the velocity structure and heterogeneity of the...

134 Physicsof theEarth and PlanetaryInteriors, 59 (1990)134—144ElsevierSciencePublishersBy., Amsterdam— Printedin The Netherlands

Thevelocity structureandheterogeneityof theuppermantle *

B.L.N. KennettandJ.R.Bowman

ResearchSchoolofEarth Sciences,AustralianNational University, G.P.O. Box 4, Canberra,A.C.T 2601 (Australia)

(ReceivedMarch20, 1988; revisionacceptedFebruary13, 1989)

Kennett,B.L.N. and Bowman,J.R., 1990. The velocity structureand heterogeneityof the upper mantle.Phys. EarthPlanet. Inter., 59: 134—144.

In a particularregion a smoothedand averagedrepresentationof thevelocity structurein theupper mantlecan bederivedfromlong-periodbody wave andhigher-modesurfacewave observations.Theverticalresolvingpowerof suchtechniquesis limited by the relatively long wavelengthsused. In contrast, short-period studies show considerablecomplexitiesin postulatedone-dimensionalmodels which areunresolvablein the long-periodband. However, thesemaybe associatedwith themappingof lateralheterogeneityinto a verticalprofile.

To assesstheextent to which lateralheterogeneityin themantlecan be resolved,we have attemptedto model thefeaturesseenon recordingsof earthquakesin the Indonesia/NewGuinea region at large-aperture(400—1000km)arraysof portableseismic recorders.With horizontal heterogeneityscalesof the orderof 300—500 km and velocityperturbationsup to 2%, theamplitudedeviationsfrom thosepredictedfor a stratified model can beconsiderableandfit in well with the patternof observations.For long-periodwavessuchlaterally heterogeneousstructureshaveonly amodesteffect, with weakinter-modecoupling resulting from the heterogeneity.As a result, a one-dimensionalmodelmaystill bea useful approximationfor long-periodstudies,but will not beadequatefor broad-bandor short-periodwork.

1. Introduction erally give an ideaof local structure,and surfacewave dispersion is dependenton a horizontally

Over the last 30 yr substantialeffort has been averagedstructure.Recently, the distinctions be-expendedby many workers on determining the tween theseapproacheshave begun to blur asstructureof the uppermantle.The dominant ap- advancesin the calculationof theoreticalseismo-proacheshavebeento use long- and short-period gramshaveled to the exploitationof moreof thebody wave observationsand the dispersion of seismic waveform, particularly for S waves. Bodysurfacewaves. In the bodywave studies,attention wavestudieshaveincludedsurfacemultiple phasesis directedto the energyreturnto the surfacefrom (Grand and Heimberger,1984), and multi-modethe structurein the uppermantle. In the surface surfacewave analyseshave included many bodywave work, on the other hand, the waves are wavephases(Nolet, 1977;Lerner-LamandJordan,generallyobservedafter a longerpropagationpath 1983;Nolet et a!., 1986).However, the best-devel-during which multiple interactionswith the struc- oped models are dependent on the as-ture haveoccurred.Thusbody wave methodsgen- sumptionof a stratifieduppermantle,eventhough

it has long beenrecognizedthat there has to benoticeableregionalvariation in the seismicveloci-

* Presentedat IASPEI symposium;Computationand Inter- . .

ties in the uppermantle(Hernn 1969).pretationof SeismicWaveform in 2-Dimensionaland3-Di- . . . .

mensional Structures, held at the IUGG meeting 1987, By treatingthe lateralvanability in the Earth’sVancouver,Canada. structureas a perturbationto a radially stratified

0031-9201/90/$03.50 © 1990 Elsevier SciencePublishersBy.

THE VELOCITY STRUCTURE AND HETEROGENEITY OF THE UPPER MANTLE 135

model, Woodhouseand Dziewonski (1984) have a km/sbeenableto map the large-scalestructurein the 0 6 7 8 ~ 1~ 1~ 1~

uppermantle.They havematchedglobal observa- .1

tions of shearwavetrainswith theoreticalseismogramsto denvea sphencalharmonicexpansionof 200

the heterogeneityin the uppermantle The honzontal resolution availableis of the order of 2000 .~ 400

km and the major featuressuch as continental ~shields are clearly visible in the shallow parts of ~the model The honzontalscalecurrently attaina ~ 600 -

ble by this approachis thusof the sameorder asthe distanceover which energy is returnedfrom 800 -

the top 800 km of the mantle.In this paper we will be concernedwith the

characterof the heterogeneityspectrumon a re- 1000 -

gional scalethat lies beneaththe resolving power Fig. 1. Models of the P-wavevelocity distribution with depth

of the global studies.Nearly all previousattempts in the upper mantle: the continuous line indicates a shieldmodel (S8—Burdick,1981) and theshadedzone encompassesto look at regional heterogeneityin the uppera wide rangeof otherproposedmodels.

mantlehavebeenbasedon tomographicmethods(e.g., Romanowicz,1980; Spakman,1986). Suchapproachesare limited in their horizontal resolu- to indicate by the shadedregion the zone oftion by the distribution of seismic stationsand velocity variation spannedby different velocitywork well whenthereare major velocity contrasts models.The zoneabove200 km showsthe largestpresentwhich may, for example,arise from the variability associatedwith the different tectonictectonicevolutionof a region. Thesestudiesrely environmentssampledin different regions, buton thetravel timedifferencesin transmissionfrom significantvariationpersiststo considerabledepththe source, with the assumptionthat any het- in modelsderivedfrom shorter-perioddata.Thoseerogeneity is concentratedin the upper mantle, modelsgeneratedby the modellingof long-periodGrand (1987) has shown how such work can be bodywave arrivalsshow muchless spreadbeneathcombinedwith studiesof the travel timesof multi- 300 km and their velocity gradientsare generallyply reflectedbody waveson long-periodrecords, concordantwith sphericallyaveragedmodelssuchto give a moreuniform datadistribution andthus as PREM (Dziewonski andAnderson,1981). Theenhanceresolution, major velocity transitionsnear 400 and 650 km

The use of permanentseismic stationsmeans stand out even in the envelope of a suite ofthat, in general, it is not possible to track the models, but individual models have significantdetailed evolution of the seismic wavefield with variationsin the velocity contrastand the char-position, which would be diagnosticof the characterof the transition.Theverticalresolvingpoweracter of the mantle heterogeneityfield. However, of long-perioddatais limited and different veloc-as we shall see in the next section, the use of ity modelscangive rise to very similar waveformsarraysof portableseismicrecorderscanfill in the (Ingateet a!., 1986).detail andso provide improved constraintson the The style of publishedmodelsdiffer consider-natureof the spatialvariationof the seismicveloc- ably. Somemodelsare constructedto fit the majority field. featuresof the travel time curves and so have

We can obtain some idea of the degreeof rather simple character,as, for example, in theheterogeneityin the uppermantle by comparing work of King and Calcagnile(1976). However,different stratified velocity models. In Fig. 1 we When an attempt is made to match a suite ofillustrate a representativevelocity model for a observationsin detail, rather complex velocityshieldregion (58—Burdick, 1981) and havetried modelsresult (Haleset a!., 1980).

136 B.L.N. KENNETTANDJR, BOWMAN

For a given region, one should thereforeview featureswhich mayappearsharpfrom long-periodthe shadedzone in Fig. 1 as providing outside observationswill not necessarilybe sharp whenlimits on any particular vertical velocity profile subjected to the greater vertical resolution ofdrawn from the ensemblewhich collectively de- shorter-periodwaves.However, the shorterwave-fines a laterally heterogeneousmodel. The allow- lengthsare also more sensitiveto the presenceofable deviations in seismic velocity away from a lateralheterogeneity,and sucheffectswill tendtosmooth,stratified, referencemodel would gener- degradethe attainablevertical resolution. Withally be less than ±3%, but we need additional sufficient datacontrol we may hope to obtain ainformation to constrain the horizontal scale of good representationof the meanvelocity structurevariation.We shall seesubsequentlythat horizon- in a regionas well as information on the charactertal heterogeneityscalesof the order of 200—400 of the deviationsfrom that structure.km at depthsbelow 200 km canexplain much of To this end, the ResearchSchool of Earththe observedseismic behaviour. Sciencesat the AustralianNationalUniversity has

deployeda numberof arraysof portableseismicrecordersover the last 12 yr. Thesearrays were

2. Observationson the Australian shield designedto recordthe abundantearthquakesfromthe Indonesianand New Guinea seismic belts,

To place strong constraintson upper mantle with propagationpaths which lie almostentirelystructurewe need to havea relatively close net- within the Indo-Australianplate. New Guineaiswork of short-periodobservations.We recall that separatedfrom Australia by the shallow Arafura

Temporary Array Studies

0. ~ ~ ~

~ .~

INDONESIA .

~ , .

-10. - .. Ar:fura

Fig. 2. Location map for the portablearray stationsand the earthquakesdisplayedin the record Sections.The NWB and TCTportablearraysareindicatedby theopensymbolsand theposition of thepermanentWarramungaarray (WRA) is alsoshown.Thesolid pentagonmarks theevent usedwith theTCT array in Fig. 3 and the solid trianglestheeventsusedin thecompositesectionofFig. 4.


Sea, which is underlain by continental material, north—south and east—westarms of the NWBand a broad continentalshelf reachesto almost arrayin Fig. 2 and closeto the westernendof thethe Indonesianarc structures(Fig. 2). TCT array.Thecombinationof the variousarrays

The arrayshavebeendeployedat a varietyof gives a detaileddataset which covers scalesfromspacings to give a total aperture ranging from 25 to 1000 km for propagationpaths from the-~ 400 km (e.g., NWB) to 1000 km (e.g.,TCT). samegenerallocation.In eachcase,a largeraperturecanbe synthesized If we look at the recordsfor a singleevent, weby using multiple sources.The size of these re- find that a numberof different seismicphasescanceiver arrays is comparableto the depth of the often be tracedover considerabledistances(Fig.uppermantle andso providesan excellentoppor- 3). However, the relative amplitude of differenttunity to investigatetheheterogeneityscaleswithin partsof the seismogramcandiffer markedlyacrossa singleregionof the uppermantle.The duration the recordsection,with a very significant effect onof recordingfor eacharray is 3 months,which the visibility of laterphases.For example,in Fig.provides a reasonablenumber of medium-sized 3, foran Indonesianeventof 66 km depthrecordedevents,sufficiently large to be effectively located at the TCT array, thereis a prominentlater phasebut not so big as to have very complex source which is especiallyclear at rangesfrom 1600 toradiation(4 � mb � 5.5). Theearly, large-aperture, 1800 km and again from 2200 to 2500 km. Overarraysconsistedentirely of direct recordingana- the intervening region this arrival is much lesslogue units,but the morerecentmedium-aperture clearandthe time—distancecurve is more subjec-arrays have been supplementedby an array of tive. The timing would fit with an arrival refractedportabledigital units with an apertureof —. 100 below the 400 km transition. Part of the amplitudekm. In addition, the observationsfor a numberof variationmay be associatedwith interferencewiththeportablearrayscanbelinked to thepermanent the reflection from the transition. However, theWarramungaarray(WRA), which hasan L-shaped changein waveformoveronly a 50 km interval isconfigurationanda 25 km aperture(Clearyet al., verydifficult to explainwith a stratifiedmodel.1968). WRA lies near the junction of the Sucha variation in the clarity of a phaseis very

ii’’ ‘I

40~-~- ~ ~

—.~-. ~ ~ © -~ ~~ ~ ~— .)__ ~. -~

35 —~~--=~/i...~- ~, .— ~ —=~--~ii---~-- ~- -~ ~. ~ :t:-~~ .~ ~i=— -~

30. - ~—~- -~ ~

— ~— -~ ~ ..;-_ z~_ — i~— 5~ ~

~YY~ H1600. 1800. 2000. 2200. 2400.

Distance kmFig. 3. Record sectionof an event at 66 km depth at the southernend of Timor recordedat the large-apertureTCT array. Thetrajectoriesof thefirstarrival andthelater arrival associatedwith the400 km transitionaremarked.All tracesarenormalizedto thesamepeak amplitude.

138 B.L.N. KENNEIT AND JR. BOWMAN

P waves

‘ I I I

30. . -

us

Lt7

20.

10. fl~ I I I

1600. 1700. 1800.

Distance kmFig. 4. Compositerecordsectionof eventsfrom theIndonesianarcrecordedattheNWB array.To reduceclutterthetraceshaveonlybeen displayed at 2 km intervals, with normalization to the samepeak amplitude. The prominentlater arrival from the 400 kmtransition shows a variableaspectacrossthesection.

common andthe behaviourbearsno simplerela- and longer ranges,but many of the traceswith ation to the particular recording site. We cannot distinct arrival comefrom the sameevent.therefore ascribe such effects to local geological With thehighdensityof datacoverageachievedstructure,but rathermust look for a deepercause in Fig. 4 onecanbegin to correlatephasesacrossfor variability on a 50—300 km scale. many seismograms,evenwhere arrivals are only

We may also synthesizea large-aperturearray weaklyrepresentedon individual traces.However,by superimposingthe recordsfrom a numberof theinterpretationis likely to bestronglyinfluencedeventsat a medium-aperturearray.With multiple by the dominant traces.The eventswhich com-earthquakes,the variation in the characterof the prise Fig. 4 haveall beenrecordedat the samerecordsfrom event to eventcan be quite striking, array so that structurebeneaththe array shouldeven when the propagationpaths are similar. A havea comparableeffect on all events.The propa-compositerecord sectionfrom the NWB array is gation pathsfrom theseIndonesianearthquakestoshownin Fig. 4 for a numberof shallow Indone- the NWB array cover a relativelynarrowrangeofsian earthquakes,whoseposition are indicatedby azimuths, and the turning point for the upperthe solid triangles in Fig. 2. Each trace in the mantlephasesshould lie in a zoneof — 200—300sectionis normalizedto the samepeakamplitude. km width beneath the northwestern coast ofThis normalization has the effect of suppressing Australia. Somepart of the changein characterthe very-low-amplitudefirst arrivalsand so all the betweenevents may arise from the sourceradia-prominent featuresin the sectionarisefrom later tion pattern. Strike-slip events along the arc givephases.The prominentarrival at — 20 s reduced particularly efficient P radiation in the directiontime near1700 km canbe trackedto bothshorter of the NWB array,but typical normal and thrust


mechanismsare not as favourable.However, it is acterof manyobservations,wewill not attempttodifficult to arrangethe sourcemechanismso as to constructa specific model but will endeavourtoselectivelysuppressan arrival from the 400 km proposea classof laterally heterogeneousmodelstransitionandallow shallowerpropagatingenergy which havethe requiredproperties.to arrive. We therefore need to look for some We require that any suitable model shouldap-structural explanation for the variability of the pear to be stratified for low-frequency propa-relative amplitudes of different upper mantle gation and so it is effective to parameterizethephasesin theseshort-periodstudies, laterally heterogeneousstructureas perturbations

On smaller scales,Kennett (1987) and Korn away from a stratified referencemodel. Suchper-(1988) have shown that the complexity of the turbationsshouldnot be greaterthan — 2% posi-recordings of Indonesianevents at the 25 km tive or negativeexcursionsfrom the reference,toapertureWarramungaarray is reducedas the de- avoidventuringtoo far outsidethe boundsderivedpth of the sourceincreases.Scatteringeffects are from a wide range of proposedmantle modelsparticularly prominentfor pathslying above — 80 (Fig. 1).km depth.The simplest records are obtainedfor After someexperimentation,it provedpossiblesource depths > 200 km, for which the propa- to find a classof modelswhich havethe requiredgation path includesonly a relatively short leg in properties: these models are characterizedbyany shallow zoneof concentratedheterogeneity. horizontal variation on a scale of 300—500 km

with a vertical scalewhich increaseswith depthfrom — 100 km scaleat 200 km deepto — 200 km

3. Models of upper mantle heterogeneity scale at 900 km depth. Three two-dimensionalsimulationsof sucha classof modelsare shownin

In the previous section we have seen that Fig. 5. Each of thesecross-sectionsof the per-detailedshort-periodstudiesof the uppermantle turbationto the referencemodel wasgeneratedbydisplay a number of featureswhich cannot be randomlyperturbingthe velocitiesspecifiedat 100describedby an individual stratified model. In km horizontal intervals with a uniform randomparticular,wehaveidentified amplitudeanomalies distribution, allowing up to ±2%change.Thein recordsof a singleeventon scalesof 150—300 modelswere thensmoothedwith a 500 km movingkm, and significant variation of the characterof window to removerapid oscillations in velocityseismic recordsbetweendifferent events, values. This imposesa preferredscale length of

Nevertheless,we must recall that for many — 400 km with a perturbation typically <1%.long-periodstudiesa radially stratifiedmodel ap- The velocity gradients, both horizontally andpears to give a good description of the seismic vertically, are strongestin relatively narrow beltsstructureof the upper mantle. For multi-mode and have a strong effect on short-periodwavesurface wavetrains with periods > 20—30 s, a propagation.Themodel in threedimensionswouldstratified model will allow a detailed fit to both havea similar modulationof the referencevelocitydispersion and waveforms,Any model which we structurewith horizontalscalesagainof the orderproposemust therefore be such that it is trans- of 400 km.parentto such horizontally travelling long-period The referencemodel chosenfor the construe-waves.In addition, we would like to explain the tion of specific laterally heterogeneoussectionssuccessof modellinglong-periodbodywave phases was the isotropic version of the PREM modelby matching theoretical seismogramscalculated (Dziewonski andAnderson,1981) with a superim-for stratifiedEarthmodels. posedcontinentalcrust, shown as the continuous

line in Fig. 7. The basic perturbationwas con-3.1. Laterally heterogeneousmodels structed for P waves,and the S wave model was

derivedassumingthat the percentagechangefromAs we are not seekingto explainoneparticular the referencemodel was the sameas for the P

set of observationsbut rather the general char- waves,which may representan underestimateof

140 B.L.N. KENNETT AND JR. BOWMAN

Model C _________________ ,-,-~ ~i the effect of the heterogeneity.Within the hetero-geneous region, the displacementand tractionfields are representedon eachdepth section as asum of the appropriate eigenfunctionsfor the

~. ~. ~ referencestructure.In a stratified region, the coef-.r~Ji ficients in the modal expansionat a particular

moo.100. 800. 1200. 1600. 2000. 2400. 2800. horizontal location would comprisea fixed part

Distance kmdeterminedby the modal content at the entry

Model M ___________________________________ location, multiplied by a phase increment de-

.-~. ~ - . ~ - terminedby the phasevelocity for eachmode. Inthe presenceof heterogeneityit is worthwhile to

400.

~. continueto extract the dominant phaseroll term

I. ~ ~ for eachmode,but now the remainingpart of the_j .~- modal coefficient is position dependent.These1000.400. 800. 1200. 1600. 2000. 2400. 2500. modal coefficients are determinedby a set of

Distance kincoupled first-order differential equations whose

Model N _______ - entriesdependon theeffect of the deviationsfrom—~z the reference model integrated over the whole

200.

~. ______________ depthsection. To avoid numericalproblemswithc ~ the specificationof boundaryconditions,it is con-

600. ~.

— - - C’ ~ - -. ‘~—“: venientto work directly with reflectionand trans-600. = ~ ~ii~-~ mission matrices for modal interaction. These

1000 ~ 400. 500. 1200. 1600. 2000 2400 2800 matrices satisfy a nonlinear Ricatti differentialDistance km

equationwith a simpleboundarycondition,whichFig. 5. Contouredplots of the deviationsfrom the stratified can readilybe integratednumericallystartingfromreference model in three heterogeneousmodels from the the far side of the heterogeneousregion. In effect,favoured class. The contour interval is 0.3%; the light linesshownegativeperturbationsand the heavy lines show positive a larger region of the heterogeneitymodel is cx-perturbations.The base model C is shownas the continuous posed with eachstep of the integration.Initially,line in Fig. 7. thereis no reflection andfull transmission,but the

matrices are modified by the propertiesof thethe S wave variation. The two-dimensional see- heterogeneousregion.tions of the velocity perturbationsillustrated in For our purposewe are interestedin the trans-Fig. 5 have beenused in studiesof travel times mitted modal field after passagethroughthe mod-and wave propagationfor both body waves and els shown in Fig. 5. To ensurethat all S bodysurfacewaves, wave interactionsdown to 1000 km as well as

surfacewave effects are included,we havetaken3.2. Multi-modesurfacewaves the modal expansion to cover all modes with

phasevelocities < 7 km s~ at each frequency.The treatmentof multi-mode surfacewavesin The number of relevant modes rises nearly un-

the laterally varying model was basedon the cou- early with increasing frequency: at 0.047 Hz apled modetreatmentintroducedby Kennett(1984) total of nine modesare needed;by 0.070 Hz thisfor two-dimensional models. The heterogeneous has risen to 14; and 28 modes are required atregionis viewed as being embeddedbetweentwo 0.141 Hz. As the computation time rises as thestratifiedzoneswith the referencestructure.Fora squareof the numberof modes,substantialcorn-given frequency,a surfacewave train is then en- putational effort is requiredat the higherfrequen-visaged to impinge on the left-hand side of the cies.heterogeneitymodel and the consequentreflected For frequenciesof <0.05 Hz the modal trans-and transmitted fields are evaluatedto examine mission is almostcomplete,with any transferbe-


tweenmodesinvolving <1% of the incident en- modes as the heterogeneityeffectsbecomedomi-ergy. Thus for periods longer than 20 s, the seis- nant.In this regimethemodal descriptionis rathermogramsafter passagethrough the heterogeneous cumbersomeandit is preferableto look directly atregionwould be essentiallyindistinguishablefrom the bodywave propagation.those for an equivalentstratifiedzone.

As the frequencyrises, the transferof energy 3.3. Body waveanalysis

between modes becomesmore important, withconsequentdistortionsof the propagationpattern. In Fig. 6 weconsidera comparisonbetweentheAt 0.141 Hz therecan be a substantialreduction travel-timebehaviourfor the referencemodel Cin the proportionof an incident modetransmitted (markedby opensymbols)andthe heterogeneousthrough the heterogeneousmodel without change model G (with the solid symbols)for a sourceatof mode type, to only 70% or so of the incident 10 km insidethe left-hand edgeof the model at aenergy. The remainingpart is redistributed into depthof 60 km. The take-off anglesat the sourceother modes,predominantly into the immediate were designedto give a relatively uniform sam-neighboursof the original mode.This transferof pling of the travel timebranchesin the caseof theenergy is selective dependingon the particular referencemedium,but the patternof symbols isheterogeneitymodel, but cangive significant cou- noticeablydistortedin the presenceof heterogene-pling between modes 3 and 6 associatedwith ity. Theclumping andthinning of the raypatternshallow structure, and also between groups of is associatedwith the developmentof local caus-higher modeswhich would interfereto give the S tics, generatedby the velocity gradientsat depth,wave phasesreturnedfrom the uppermantle.The of the type discussedby Nyc (1985). Thesecaus-distortion of the incident modal distribution is tics will be associatedwith significant changesinconsiderablebut the behaviouris dominatedby amplitude, with maxima in those parts of thestraight transmission.This frequency(0.141Hz) is seismic section where solid symbols are con-at the upperlimit of thoseincluded in modelling centrated.Once we allow for diffraction effects,body wave phaseson long-periodrecords,so we the amplitude anomalieshavea scaleof the ordercan seewhy a stratified mediumcanconstitutea of 150—300 km. in agreementwith the observa-usefuldescriptionof longer-periodphases. tions from the portablearrays.

At even higher frequencies(and thus shorter In addition to arrivals representingdistortedwavelengths)the numberof modesbecomesvery but recognizable travel time branchesfrom thelarge and there is complex interaction between referencemodel, the combination of horizontal

I I I I I I I I I I 1 I I I I

CoG.

30.- ° -

6151 %o 0

~ ~. •0• ° 0~~T

600. 1200. 1800. 2400.Distance km

Fig. 6. Comparisonof travel time curvesfor thestratified referencemodel C (open symbols)and theheterogeneousmodel G shownin Fig. 5 (solid symbols).The distributionof ray endpoints for G showsthe irregularpatternassociatedwith causticsinducedby themodecomplex velocity model.

142 B.L.N. KENNET1T AND J.R. BOWMAN

andverticalgradientsin the heterogeneousmodel a km/scan combineto producenew features.For exam- 0 ~‘ ~ 1~ 1~ 1~

pie, in the caseof model G, an apparentreflection (1from 500 km deptharisesfrom thegradientstruc- 200

turenear1200 km range,which leadsto a complex -

interferenceof travel time curvesnear2200 km inthe time section. Becauseof our assumptionof .~ 400 -

comparableheterogeneityscalesin the transverse ‘~

direction we can anticipatethat there could beabruptchangesin the characterof anarrival across 600a spatiallydistributed array arising from the pat-tern of causticsat the surface. Such effects are 800 -

seenfor someeventsat the digital subarrayof the G \ N M

NWB experiments. 0

In Fig. 6, for clarity, we haveshown only the 1000 -

time sectionfor oneof the heterogeneousmodels Fig. 7. Comparisonof radially stratified modelsderived fromfrom our favoured class, If, however, the time theinversionof the travel timesfrom theheterogeneousmodel

shown in Fig. 5. The referencemodel C is shown as thesectionsfor the threemodels shown in Fig. 5 are continuousline. For all three heterogeneousmodels, the at-

superimposed,the scatterof — 1 s aroundeach tempt to fit the behaviourwith stratification hasresulted in

travel timebranchis similar to that observedfrom alternatingpositive and negativevelocity gradients.upper mantle phases(Simpson, 1973), and theamplitudedistributionsshowa markedlydifferent the form of a depthsection,it shouldbe recalledcharacter. that different parts of a heterogeneousmodel are

To investigatetheeffectsof neglectingthepres- sampled in constructing the travel time curves.enceof lateralheterogeneity,we haveundertaken The modelsin Fig. 7 should thereforebe viewedinversion of the travel time curves for modelsG, as actually sampling along a trajectory corre-M andN to producestratifiedEarth models.The sponding to the turning points of rays in theinversion was undertakenin the tau—p domain, referencemodel.Whenwe trace out this pathweusing the referencemodel as the starting point find that thereis a reasonablecorrelationbetween(Kennett, 1976). It proved difficult to construct the inferred deviationsfrom the referencemodelstratified modelswhich would give a satisfactory in the stratified inversions and the actual per-fit to data from the heterogeneitysuite,evenwith turbation at the corresponding depth in thean allowancefor generous‘picking’ errors,Repre- neighbourhoodof the turningpoint. For example,sentativemodels derivedfrom the inversion are the small low-velocity zone above the 670 kmillustrated in Fig. 7, togetherwith the reference discontinuityin the inversionfor model M corre-model C shown as a continuousline. There was lateswith the alternationof high andlow veloci-little constrainton the behaviourbelow the 670 ties in this regionaround1200 km in the originalkm discontinuityand this is reflectedin the struc- heterogeneousmodel. Thuswith a numberof dif-ture producedfor model M. ferent profiles in a region it is possible to make

The most noticeablefeatureof Fig. 7 is that some progresstowardsinferring the characterofeach inversion for a heterogeneouscasetends to the heterogeneity field from one-dimensionalwobble aboutthe referencemodel with alternate inversions.zonesof positive andnegativegradientsand per-turbationsof the order of 1% from the reference.Such an alternationis often found in previous 4. Discussionmodelswhich attemptedto explain the fine struc-ture of a record section in terms of a radially In this paper, we have shown that within astratified model. Although Fig. 7 is presentedin singleregionof the uppermantlesuchas the zone


beneaththe northern Australian shield, there is a stratified model can provide a very effectivesignificant heterogeneityin seismic propertieson summarydescriptionof the dominantcharacterofscalesof hundredsof kilometres. This scale of the seismic velocity distribution (see,e.g., Grandvariation is too small to be detectableby global and Helmberger, 1984). However, the highest-studiesandfits within the scaleof a singleunit in frequencywavesused in the study of long-periodglobal heterogeneitymodels.The size of the fea- bodywave phasesarebeginningto be sensitivetotures we proposeto occur in the uppermantle is the detailednatureof the heterogeneityfield andsuch that they havethe greatesteffect on short- this could give some mild bias to the resultingperiodwaves,whereaslong-periodwavescanpass models,Stronghorizontalvelocity gradientswithinthrough the structurewith comparativelylittle in- the mantlehavebeenrecognizedfrom the model!-teractive. ing of the body waves on long-period records

The natureof the observationswhich lead to (Rial et al., 1984) correspondingto regionswiththe developmentof our laterally heterogeneous different tectonichistories.Theevenlonger-periodmodelsof the uppermantle is that they are most studiesof multi-modesurfacewavescould berea-sensitiveto featuresat the 100—400km scalelevel. sonably well described by a stratified velocityThere is evidencefrom the smaller, permanent, model within oneregion. However,the longprop-Warramungaarrayof complicationsin the seismic agationpathscommonlyanalysedmay havesam-wavefield on somewhat smaller scales(Kennett, pled a number of such regions and so be in-1987). However, it is interestingto note that an fluencedby larger-scaleheterogeneity.entirely different analysis of the complexities ofsurfacewave trains in Europe by Snieder(1987)also infers horizontal scalesof the order of 300 Acknowledgementskm.

A full model of the lateralheterogeneityin the We are grateful to D.R. Christie and the staffuppermantle must take into accounta hierarchy of the Warramungaarrayfor their supportof theof scales from tens to thousandsof kilometres. portablearray program,and to J. Hulse and G.The shortest-scalefeaturesare most evident near .

McAllister for their efforts in the processingof thethe surfaceand it appearslikely that the dominant

arraydata.horizontaland vertical scalesof heterogeneityin-creasewith depth.In the 200—800km depthrangea model with horizontal variationsat a scaleof200—400km appearsto give a good representation Referencesof the major behaviourof the seismic wavefield.Smaller-scalefeaturesmaybe superimposed,which Burdick, L.J., 1981. A comparisonof the upper mantlestruc-

give rise to scattering and hence the complex ture betweenAmerica and Europe. J. Geophys.Res., 86:

observedwaveforms,but theseare concentrated Cleary, J., Wright, C. and Muirhead, K.J.,1968. The effect of

above200 km (Korn, 1988). local structureon measurementsof thetravel time gradientAnalysis of the detail of a set of short-period at theWarramungaseismic array. Geophys.J. R. Astron.

observationsfrom such a heterogeneousregionin Soc., 16: 21—29.terms of a stratified model is likely to be mis- Dziewonski, AM. and Anderson,DL., 1981. Preliminaryref-

erenceearthmodel. Phys.EarthPlanet. Inter.,25: 297—356.leading.However, it is reasonableto infer a refer- Grand, S.P., 1987. Tomographic inversion for shearvelocity

encestructurewhich fits the main behaviourand beneaththe North American plate. J. Geophys.Res., 92:

then seekto map out the distribution of hetero- 14065—14090.

geneity.Sucha laterallyheterogeneousmodel will Grand,S.P.,andHelmberger,D.V., 1984. Uppermantleshear

be needed to provide a full description of the structureof North America. Geophys.JR. Astron. Soc.,

wavefield for both short-periodand broad-band Hales, AL., Muirhead, K.J and Rynn,J., 1980. A compres-studies. sional velocity distribution for the upper mantle.

Within a singlemajorunit of the uppermantle, Tectonophysics,63: 309—348.

144 B.L.N. KENNETT AND JR. BOWMAN

Herrin. E., 1969. Regionalvariation of P-wavevelocity in the inferred from the dispersionof Rayleigh modes.J. Geo-upper mantlebeneathNorth America. In: P.J. Hart (Edi- phys., 43: 265—285.tor), The Earth’s Crustand UpperMantle. Am. Geophys. Nolet, G., vanTrier, J. and Huisman,R., 1986. A formalismUnion Monogr. 13: 242—246. for the nonlinear inversionof seismic surfacewaves.Geo-

Ingate. S., Ha, J. and Muirhead, K.J.. 1986. Limitations of phys. Res. Lett., 13: 26—29.waveformmodelling of long-periodseismograms.Geophys. Nyc, J.F.. 1985. Causticsin seismology.Geophys.J. R. Astron.J. R. Astron. Soc.,86; 57—61. Soc., 83: 477—485.

Kennett,B.L.N., 1976. A comparisonof travel time inversion. Rial, J.A., Grand, S. and Helmberger,DV., 1984. A note onGeophys.J. R. Astron. Soc., 44: 517—536. lateralvariation in uppermantleshear-wavevelocity across

Kennett,B.L.N., 1984. Guidedwave propagationin laterally theAlpine front. Geophys.J. R. Astron. Soc., 77: 639—654.varying media—I. Theoreticalseismograms.Geophys.J. R. Romanowicz,B., 1980. A study of large-scalelateralvariationsAstron. Soc., 79: 235—355. of P-velocityin theupper mantlebeneathwesternEurope.

Kennett. B.L.N., 1987. Observationaland theoretical con- Geophys.J. R. Astron. Soc., 63: 21 7—232.straints on crustal and upper mantleheterogeneity.Phys. Simpson,D.W., 1973. P WaveVelocity Structureof theUpperEarthPlanet Inter., 47: 319—332. Mantle in theAustralian Region. Ph. D. Thesis,Australian

King. D.W. and Calcagnile,G.. 1976. P wave velocities in the National University.upper mantle beneathFennoscandiaand westernRussia. Snieder,R.. 1987. Mapping lateralheterogeneityin the EarthGeophys.J. R. Astron. Soc.,46: 407—432. using surfacewave scatteringtheory. Abstr. Symp. S5, XIX

Korn, M., 1988. P wave coda analysisof short period array GeneralAssemblyIUGG, p. 317.data and the scatteringand absorptivepropertiesof the Spakman,W., 1986. SubductionbeneathEurasiain connectionlithosphere.Geophys.J., 93: 437—449. with mesozoicTethys. Geol. Mijn., 65: 145—153.

Lerner-Lam, A.L. and Jordan, T.H., 1985. Earth structure Woodhouse,J.H. and Dziewonski, AM., 1984. Mapping thefrom fundamentaland higher-mode waveform analysis. upper mantle: threedimensionalmodellingof Earth struc-Geophys.J. R. Astron. Soc.. 75: 759—797. ture by inversionof seismic waveforms.J. Geophys.Res.,

Nolet. G., 1977. The upper mantle under western Europe 89: 5953—5986.

the velocity structure and heterogeneity of the...

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