitiesatdepthsof200kmandshallowerandthe537

robustnessofthesecorrelationsareconsistentbetweenmodels.538

Totestthedependenceofcorrelationonthepatternofhotspots,inaddition539

to comparing with rotated hotspot locations, we create a population of randomly540

locatedhotspots,equalinnumbertotheprimaryandclearhotspotsfromCourtillot541

et al., [2003] and French and Romanowicz [2015]. We find that a synthetic542

population generates no preferential spatial correlation with the scattering543

heterogeneities (Fig. S10). Furthermore, when the population of random hotspot544

locations isrotatedto test therobustnessof thecorrelation, thecorrelationof the545

randompopulationveryoftenfallswellwithintheonestandarddeviationrangeof546

the rotated data (Fig. S12). This implies that the observed correlation between547

hotspot locations and scattering heterogeneities in the lowermantle is caused by548

thespecificdistributionofhotspots.549

Wetesttheinfluenceofourdecisiontouseonlythesurfaceslablocationsof550

the RUM model. We calculate the spatial correlation between scattering551

heterogeneitiesandslablocationsasdescribedabove,butuseslablocationsatthe552

depthof theheterogeneity.Whenconsideringscatteringheterogeneitiesatdepths553

greaterthanthatwhichtheslabismappedtoweusethelocationoftheslabatthe554

last mapped depth and project this position vertically down to the CMB. This555

27

method of vertical extrapolation likely still misrepresents the locations of slabs:556

someamountoflateralmovementatgreaterdepthsisevidentintomographicand557

geodynamicmodelsbut is typicallyontheorderofa fewdegrees[e.g.Frenchand558

Romanowicz,2014andSteinbergeretal.,2012].Nonetheless,wefindnosignificant559

difference in the correlations between using the surface slab location and slab560

locationswithdepth(Fig.7andFigs.S11andS12).561

562

563Figure 6: Tomography and distance from subduction zones and hotspots by564

percentage area calculated for sampling at the CMB. (a) The magnitude of the565

velocity anomalies in SEMUCB-WM1 [French and Romanowicz, 2014] in the area566

sampledbyourdatasetattheCMBdisplayedbydecreasinganomaly(fromfastblue567

28

areastoslowredareas)inregionsoccupying20%oftheareaoftheCMB.(b)The568

magnitudeofthelateralvelocitygradientdecreasingfromhightolowin20%area569

regions. (c) Distance from hotspots (connected to plumes identified as either570

primary or clear in the analysis of French and Romanowicz [2015]). (d) Distance571

fromslabs(atzerodepthsliceinRUM[GudmundssonandSambridge,1998].Black572

linemarkstheextentofthesampledarea(asinFigure3d).573

[2COLUMNFIGURE]574

575

576

577Figure 7: Scattering abundance (bar width) with depth compared with the578

distribution of large-scale heterogeneity throughout the mantle (colour scale).579

Scattering abundance is calculated cumulatively across all areas, is divided by580

0

200

400

600

800

1000

1200

1400

1600

1800

2000

2200

2400

2600

2800

Depth

(km

)

0 0.25 0.5 0.75 1.0

0 20 40 60 80 100Dist. from HIGH dVs by % area

a dVs by area

0 0.25 0.5 0.75 1.0

0 20 40 60 80 100Dist from HIGH D(dVs) by % area

b D(dVs) by area

Dist. from SLABS by % area 0 20 40 60 80 100

0 0.25 0.5 0.75 1.0

d Dist. to Slabs at z=0

Dist. from HOTSPOTS by % area 0 20 40 60 80 100

0 0.25 0.5 0.75 1.0

c Dist. to Hotspots

Normalised cumulative

scattering/sampling

Normalised cumulative

scattering/sampling

Normalised cumulative

scattering/sampling

Normalised cumulative

scattering/sampling

29

sampling, and is normalised to unity, representing the maximum scattering581

abundance at any depth. (a) Scattering heterogeneity and tomographic velocity582

anomalies (from SEMUCB-WM1 [French and Romanowicz, 2014]) sorted from583

highest (blue) to lowest (red)measuredasa functionofsurfacearea in20%area584

bins.(b)Scatteringheterogeneityandlateraltomographicvelocitygradientsorted585

fromhighest (dark blue) to lowest (light green). (c) Scattering heterogeneity and586

distance from hotspots from low to high (red and yellow, respectively). (d)587

Scatteringheterogeneityanddistancefromslabsfromlowtohigh(redandyellow,588

respectively). Scattering heterogeneity in the lower mantle shows an affinity for589

both low seismic velocities and hotspots. Black lines encapsulate the highest and590

lowest40%arearegions.591

[2COLUMNFIGURE]592

593

30

594Figure 8: Scattering abundance with depth, divided by sampling, showing the595

unrotated model (red line) compared with rotated models (grey). The unrotated596

0

200

400

600

800

1000

1200

1400

1600

1800

2000

2200

2400

2600

2800

Lowest 20% dist. area Highest 20% dist. area

0 0.25 0.5 0.75 1.00 0.25 0.5 0.75 1.0

0

200

400

600

800

1000

1200

1400

1600

1800

2000

2200

2400

2600

2800

Lowest 20% dVs area Highest 20% dVs area

0 0.25 0.5 0.75 1.00 0.25 0.5 0.75 1.0

0

200

400

600

800

1000

1200

1400

1600

1800

2000

2200

2400

2600

2800

0 0.25 0.5 0.75 1.00 0.25 0.5 0.75 1.0

Lowest 20% D(dVs) area Highest 20% D(dVs) area

0

200

400

600

800

1000

1200

1400

1600

1800

2000

2200

2400

2600

2800

Lowest 20% dist. area Highest 20% dist. area

0 0.25 0.5 0.75 1.00 0.25 0.5 0.75 1.0

d

ba

c

dVs heterogeneity gradient

Hotspot locations Subduction zone locations

dVs heterogeneity

Depth

(km

)D

epth

(km

)

Depth

(km

)D

epth

(km

)

Normalised

scattering/sampling

Normalised

scattering/sampling

Normalised

scattering/sampling

Normalised

scattering/sampling

Normalised

scattering/sampling

Normalised

scattering/sampling

Normalised

scattering/sampling

Normalised

scattering/sampling

31

model(redline)isdashedwhenwithinonestandarddeviation(darkgrayshading)597

of themeanof the spatial correlations (blackdiamonds)with the rotatedmodels,598

andsolidwhenoutsidethis level.Thelightershadedregionmarkstherangeofall599

correlationswiththerandomlyrotatedphenomena.Comparisonsareshownfor:(a)600

tomographically derived velocity heterogeneity from SEMUCB-WM1 for the 20%601

area corresponding to the lowest (left panel) and highest velocities (right panel).602

Correlation between increased scattering abundance and low velocities appears603

robust in the deepest mantle, and correlation to high velocities is robust in the604

shallowest200kmof themantle, aswell asaround1200kmdepth.(b)As in(a)605

except correlations are between observed scattering and rotated shear velocity606

gradients in model SEMUCB-WM1. Correlations are most significant for the607

strongest gradients (right panel) at the base of the mantle. (c) As in (a) except608

correlations are between scatterers and distance to rotated hotspot regions.609

Correlationsaremostsignificant inthedeepestmantle incloseproximitytobeing610

beneath hotspots (left panel). (d) as in (c) except correlations are between611

scatterersanddistancetorotatedslabregions.Ourrandomrotationtestshowsno612

significantcorrelationbetweenscatterersandproximitytoslabs.613

[2COLUMNFIGURE]614

615

32

6165.Discussion617618

In this study we mapped scattering heterogeneities and explored their619

geographical relationship to tomographic velocities and gradients, as well as620

hotspotsandslabs. Ourresultsmaybe interpreted in termsof thedistributionof621

mantleheterogeneity,whichwewilldiscusshere.622

6235.1Possibleoriginsofscatteringheterogeneityinthemantle624625

We observe scattering from small-scale heterogeneity throughout the626

mantle,with increasedheterogeneityat thetopandbottomofthemantle.Seismic627

waves can be scattered by volumetric heterogeneity with sharp impedance628

contrasts,when theheterogeneity has aminimumscale length comparable to the629

wavelengthoftheincidentwave.Ourmethodisnotcapableofresolvingtheprecise630

partitioning of the incident wavefield into scattered versus transmitted energy,631

sincewedonothaveaconsistentreferencephasetocomparetotheamplitudeof632

the scattered wave. Thus we are unable to constrain the properties of the633

heterogeneities (e.g. impedance contrast). Nonetheless, the frequencies of waves634

that we study (between 0.5 and 2.0 Hz) imply that observed scattering635

heterogeneitieshaveaminimumscalelengthofonetotensofkm.636

Avarietyofstructurescouldscattertheenergyobservedinourdata.Wecan637

usethedistributionandsizesofscatteringheterogeneitiestoaddressthefeasibility638

ofpossiblecauses.Materialundergoingphasechangessuchasfrombridgmaniteto639

post-perovskite(pPv)inthelowermantle(orthebacktransformation)[Murakami640

etal.,2004;OganovandOno,2004],aswellastransitionsofolivinetowadsleyiteto641

33

ringwooditetoperovskitethroughtheuppermantletransitionzonecouldprovide642

an impedance contrast with the ambient mantle. The bridgmanite to pPv phase643

transitionispredictedtooccurinthedeepestfew100kmofthemantle,andonlyin644

relatively cold regions of the mantle for a standard pyrolitic composition, thus645

would not be appropriate to explain scattering at all depths and locations, unless646

mineralogical alterations are considered [Lay et al. 2006]. Thephase transition is647

controlledby temperature, composition, andpressure.Whilepressure is assumed648

hydrostatic, localchanges incomposition,perhapsbycontaminationof themantle649

by subducted mid-ocean ridge basalt (MORB), may influence the pPv transition650

[Grocholski et al., 2012], possibly causing the transition to occur locally in the651

vicinity of the MORB contamination. Metastability of phase transitions due to652

chemical heterogeneity [Catalli et al., 2009] could allow transformed minerals to653

persist outside of their expected stability range. High thermal conductivity in the654

lowermantle[Stackhouseetal.,2015]renderssmall-scaletemperaturechangesan655

unlikely cause of spatially limited occurrence of the pPv transition. While many656

morphologies and scale lengths of pPv regions can be envisioned that could657

contributetowavefieldscatteringobservedhere,thedetailsofsuchprocessesare658

notconstrained.However,pPvshouldnotbestable in theuppermantle,andthus659

cannot explain observed scattering there. Nonetheless, pPv remains a viable660

contributortowavefieldscatteringinthedeepestmantle.661

The subduction process continuously introduces compositional662

heterogeneityintothemantle.Scatteringhaspreviouslybeenmappedintheupper663

mantle and lower mantle in the proximity of subduction zones [Kaneshima and664

34

Helffrich, 1998; Rost and Earle, 2010; Miller and Niu, 2008; Bentham and Rost,665

2014].Wedonotobservearobustpreferenceofscatteringheterogeneityinupper666

mantle regions of subduction over other regions. While we do observe slightly667

increasedscatteringinregionsassociatedwithsubductionataround600to900km668

depth (Fig. 7a), this does not appear to be statistically significant (Fig. 8a, right669

panel). Nonetheless, the increased concentration of scattering heterogeneity670

between600and900kmdepthshowsrobustspatialcorrelationwithregionsaway671

fromsubductionzonesandareasoflowamplitudelateralvelocitygradient(Figs.7672

and7). Insome tomographicmodelssubductingslabsareobserved to flattenata673

similardepth,between~800-1200kmdepth[e.g.FrenchandRomanowicz,2015].674

Oceanic crust may be responsible for scattering throughout the mantle.675

Subductedoceaniccrustmayremainunmixedduetoslowchemicaldiffusionrates676

[Olson et al., 1984] and is only homogenised into the mantle through mechanical677

stirring. If the observed scattering heterogeneities are oceanic crust then the678

dispersalofheterogeneitiesthroughoutthemantlemustbefasterthanstirringand679

removal of heterogeneities since scattering heterogeneity is also observed in680

regionsthathavenotbeeninfluencedbysubductionforalongtime.681

The iron spin transition affects the velocity and density of iron-bearing682

mantlematerials[Linetal.,2005].Recently,thishasbeenobservedtooccurovera683

60GPapressurerange(~600to2000kmdepth)[HolmstromandStixrude,2015]684

and thus would likely not generate discrete heterogeneities capable of causing685

scattering.686

35

Products of chemical reactions between core and mantle materials are687

predictedtohavephysicalpropertiesincontrastwiththeambientmantle[Knittle688

andJeanloz,1989]thusmaybecapableofcausingseismicscattering.Experiments689

demonstratethatsuchmantlematerialenrichedinironwouldlikelybedenserthan690

the ambient mantle [Wicks et al., 2010]. An interesting possibility is the691

developmentofareactionproductlayerthatwouldinhibitfurtherinteractionwith692

the core; for this case, products are likely to be constrained to a very limited693

thicknessclosetotheCMB,ontheorderofafewmeterstokilometers[Kandaand694

Stevenson, 2006]. However, flow in the deep mantle could generate thicker695

accumulationsofreactionproducts[Maoetal.,2006],whichcouldscatterwaves.In696

addition,ULVZsarecommonly imagedtohavevastlyreducedseismicvelocitiesof697

up to -10%dVp and -30%dVs, and increased density of +10-20% relative to the698

surroundingmantle[e.g.,McNamaraetal.,2010].Partialmeltofmantlematerialhas699

been proposed as an explanation of ULVZs [Williams and Garnero, 1996]. Partial700

meltmaybedenserthanthesolidstate[OhtaniandMaeda,2001]aswellashaving701

stronglyreducedseismicvelocities.WhileULVZsandCMBreactionproductscould702

explain deeper scattering heterogeneities, simulations have suggested that dense703

materialmayalsobeentrainedupto200kmabovetheCMB,dependentondensity,704

viscosity, and vigor of mantle flow [Bower et al., 2011]. CMB topography or705

roughnessmightcausescattering[ChangandCleary,1981;Mancinellietal.,2016],706

butthiscouldnotexplainheterogeneitieswemapupoffoftheCMBthroughoutthe707

mantle.LLSVPsmaybecompositionallydistinct fromthesurroundingmantle [e.g.708

Garnero et al., 2016], anddynamical flowmodels predict that the LLSVPmaterial709

36

willbegraduallyentrainedintomantleflowonsmall lengthscales[Lietal.,2014;710

Williams et al., 2015; Mulyukova et al., 2015]. Thus, depending on the LLSVP711

properties and entrained heterogeneity scale, this process might give rise to712

scattering. Geodynamic models also predict that surrounding ambient mantle713

material can be downward entrained into the LLSVPs, thus offering an origin of714

scatteringwithinLLSVPregions.715

7165.2Distributionofscatteringheterogeneity717718

Thedistributionof small-scale volumetric heterogeneities is likely strongly719

dependentonthedynamicpropertiesandprocesseswithintheEarth.Innumerical720

simulationsofmantledynamicssmall-scaleheterogeneity,particularlythatderived721

fromsubductedoceaniccrust,tendstobeconcentratedinregionsofupwellingfrom722

the lower mantle around plumes and downwelling from the surface around723

subductionzones(Fig.1ofLietal.,[2014]).Thesamefocusingbeneathupwellings724

isexpectedforbasalheterogeneities[McNamaraetal.,2010](e.g.,compositionally725

distinct ULVZ material, CMB reaction products, and entrained LLSVP material).726

Furthermore, large-scale mantle heterogeneity may influence radial small-scale727

heterogeneity distribution by modifying the convective flows in which the728

heterogeneitiescouldbeentrained[Lietal.,2014].729

As wavelength at some fixed frequency is a function of the local velocity,730

whichchangeswithdepth, and thewavelengthof scattering structure that canbe731

resolvedisdependentontheincidentfrequency,itfollowsthatinbandlimiteddata,732

theresolvablescatteringwavelengthchangeswithdepth.Wefilteralldatabetween733

0.5 and 2.0 Hz, therefore, we resolve scattering heterogeneity with wavelengths734

37

between about 7-28 km at the CMB, decreasing to about 3-12 km at the surface.735

Stirring of initially larger-scale heterogeneity is suggested to lead to a cascade of736

heterogeneity sizes, increasing in abundance with decreasing scale [Olson et al.,737

1984].Apreviousstudyofthescaleofscatteringheterogeneitiesinthelowermost738

mantle found the most common scale-length to be 4-7 km, but other scales were739

also present [Frost et al., 2017]. Despite the limited frequency range used in this740

study, we are likely imaging heterogeneity of a similar size (around 7 km)741

throughoutthemantle.742

Thesimilaritybetweenscatteringheterogeneityabundanceandtomographic743

amplitude (Fig. 5) may arise from processes relating to convection and chemical744

differentiationthat likelygeneratestrong lateralvelocityvariationsoncontinental745

scalesandsmallerthroughstirringanddiffusion.Lowermantleanomaliesmanifest746

atarangeofspatialscales(LLSVPs,ULVZs,D′′,CMBreactionproducts),andstirring747

andentrainmentmayfurtherdecreasetheirsize[Olsonetal.,1984,Lietal.,2014],748

leadingbothtohigh-amplitudelarge-scalevelocityanomaliesandabundantsmall-749

scalescattering.Uppermantleheterogeneityrelatedtosubduction,magmatism,and750

convectiveprocessesarealsolikelytooccuracrossscales.Inadditiontoincreased751

scatteringatthetopandbottomofthemantle,wealsoobserveaslightbutmarked752

increase in scattering abundance from 600-900 km depth, independent of the753

tomographic velocity structure,whichmay relate to slab subductionprocesses or754

large-scaleverticalviscositychanges[Rudolphetal.,2015].755

7566.Conclusion757758

38

Through analysis of the high-frequency seismic wavefield we map the759

distributionofsmall-scaleseismicheterogeneity,ontheorderof~1-10kminsize,760

throughout Earth’s mantle. We deterministically locate vastly more scattering761

heterogeneities than has been done previously, significantly improving our762

understanding of small-scale mantle structure. The spatial distribution and scale-763

lengthofthisscatteringheterogeneitysuggestsitmaybetheproductofseveralon-764

goingprocessesinthemantle.Theseincludeoceaniccrustdisseminatedthroughout765

the mantle, entrainment of basal heterogeneities such as ULVZ material or core-766

mantle reaction product, and compositionally distinct LLSVP material swept into767

mantle flow. Subducted MORB may suitably explain all scattering observations768

withoutscatteringcontributions fromothersources.However,wecannotruleout769

that scattering is caused by a mixture of heterogeneities with different origins in770

different regions and depths. While small-scale heterogeneity appears present in771

much of the mantle, we find increased scattering heterogeneity within the772

uppermost200kmofthemantleandthelowermost300kmofthemantle,similar773

to heterogeneity amplitudes seen in tomography models. We find no statistically774

significant correlationbetweenscatteringandsubductingslabs in theupper1000775

kmof themantle. In the lowermantle (fromaround1500kmdepthdown to the776

CMB), scattering is most common in regions related to the LLSVPs and close to777

deeply sourcedmantlehotspots.Meanwhile, scattering is rare in regions far from778

deeply sourced mantle hotspots. This suggests that large-scale convective lower779

mantlestructuresmayentrainandconcentratesmall-scaleheterogeneityinregions780

ofupwelling,downwelling,andstagnantflow.781

39

782Acknowledgements:ThisworkwassupportedNSFgrantEAR1401270andNERC783

grantsNE/K006290/1andNE/H022473/1.CTBTInternationalMonitoringSystem784

datausedherewereacquiredwhiletheauthorwasundertakingastudentship785

sponsoredbytheUKNationalDataCentreatAWEBlacknest.Thepaperbenefited786

fromdiscussionswithBarbaraRomanowicz,andimprovedfromhelpfulcomments787

oftworeviewers.788

789

790

791

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