PHYSICSOFTHE EARTH

~‘ ~tQi1 ANDPLANETARY________ INTERIORSELSEVIER Physicsof theEarth andPlanetaryInteriors 84(1994)179—191

On the measurementof anelasticattenuationusingamplitudesof low-frequencysurfacewaves

BarbaraRomanowiczSeismographicStationandDepartmentof Geologyand Geophysics,UniversiEy ofCalifornia, Berkeley,CA 94720,USA

(Received9 February1993;revisionaccepted8 December1993)

Abstract

A methodis presentedfor themeasurementof attenuationof long-periodRayleighwaveswhich minimizes twoeffects: thatof biasesowing to uncertaintiesin the sourcemomenttensorandthat of focusingowingto propagationin a laterallyheterogeneouselasticEarth. In this manner,by measuringattenuationover minorarcs, odd termsoflateralheterogeneityin Q canberesolved.Global averageQ estimatesare in good agreementwith the PreliminaryReferenceEarthModel (PREM)in the periodrange180—285 s. At periodsshorterthan 180 s, our estimatesof Qare lower thanpredictedby PREM.Maps of lateralvariationsin ~ 1 showa generalcorrespondenceof high Q tohigh shearvelocity andlow Q to low shearvelocity. In particular, theshift to thewest,at increasingperiod, of thelocus of theminimum in thePacific Oceanis also observedin the ~ maps.

1. Introduction Masters,1991) havebeenobtainedin ways thatlargely ignoredthe effectsof anelasticity.

With the availability of high-qualitydigital data One of the advantagesof the new generationfrom recently deployed global broadbandnet- of data is the possibility to measureelastic andworks such as GEOSCOPE and IRIS, thereare anelastic properties of low-frequency mantlenow unprecedentedopportunitiesto improveour waveson the minor arc,yielding increasedresolu-knowledgeof not only elastic, but also anelastic tion of odd terms of structure.This was previ-three-dimensional(3D) mantle structure. It is ously not possiblebecauseof limitations in theparticularly importantto determinethe size and dynamicrangeof instruments.location of large lateral variations in Q in the A very difficult problem neverthelessinhibitsuppermantlewith someaccuracy,andto seehow the determination of accurateanelasticmodelsthey relate to lateral variations in elastic struc- from measurementsof seismic amplitudes: theture. Indeed, the strong dependenceof Q on need to separatethe effect of intrinsic attenua-temperaturecan provide new constraintson the tion from thoseof focusing/defocusingowing topatternsof convectionin the mantle.Also, large propagationin a laterally heterogeneouselasticlateralvariationsin Q may causebiases,through medium. In what follows, this problem is ad-anelasticdispersion(Liu et a!., 1976),in the exist- dressedfor the case of long-period(80—300 s)ing 3D elastic models.Eventhe latestsuchmod- fundamentalmode Rayleighwaves,which canbeels (Su and Dziewonski, 1992; Woodward and studiedin the frequencydomain,using standard

0031-9201/94/$07.00© 1994 Elsevier ScienceB.V. All rights reservedSSDI0031-9201(94)05032-S

180 B. Romanowicz/Physicsof theEarth andPlanetaryInteriors 84 (1994) 179—191

processingtechniques.A descriptionis given of necessaryto incorporatemeasurementson singlean approachthat aimsto minimize the effectsof wavetrains,preferably those that correspondtounknownbiasesboth in the estimationof source low-orderorbits, as they travel shorterpathsandamplitude andof focusing along the propagation therefore contain more shorter-period energy,path,andsomepreliminaryresultsof the applica- and more information on local structure.Singletion of this approachto upper-mantleQ tomog- station measurementsof first arriving Rayleighraphyarepresented. wavetrains(Ri andR2) are now possible,owing

to the on-scalerecordingof largeearthquakesbymoderninstrumentationof the new generationglobal networks. Attempts at measuringlateral2. Attenuationmeasurementsusingmantlewaves . .

variationsof Q at the regionallevel using singlestationmeasurementshavebeennumerous(Mit-

To first order, the observedamplitude spec- chell, 1975; Canasand Mitchell 1978; Bussy ettrum A(w) of a single mode mantle Rayleigh al., 1994). However, thesemeasurementsremainwaveis, after instrumentcorrection,a productof sensitiveto errorsin the sourceamplitude.threefactors: One way to eliminate the source biases and

A(w) =A~(o~i)exp[ —i~(w)XJF(w) (1) retainthe ability to resolveodd-orderstructureisto considerthreeconsecutivewavetrainsfor each

whereA~(w)is the sourceamplitude,i~(w)is the source—stationpath (Romanowicz, 1990). Theaverageattenuationcoefficient alongthe path,X following systemof threeequationsin threeUn-is the epicentraldistance(in km), and F(o) de- knownsis thensolvedfor eachpath:scribesthe focusing effects. log A.(w) =log A (w) —~(o)X. (2)

The sourceterm A~(~)is a functionof seismicmoment M0, as well as sourcemechanism.We for I = 1,3, where i refers to the wavetrainR~,here neglecteffects of directivity of the source and we assumethat source directivity can berupture. Although much progress has been neglectedand that attenuationis additive alongachievedin recentyearsin the systematicestima- the path:tion andreportingof seismicmomentsandmech- — 2 X ~anismsof large earthquakes(Dziewonski et a!., fl3~3— ?1i i + ~12 21981; Sipkin, 1982), uncertaintiesin seismic mo- The drawbacksof this approachare twofold.ment are still of the order of 30—50%,andocca- As in the caseof greatcircle measurements,thesionally more. To circumvent this problem, one frequency range is limited. Also, sensitivity tocan measureaverageproperties over complete focusingeffectsis increased,especiallybecauseofgreatcircle paths (Dziewonski and Steim, 1983; the longer path travelled by the R3 wavetrain.Durek et al., 1993), thus eliminating the source Fig. 1 illustratesthis point by showingexamplesterm.Owing to symmetryproperties,the sensitiv- of spectraof fundamentalmode Rayleigh wavesity to odd terms of lateral heterogeneityis then recordedon vertical-componentinstruments.Thelost, andthe resultingmodelsare incomplete:as amplitude spectraof Ri, R2 and R3 are com-are modelsbasedon normalmodemeasurements paredwith the theoreticalsource spectrum,cal-(e.g.Sudaet a!., 1991).Also, the frequencyrange culatedfor the centroid-momenttensor (CMT)of study is limited, as higher frequenciesare solution (Dziewonski et al., 1988). We observeattenuatedrapidly during propagationand, for theoverall decreasein amplitudeas a function ofpaths that havecircled severaltimes aroundthe orbit numberowing to attenuation,as expected.Earth, the signal-to-noiseratio becomespoor be- The smoothnessof the spectrum,however,dete-low periodsof 130—150s. riorates as a function of orbit number, and is

To resolve odd-order lateral heterogeneity significantly poorer for R3, especiallyat periods(that is, heterogeneitywhich is not symmetrical shorterthan 150 s, as a result of focusingeffectswith respect to the center of the Earth), it is as well as contaminationfrom highermodes.

B. Romanowicz/PhysicsoftheEarth and PlanetaryInteriors84 (1994) 179—191 181

We are therefore faced with a trade-off: to agreein their shorter-wavelengthfeatures,Ro-eliminate the source,weneedat leastthreecon- manowicz(1990)attemptedto eliminatefocusingsecutivetrains; on theotherhand,to makeuseof effects by taking advantageof their additivityR3andlaterarriving trains,it is necessaryto take properties, which are different from those offocusing effectsinto account,andin anycasethe anelastic attenuation.This involved measuringfrequencyrangeof study is limited at the short- amplitudesof Rayleighwavetrainsup to R4, andperiodend.Onepotentiallypowerful approachis solving a system of four equations for eachto calculatethe focusingeffects directly, assum- source—stationpair:ing that the 3D elasticmodel in which the wavespropagateis known accuratelyenough,andusing log A1(w) = log A0(w) — ~(w)X1 + 1~ (3)a theorywhich allows the calculationof relevant for i = 1 4, where the numberof unknowns cancoupling effects (e.g. Lognonne, 199i; Tromp, be reduced to four by assumingadditivity ofi992). Eventually, simultaneousinversion for attenuatioivelasticand anelasticstructureis likely to becomethe appropriateapproach. rj3X3 = 2~1X1+ ~2X2

Bearing in mind that currently available 3Delastic models of the upper mantle do not yet ri4X4 = 2~2X2+ ii1X~ (4)

COLUMBIA 03/06/87 AGD 13350.38 COLUMBIA 03/06/87 PPT 8088.88

0.0 11111 0.0 ~—10 ~ — —— ———~~: —10 —

1’ ~D —2.0 —2.0 — .-. - -

/~ —3.0 / ~ —3.0 — .1

P 3 E0 —43 ~ / 0 4.0 ~ ‘.1~‘ —5.0~J~ —5.0 ~_~1 I i I I

—6.0 1.0 1.52 2.0 2.5 3.0 3.5 1.0 1.5 2.0. 2.5 3.0 3.Period (s) *10 6.0 Period (s)~ia2

MARIANA 04/05/90 HYB 7343.56 MARIANA 04/05/90 PPT 7785.69

1 .0 ~ —

00 — -—-—-———--...-.--—..-. 00 — _..... — —

-10_ -10_

-20.. /P P —3.00 -3.0 0lv —40 f

_____________ 8’ _____________

-~ _____________________ — —5.0___ I I I

—5.0 1.0 1.5 2.0 2.5 3.0 3.5 1.0 1.5 2.0 2.5 3.0 3.5Period (s) *102 Period (s)~io2

Fig. 1. Exampleof vertical-componentRayleighwaveamplitude spectra.Thesolid line is thetheoreticalsourceamplitudefor theCMT solution.The brokenline is for Ri, the dottedline for R2 and the dashed—dottedline for R3. The logarithm of observedampolitudeis plotted aftercorrectionfor instrumentandgeometricalspreading.Foreachpath,epicentraldistance(in km)is givenafterthe nameof the station.

182 B. Romanowicz/PhysicsoftheEarth andPlanetaryInteriors 84 (1994) 179—191

and‘algebraic’ additivity of focusing: andusingEq. (1) (Method 1); (2) usingR1, i = 1,3

F = 2F — F andEqns. (2) (Method2).3 1 2 Wefirst reject thosepathsfor whichMethod 1

F4 = 2F2 — F1 (5) yieldsattenuationcoefficientsthatarenot smoothas a function of frequency,which is indicativeof

This latter propertyarisesfrom higher-order contaminationby focusing and other perturbingasymptoticcalculations(Park,1987;Romanowicz, effects (e.g. higher-mode contaminationat the1987), underthe strong assumptionthat focusing shorter periods). Then we compare the resultsbehavesin a linear fashion. obtainedusing Methods 1 and 2. In manycases,

Romanowicz(1990) showedthat such an ap- the results agreeto within 10% at the low fre-proach could indeed improve the resolution of quencies(200—250s), but Method 2 yieldsmuchanelasticattenuation,providedthe dataselection more oscillatory results for periodsshorterthanwas conductedvery conservatively,to eliminate 150 s. Occasionally,the two curves are shiftedpaths where focusing effects are strongerthan with respectto eachother by a roughly constantallowed by the linearity assumptionunderlying amount. This is primarily due to bias in theEqs.(5). estimateof the sourcemoment,aswell as possi-

We here describea ‘hybrid’ approachwhich ble errorsin the instrumentresponsefunction.takesinto accountthe advantagesof using first We have developed an interactive methodarriving trains (broaderfrequencyrange,lesssen- which allows us to pick a suitable referencepe-sitivity to focusing)comparedwith thoseof using nod rangefor the curve from Method 2 (in gen-threeconsecutivewavetrainsto eliminatethe sen- era! around200 s), andwe shift the curve fromsitivity to sourcebiases.To do so, we first mea- Method 1 to make the levels of the two curvessureattenuationcoefficientsas a function of pe- agreein that periodrange.This shift is modelednod, for eachsource—stationpair, in two differ- by a constant plus a linear trend, the latter,ent ways: (1) assuminga known sourcemecha- usually very small, accountingfor errors in thenism andmoment(in general,the CMT solution), sourcemechanism.We havetested this method

MARIRNA 04/05/90 COLUMBIA 03/08/87PERIOD 196.92 SEC PERIOD 256.00 SEC

01

~2 01 ol 01: — ~2 ~ •g1 = 01I • o.. .

E 0~ 0cr 0 0’ 0

-~ ~.01

I I I I I I I ~- I I I I30 00 93 120 ISO 180 210 240 270 300 330 360 30 60 90 120 150 180 210 240 270 300 33b 360

AZIMUTH bEG) AZIMUTH IOEGI

Fig. 2. Examplesof amplitude radiationpatternsasa functionof azimuth.The dottedline is the theoreticalradiationpattern fortheCMT solution.o, Data aftercorrectionfor propagationusingmodel 1066b.Numbersindicatewhetherthe train usedis Ri (1)or R2 (2). Namesof stationsaregiven above eachobservationpoint. Left: Marianaevent of 5 April 1990, at a periodof 197 s.Right: Colombiaeventof 6 March 1987, at a periodof 256 s.

B. Romanowicz/Physicsof theEarth and PlanetaryInteriors84 (1994)179—191 183

usingsyntheticdatageneratedusingnormalmode all levels in the period range200—250 s, and thesummationin a sphericallysymmetricEarth.The much better-behavedcharacterof the ‘Ri only’testsindicatethat reliableresultscanbe obtained measurement,allowing us to measureattenuationin the periodrange100—285s. down to periodsof 80—90 s for Ri and approxi-

We note that this procedure amounts to mately 100 s for R2.A verysmall shift is requiredsmoothingthe estimateof attenuationcoefficient to bring the levels of both measurementsinas a function of period obtained in Method 2, agreementfor all stationsandtrains.Welimit theusing as ‘physical’ constraint the shapeof the measurementat the low-frequencyendbasedoncurve obtainedusingMethod 1. The sourceterm the level of agreementof the two determinations,A0 could also be obtained,in principle, from the andthe synthetictests.The comparisonbetweensolution of the equationsfor the threeconsecu- the two measurementsallows us to assessthetive trains (Method 2), but it would be more very largesizeof focusingeffectsat somestationsstronglycontaminatedby focusingandwould have and in some frequencybands.For example, atto be smoothed using some running average KIP, in the period range 120—200 s and for Ri,method with arbitrary choice of smoothing pa- the hole in the spectrumobservedin Fig. 1 isrameters.Also, if our assumptionsarecorrect,we reflected in an effect which is twice as large asexpect to obtain the same ‘source shift’ for Ri the theoreticalvalue for model 1066b (Gilbertand R2. This is indeedthe casefor most of the and Dziewonski, 1975), although the departureanalyzeddata. We reject paths for which the from model 1066busingRi is, in thiscase,only adifferenceis significant, few percent. It shouldbe notedthat thishole in

We also note that, although Eqns. (5) imply a the spectrumcannotbe accountedfor by higher-linear behavior for focusing, there are strong mode contamination,as synthetic tests indicate.indicationsthat in practicefocusingbehavesvery Also, a simplesmoothingprocedure,suchas run-non-linearly. In our approach,thereare no cx- ning average,appliedto the curve obtainedusingplicit restrictions on the behavior of focusing, Method 2 would have led to biased results atbeyondthe fact that we assumethat it is band- periodsshorterthan 200 s. Theseexamplesalsolimited within the frequencyband of the mea- showthat it is generallyimpossibleto useMethodsurement,andnotconstantover thisentireband. 2 for periodsshorterthan 130 s.

To illustrate thisprocedure,we showexamples Fig. 4 shows correspondingexamplesfor thefor two events;the 5 April 1990 Mariana earth- 1987 Colombiaevent. In this case,in additiontoquake(M0 1.6 x 1020 N m) and the 6 March muchsmootherresultsusingMethod 1, we notea1987 Colombia earthquake(M0 0.64x 1020 N large shift betweenthe curves from Methods 1m) observedat stationsof the GEOSCOPEnet- and2. This shift is consistentbetweenRi andR2work (Romanowiczet al., 1991). Fig. 2 shows the for a given station,as well as from onestationtofit of the CMT solution to the observedampli- the other (it is of the order of —0.3), indicatingtude radiation pattern at all available GEO- that it is mostly due to bias in the seismic mo-SCOPEstationsfor theseevents,at a period of ment of the earthquake,which is overestimated256 s. We seethat the fit is good for the Mariana by about 30%. This is in agreementwith theevent,and much poorer for the Colombiaevent, differencein moment reported in the Nationalfor which thereis also much morescatterin the EarthquakeInformation Center(NEIC) bulletindata, for the CMT (0.64x 1020 N m) andabody-wave

Fig. 3 showsthe minor andmajor arc attenua- momenttensor solution (0.35x 1020 N m). Ourtion coefficientas a function of period for several measurementindicates a moment of approxi-stationsin the lobe of the radiationpattern,cal- mately 0.4x 1020 N m. The differencesbetweenculatedusing Methods 1 and2, for the Mariana the final determination(Ri only, after shifting)event. The theoreticalcurve obtainedfor PREM and PREM are severaltimes smaller thanwhat(Dziewonskj and Anderson, i981) is given for theywould be if the theoreticalsourceamplitudecomparison.We note the agreementof the over- wastakenat facevalue.The residualdifferences,

184 B. Romanowicz/Physicsof theEarth and PlanetaryInteriors 84 (1994)179—191

MARIANA 04/05/90 RER 10798.76 MARIANA 04/05/90 KIP 5766.61

2.0 •~.. 161-1.8 .~ Ri 1.4 L Ri

0.2 ~~.~---- -- -0.2

1.0 1.5 2.0 2.5 .3.0 .3.5 1.0 1.5 2.0 2.5 3.0 3.5

PerIod (s) 4102 Period (3)*102

1.4 —

1.2!~

101520253035

Period (~)*102 Period (~)6io2

Fig. 3. Examplesof attenuationcoefficient determinationfor the5 April 1990 Marianaeventat GEOSCOPEStationsRER(left)and KIP (right). Epicentraldistance(in km) is given after the nameof the station. (Attenuationcoefficientsare in kin 1 X 10~.)Thin solid line: referencemodel 1066b. Thick solid line: determinationusing Ri, R2 and R3 (Method 2). Thick broken line:determinationusingonly Ri (Method 1). Dottedline: final determinationusingRi aftershiftingthebrokenline curveto matchthethick solidline in theperiodrangeindicatedby crosses.Arrows indicatetheperiodrangein which thefinal dataarekept for futureinversion.

B. Romanowicz/Physicsof theEarth and PlanetaryInteriors84 (1994)179—191 185

in the period rangewherethe curve from Method measureof the uncertaintyin the measurement2 is ‘well-behaved’, betweenthe two determina- of attenuationcoefficient, which is here of thetions after the shift hasbeenapplied, give us a order of 10—15%.

COLUMBIA 03/06/87 NOC 1 2679.60 COLUMBIA 03/06/87 AGD 1 3350.38

2.0 1.8

1.BL

i.e Ri 1.6 .1 Ri

1.4 \

1.2 ~t1.2 —~

20 25 35 0200: :

Period (s)*b02 Period (s)*102

1.2 ~_. 1.8

1.0 ~ R2 R21 l.4~

Period (s~*iO2 Period (~)*102

Fig. 4. SameasFig. 3 for theColombiaeventof 6 March 1987,observedatGEOSCOPEStationsNOC(left) andAGD (right).

i86 B. Romanowicz/PhysicsoftheEarth andPlanetaryInteriors84 (1994)1 79—191

In summary,our approachallows usto reduce of the globe (the latter group has averagedmea-considerablythe uncertaintyin the measurement surementsovermore pathsthan the former), orof attenuationcoefficientsalongminor andmajor one owing to the influence of elastic structure,arcsby: (i) selectingpathsandperiod rangesfor which could affect the amplitude measurementswhich the Ri-only and R2-only measurements differently from thoseof complex eigenfrequen-are minimally affectedby focusing;(2) correcting cies.for biasesin the source amplitude when neces- In Tablei andFig. 5, we presentourmeasure-sary; (3) extendingthe period rangeof measure- ments of global average Q and comparethemment to below 100 s. with PREM andvaluesof Widmer et a!. (1991).

The examplesshown indicate that errors as Our datasetoriginally consistsof 722 singletrainlarge as 50—100% can be introducedif precau- measurements(Ri and R2) using the methodtions equivalentto thosedescribedhere are not describedin this paper. Recordsused are forapplied. Although iterative simultaneousinver- largeearthquakes(M9> 6.7) in the 5 yearperiodsion for elasticand anelasticstructureaswell as i987—i992 observed at stations of the GEO-source parametersshould, in the future, allow SCOPE and IRIS—IDA networks. After visualmuch less time-consuming, automatized algo- inspection of amplitude plots (e.g. Fig. 3), werithms to be usedin attenuationtomography,we rejectpathsfor which the final attenuationcoeffi-feel that, at present, the careful inspection of cient is notsmoothas a function of frequency,ordatainvolved in our procedureis necessary. for which the sourcelevel cannotbe determined

accuratelythrough a comparisonof Methods iand 2. We also reject outliers by imposing the

3. Estimation of global average Q and departure constraintthat relative departurefrom the meanfrom spherical symmetry shouldnot exceed50% for Ri and 30% for R2.

Many workers have published estimates ofglobal averagesof Q in the uppermantle,using Table ivarious datasetsand measurementtechniques.A Comparisonof measurementsof Q’ X i0

3 obtainedin this

debatehas recentlybeen opened(Durek, 1993) study with PREM (Dziewonski and Anderson, 1981) and

as to which of thesemeasurementsrepresentthe measurementsreportedby Widmer et al. (1991)(‘QM1’)

‘true’ averageglobal Q. Indeed,results fall into Period y1 Eli N1 y2 o~ N2 PREM QM1

two subsets. The first subset includes studies _____________________________________________basedon normalmode amplitude measurements 284.44 5.26 li 265 5.23 0.87 61 5.09 4.34

(Deschamps,1977; Sailor and Dziewonski, i978; 269.47 5.34 1.0 332 5.37 0.6 63 5.34 4.50256.00 5.45 1.0 354 5.52 0.6 64 5.57 4.95

Jobertand Roult, 1978) and studiesbased on 232.73 5.95 1.i 37i 5.99 0.7 64 5.98 5.37measurements of mantle wave amplitudes 213.33 6.48 1.2 378 6.52 0.7 65 6.32 5.64

(Dziewonskiand Steim,1983;Romanowicz,1990; 200.78 6.80 1.2 373 6.84 0.7 65 6.55 6.00

Durek et al., 1993). Thesemeasurementsagree, 182.86 7.28 1.2 376 7.32 0.8 65 6.90 6.55

within their standard deviations, with PREM 170.67 7.67 1.3 365 7.68 1.0 65 7.13 6.83160.00 7.98 1.4 352 8.07 1.1 65 7.36 6.80

(Dziewonski andAnderson,i98i), at leastin the 150.59 8.25 1.4 328 8.21 i.o 65 7.56

periodrange 140—250s. The secondsubsetcom- 140.27 8.57 1.5 300 8.48 1.0 65 7.8prisesresultsof measurementsof complexampli- 128.00 8.87 1.5 281 8.77 1.0 64 8.06

tudes of normal modes (Masters and Gilbert, i20.47 8.96 1.5 269 8.95 0.9 65 8.18110.11 9.15 1.4 258 9.20 0.8 63 8.331983; Smith and Masters,1989; Widmer et al., 100.39 9.30 1.4 245 9.34 0.9 62 8.4

1991),which consistentlyyield higherQ valuesatperiodsgreaterthan180 ~. y~,o~and IV~are respectivelyestimatesof standarddeviation

and numberor measurementsusedin the calculation; i = 1The reasonfor thesedifferencesis asyet un- correspondsto a straight averageof the data; i = 2 is a

known and is the subject of current investiga- weightedaverage,accordingto a schemedescribedin the text;tions.It couldeitherbea biascausedby sampling N2 representsthe numberof cellshit by the data.

B. Romanowicz/Physicsof theEarthand PlanetaryInteriors84 (1994) 179—191 187

This reducesthe datasetto some350 measure- sults indicate a lower on averageQ than pre-ments. dicted by PREM, although the latter does lie

To minimizebiasescausedby unevensampling within the error barsof our measurements.How-of the globe, we attachweights to the data, in- ever,PREMwasconstructedfrom a datasetwhichverselyproportionalto the numberof samplesin did not include any fundamental mode con-thebin theybelongto. The binning is donein the straintsat periodsshorterthan150 s.following way. We divide the Earth’s surfaceinto In our global average measurements,the30°by 30°cells and assigneachpath to the cell standarddeviationsare large. Our 3D modelingwhich contains the pole position for the great shows that a largeproportion of the varianceincircle joining epicenter and station. The pole the datacan be explainedby simple modelsofposition is the positive pole (in a counter-clock- lateral heterogeneityin Q. There is now abun-wiseconvention)if the longitudeof the mid-point dant evidencefrom surface-wavesandfree oscil-on thepath is in onemeridianhemisphere,andit lationsfor the existenceof largelateralvariationsis the negativepole otherwise.This allows usto in upper-mantleQ, reachingin excessof 50%distinguish contributions from minor and major (Nakanishi, 1978; Roult, 1982; Dziewonski andarcs. We note that 65 out of 72 cells havebeen Steim, 1983; Romanowicz, 1990). To illustratehit at leastoncein the binningprocess. this, Fig. 6 gives an exampleof two pathssam-

The global averagevaluesof (i/Q) x 1000ob- pling different geographicalregions,for whichwetamedin this fashion are given in Table 1 and havefour independentmeasurementsof attenua-comparedwith averagesobtained without bin- tion coefficient, using the method describedinfling. The differencesare small, indicating that thispaper,allowing usto estimateanupperboundspatial biasingis mostprobablynot an issue.The on standarddeviationsin the measurements.Foraverage values are in better agreementwith each examplepresented,the four eventswerePREM thanwith the measurementsof Widmer locatedwithin 500 km of eachother.et al. The agreementwith PREM is excellent The Ri path from the Solomon Islands tobetween180—285 s. At shorterperiods,our re- Station KIP in Hawaii is entirely within the Pa-

cific Ocean, and the measurementreflects thehigh attenuationin this area acrossthe entire

Comparisonof global frequencyband.On the otherhand,R2 averages

10 average01 over a longer distance,and the values obtained• Y

1 are close to PREM except below a period of91

T • y2 i2Os.8 A A 1uJ

1 A PREM The Ri pathfrom the Philippines to TAM inA ~ T • QM1 Algeria is a continentalpathsamplingin particu-

8 7 A 4 lar the ‘cold’ western Pacific subductionzone

6 area.The attenuationcoefficient for this path is• • small at periods longer than 150 s. For R2, the

• I’ path samplesparts of the Pacific and Atlantic4 • Oceans,and the resulting average attenuation

coefficientis high at periodsshorterthan200 s.3 Thesetwo examplesconfirm the existenceof

8 ~ 8 strong lateralvariationsin Q in the upperman-Period (sec) tie, which can reach in excess of ±50% and

Fig. 5. Comparison of global averageQ—‘ measurements, contributeto the standarddeviationin the globalAveragesfor this study are y1 (unweightedaverage)and ~‘2 averageQ. The bias to lower Q valuesas corn-(weightedaverage)and are comparedwith PREM(Dziewon- .

ski and Anderson, 1981)and thevaluesreportedby Widmer paredwith the Widmeret al. measurementscan-et a!. (1991)(QM1). Errorbarscorrespondto they2 measure- not be explainedby a straightforwardeffect ofment. sampling.It is probablyrelatedto the interaction

188 B. Romanowicz/Physicsof theEarthand PlanetaryInteriors84 (1994) 179—191

PHILIPPINES 07 TAM 11765.50

1.2 - 1.0

Ri k1.0

0.8

0.8 _______

0.6 —

0.6 —

0.4 — 0.4 —

2 233 0.2 8)0 0

1.0 1.5 2.0 2.5 3.0 o 0.2 1.0 1.5 2.0 2.5 3.0

Period (~).~102 Period (5)8102

SOLOMONKIP 5827.12

1.01.4

Ri R2

1.2 0.8

::

0.2 L~ 1.5~2.53.o 0.2 1.0 1.5 2.0 2.5 3.0

Period (5)8102 Period (~),102

Fig. 6. Examplesof averageattenuationcoefficients and correspondingstandard deviationsfor two paths for which fourearthquakeswere availablewithin 500 km of eachother.The thin solid line is the reference1066bmodel.Theaverageepicentraldistanceis indicatedafter thenameof thestation.

B. Romanowicz/Physicsof theEarth and PlanetaryInteriors84 (1994)1 79—191 189

of lateralheterogeneityin the elasticand anelas- sion method with no a priori basis functionstic partsof the Earththataretakeninto account (Tarantolaand Valette, 1982) as adaptedto thedifferently according to the methodused.Com- caseof surfacewavesby Montagner(1986). Theparisonsof single recordmeasurementsarenow spatial wavelength resolution correspondsto abeing conducted,to clarify this point, spherical harmonics expansionup to approxi-

mately order six. The mapsshown in Fig. 7 con-firm our previousresults(Romanowicz,1990) and

4. Examplesof maps of lateralvariations in Q ~ show that, in general,oceanicregionsare charac-terized by high attenuationwhereasstable re-

We presentin Fig. 7 some examplesof maps gionsandsubductionzoneshavelow attenuation.of lateral variations in ~ 1 obtained using the At shorterperiods(e.g. 128 s), the high-attenua-datasetand the method describedin this paper. tion regionsare concentratedaroundmid-oceanComplete 3D models will be presentedelse- ridges, especiallyin the Pacific, but also in thewhere.Thesemapswere obtainedusingan inver- Atlantic and Indian Oceans. At progressively

1~84s~~4OOOkm) 1~16O ~3OOOkin)

_ (1 (1

-85%[ i~~ui~+,ssz -~j_____________

1~O ~0OO kin) T=128 ~ ~O0O kin)

_______ 35~_______

Fig. 7. Examplesof mapsof lateralvariationsin Q5 X iO~,with respectto the meanat eachperiod. The correlation length isL 3000kmat all periodsexceptat 284 s whereit is 4000 km. Variancereductionis 46%at284 s, 60% at200 s,55% at 160 s and42% at 128 s. Final errorsin the mapsarevery uniform andof the orderof 15%.

190 B. Romanowicz/PhysicsoftheEarth andPlanetaryInteriors 84 (1994)179—191

longerperiods,in the PacificOcean,the high-at- Acknowledgmentstenuationzone is shifted from the East PacificRise towardsthe central Pacific. Such a shift is This work wassupportedthroughNSF Grantsalsoobservedin a recentregionalstudy(Bussyet EAR-9i04674 and EAR-920463i. David Shar-al., 1994) as well as in elastic models(e.g.Mon- rock participatedin the developmentof the inter-tagnerand Tanimoto, 1991; Su and Dziewonski, activegraphicsoftwareusedin this study.1992).The largestlateralvariationsseemto occurin the period range 150—200 s, but persist atlongerperiods,indicating that largelateralvaria- Referencestionsin Q persistthroughoutthe uppermantle.

Bussy,M., Montagner,J.P.andRomanowicz,B., 1994. Tomo-

graphicstudyof uppermantleattenuationin the PacificOcean.Geophys.Res.Lett., 20: 663—666.

5. Discussionand conclusions Canas, J.A. and Mitchell, B.J., 1978. Lateral variation ofsurface-waveanelasticattenuationacrossthePacific. Bull.Seismol.Soc. Am., 68: 1637—1650.

We havepresenteda methodof measurement Deschamps,A., 1977. Inversion of the attenuationdata ofof mantle wave attenuationwhich allows us to freeoscillationsof theEarth(fundamentalandfirst higher

retrieve information on the odd part of lateral modes).Geophys.JR.Astron. Soc., 50: 699—722.

heterogeneityin theuppermantleQ. Thismethod Durek, J. andEkstrom, G., 1992. Differencesbetweenobser-

requirescarefulinspectionof the data, andmany vations of fundamentalmode attenuation.EOS Trans.Am. Geophys.Union, 73: 402.observationsneedto be rejectedbecausethey are Durek, J., Ritzwoiler, M. andWoodhouse,J:H., 1993. Con-

strongly contaminatedby focusing effects. Sam- straining upper mantle anelasticity using surface wave

pling testsindicatethat this doesnot significantly amplitudeanomalies.Geophys.J. mt., 114: 249—272.

affect the resultingglobal averageQ(w), which is Dziewonski, AM. and Anderson, DL., 1981. Preliminary

closerto PREM thanto recentresultsof Widmer ReferenceEarth Model. Phys. Earth Planet. Inter., 25:297—356.

et al. (1991), but in agreementwith otherstudies Dziewonski,A.M. andSteim,J., 1983. Dispersionandattenu-

(Durek andEkstrom, 1992).Maps of lateralvan- ation of mantlewavesthroughwaveform inversion. Geo-

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this new procedureconfirm earlier results and Dziewonski, AM., Chou, G. and Woodhouse,J.H., 1981.indicate a generalcorrespondenceof regionsof Determination of earthquake source parameters from

waveformmodelling.J. Geophys.Res., 86: 2825—2852.highvelocity to regionsof high Q andregionsof Dziewonski, A.M., Ekstrom, G., Woodhouse,J. and Zwart,

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ing becauseit involves measurementson short oscillationsobservedin Franceafter sixteenearthquakes.

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