Physicsof the Earth andPlanetaiyInteriors, 47 (1987) 267—287 267ElsevierSciencePublishersB.V., Amsterdam— Printedin TheNetherlands

Surfacewaveamplitudeanomalies:is reciprocityvalid?

FumikoTajimaandJanD. Garmany

Institutefor Geophysics,The Universityof Texasat Austin,4920 North I.H. 35, Austin, TX 78751 (USA.)

(ReceivedFebruary21, 1986; revisionaccepted October1, 1986)

Tajima, F. andGarmany,J.D.,1987. Surfacewaveamplitudeanomalies:is reciprocityvalid? Phys.Earth Planet. Inter.,47: 267—287.

SurfacewaveamplitudeanomaliesarestudiedusingGlobal Digital SeismographNetwork(GDSN) recordsof somerecentcircum-Pacific events (e.g., 1983CostaRica, 1983 Akita-oki, 1982 Ometepecand 1983 Peru—Ecuador). Someevent—stationpairs can be effectivelyusedto interchangethe sourceand receiveron agivenpath,and thusprovideinformation on an approximately reciprocal path. At certain stations, amplitude asymmetriesof R

3 to R2 aresignificant.Band-passfiltered recordsshowthat suchasymmetriesare frequencydependent.As theseanomaliesareprimarily causedby focusingand defocusingeffects, we havedone ray tracingexperimentsusing the phasevelocitymodel of Tanimotoin an attempt to accountfor theobserved anomalies.Whileanomaliessuch asthoseatTATO andMAJO for theCostaRicaeventor atCOL for theAkita-oki eventarewell predictedby theray tracing,othersarenot.At station RON, where the ray tracing experimentfailed to predict any asymmetry,we studied surfacewavepropagationon nearly reciprocalpathsin somedetailusing recordsof smallerevents.Theresultsindicate that actualpropagationin the heterogeneousEarth considerablyvaries betweenclosely spaced,but not exactly reciprocalpaths.Suchsensitivityto sourceandreceiverplacementis notpredictedby smoothEarth structures.This suggeststhat theremustbesubstantialsmall scalestructural variations.The lengthscaleof these variationsis presumablyon theorderofthe wavelengthsof 100—250 s surfacewaves (400—1000km). There is an unexpectedlylargevertical componentassociatedwith theovertonephaseX3 at somestations.In theradial componentof theserecordswe identify two grouparrivals around the X3 phase;the first one directly propagatedfrom the sourceand the secondone, which hasaprominentvertical component,maybe dueto modal conversionthroughthepath.

1. Introduction cern in the sourcestudies(150 s 250 s) showstrong effectsof suchinteractions.

Attenuationof seismicsurfacewaveshas been Lay and Kanamori(1985) performed a raywell measured accordingto the classicalformulas tracing experimentthat models multiplepassings(Kanamori, 1970; Nakanishi, 1979). Thesemea- of rays of surfacewavesbetweena sourceand asurementsare basedon the assumptionof mono- station. Lateral heterogeneityof surface wavetonic attenuationof successiveorbits of surface phasevelocity causesfocusing or defocusingofwaves. Intheanalysisof long-periodsurfacewaves, seismicwaves which creates observableamplitudehowever, we often observeamplitude anomalies anomalies.Lay and Kanamorisucceededin pre-which departfrom the classicalattenuationlaw. dicting amplitude anomaliesin terms ofray den-For instance,the amplitude of a later phaseat a sity orrayintensityat certainobservationstationsgiven stationmay be even larger than thatof an usingthe phasevelocity distribution of Nakanishiearlierone. This phenomenon hasbeen explained and Anderson(1984).This approachis, of course,in terms of ray theory. The interactionof seismic strongly model-dependent.Schwartz and Layrays with the lateral heterogeneityof the Earth (1985) compared predicted anomaliesof surfacecausesfocusing and defocusingof surfacewave waveamplitudesandphasesbetweenthe modelofenergy. Surfacewavesin the periodrangeof con- Nakanishi and Anderson(1984) and that of

0031-9201/87/$03.50 © 1987 Elsevier SciencePublishersB.V.

268

TABLE I

List of earthquakes

Event Date Origin time M~ Location Depth(km)

CostaRica April 3,1983 02:50:01.2 7.3 8.72°N,83.12°W 37.0Akita-oki May 26, 1983 02:59:59.6 7.7 40.6°N,139.10°E 23.7Ometepec June7,1982 10:59:40.9 7.0 16.59°N,98.32°W 33.0

mb

Peru—Ecuador April 12, 1983 12:07:54.6 (6.5) 4.89°S,78.18°W 120.0

Woodhouse and Dziewonski (1984). Although surfacewaves at thefrequenciesat which sourcethesemodels providea reasonablematch to the studiesare done. It may be that an attempt tophasedata,neitherof them satisfactorilyexplains synthesizeobserved amplitudesusing decoupledtheobservedamplitudeasymmetriesat thepresent scalarwave propagationandjust a phasevelocitystage. Onereasonfor this is the limited order of model may not be adequate(Yomogida and Aki,the sphericalharmonicexpansionwith which they 1985). Observationalevidence suggeststhat wedescribedthe phasevelocity distributions: 1= 6 mayhaveto considermodeconversions,coupling(Nakanishi andAnderson,1984) or 8 (Woodhouse and scatteringin addition to geometricaleffectsand Dziewonski, 1984). The measurementsof on surfacewave propagation. Propagationin thephasevelocitiesfor thesemodelsare basedon the smoothphasevelocity structureusedhereshouldassumption thatsurfacewave rays follow great- be adequatelymodeled by scalarwave methods,circle paths, a highly smoothing and typically butwe find thatsmooth modelscannot predictthenon-realisticassumption.The resolution of these observationsexcept in somefortuitous cases.studies correspondsto scalelengthsof over4000 Here,we presentsome surfacewave observa-km, while structural features of approximately tionsof recentevents whichoccurredin circum-1000 km size will strongly affect propagationof Pacific regions(Table I). The datawere retrieved

f~O 600 120° 180° 120° 60° 00

I I I I I

KO

AC

ANTO 05 AMN~ 450

T P

HON06/07/82

04/03/00

— 04/ /3CTA -

(.1 WAO

SNZO - 450

Fig. 1. Great-circlepathsbetweenGDSN stationsandsomerecentcircum-Pacificevents,1983 CostaRica,1983 Peru—Ecuador,1982Ometepecand 1983 Akita-oki.

269

TABLE II

List of earthquakesnearGSDN stations

Event Date Origin time M~ Location Depth(km)

Hawaii Nov. 16, 1983 16:13:00.1 6.7 19.43°N, 155.45°W 12.0Hachijo,Japan Sept.18, 1984 17:02:42.5 6.9 33.97°N,141.44°E 33.0NewZealand Dec. 30, 1984 21:36:55.8 6.9 36.73°S,177.50°E 33.0* Taiwan June24, 1983 09:06:45.8 6.7 24.18°N,122.40°E 44.0

TABLE III through stationsLON and ANMO cover ap-

GSDN stationsnearearthquakes proximately reciprocal pathsalong the northern

StationID. Location Altitude Pacific boundary. The great-circle path for the1982 Ometepec eventthroughTATO almostover-HON (DWWSSN) 21.32°N 158.01°W 2.OmMAJO (ASRO) 36.54°N 138.21°E 422.Om laps thatfor the 1983 Peru—EcuadoreventthroughTATO (SRO) 24.98°N 121.49°E 53.Om MAJO.SNZO(SRO) 41.31°S174.70°E 12.Om

2.1. Low-passfilteredsurface waves

from Global Digital Seismograph Network Multiple Rayleighwavesobservedfor the 1983(GDSN) records. Thedi~tributionof sourcesand CostaRicanearthquake(M~= 7.3, h 30 km) arereceivers yield somesetsof very similar great-circle shownin orderof distance(Fig. 2). The datawerepaths (Fig. 1). This dataset includessomenearly low-passfiltered at around100 s. The R2 and R4reciprocal pathsalong the northernboundarybe- phasesare roughly lined up. The epicentraldis-tween the Pacific plate and the North America tancesof SCP, GAC and ANMO rangebetweenplate.To providemoreprecisereciprocal pathsto 32°and37°.However,the amplituderatios of R3thosebetweenthe circum-Pacificevents and sta- to R2 differ strongly from station to station. Attion HON, whereanomaliesare pronounced,we GAC the R3 amplitude is larger than thatof thealso examine the records of the 1983 Hawaii R2 phase.At SCP the R3 amplitudeis about theearthquake(M~= 6.7) andsimilar size eventsnear sameas that of the R2 phase.Theseamplitudethe GDSN stations (Tables II and III). We pre- anomalies arisedespitethe verysimilar azimuthalsent someraytracingexperimentsusingthe phase directions of SCP (70) and GAC (90). Thevelocity variationmodel of Tanimoto(1985) (1 = anomalousrelativeamplitudeasymmetryof R3 to10) and comparethe resultswith observationsof R2 may have beencausedby the superpositionofGDSNrecords. overtone phaseX4 (Jobert, 1978; Roult and

Romanowicz,1984).On theotherhand,at ANMOthe amplitude attenuation of the R3 phase is

2. Observation of surfacewave amplitude anomaly substantialcompared with the R2 amplitude.Among the stationsMAJO, TAU, CTAO, TATO

To addressproblemsof surfacewave amplitude andNWAO, considerablevariationsof R3 to R2anomalies,we first examinelow-passedor band- amplituderatios are observed.Thesestationslie inpassedrecordsof long-periodsurfacewaves(T~ the distancebetween1200 and1490 andazimuths100 s) of a few large events whichoccurredin the between215°and325°.At MAJO the amplitudecircum-Pacificregions(Table I). The great-circle of the R3 phaseis aboutthe sameas that of thepathsbetweenthe epicentersand GDSNstations R2 phase,althoughthe travel distanceof the R3are shownin Fig. 1. Somegreat-circlepathssuch phaseis twice as long as that of the R2 phase.as those through stations ANMO,LON, MAJO This is in greatcontrastto the amplitudebehaviorand TATO for the 1983 CostaRican event are at TAU, CTAO, and NWAO. At TATO a similarvery similar. Thoseof the 1983 Akita-Oki event patternto that at MAJO is observed.As is shown

270

1983 CostaRica 1983 Akita—oki

P2 P3 sc~ A— 320 P4 CTAO

~ANM0~~~324 R2 R n 336

~ —ij~ ~4hio ~ ... .......

GAC ANTO 3~QO

~IrLONS~~ H~760 -

326° NWAO 199

1 ~. .~ .,~,.:

COL 336° GRFO 329°

• ~ ~ ‘1W’~-~~~ .

SNZO 154°

A2 X3 x MAJO P3 120 ‘i~r5322° ~l

~ ~ 0

TAU 224°223° hour

Fig. 3. Same as in Fig.2 for the1983 Alilta-Oki earthquake.

I CTAO 1310

H 251°

larger at MAJO and TATO than at ANMO andx~ TATO LON. This observationimplies that the directivity

X: effect at the sourcecannotaccountfor the anoma-busamplitudesof this event. AtMAJO andTATO

NWAO 149° a substantialovertonephase, whichmay be X3- ~°° - and is comparablein amplitude to that of the

fundamentalmodel R2 or R3, is noted betweeno ~ R~andR3.At stationsTAU, CTAO andNWAO,

__________ _________ whichare at asimilardistanceto MAJO or TATO,

Hour no suchphasesare predominant.Figure 3 shows

Fig. 2. Low-pass filtered long-period surfacewaves (vertical the low-passfiltered surfacewaves(T ~ 100 s) ofcomponent)of the1983 CostaRicaearthquakeat 100 s. The the 1983 Akita-Oki earthquakesin the distanceR2 and R4 phasesareroughly lined up.Note thevariationsof between610 and 890. They are alsoarrangedinthe R3 to R2 ratios amongthe stations, order of distance.Again we observeconsiderable

variationof the R3 to R2 amplituderatios among

in Fig. 1, stations ANMO and LON also have thestations.very similar great-circlepaths to MAJO andTATO. Although the travel distanceof the R3 2.2 Frequencydependentanomaliesphasecomparedwith that of the R2 phaseismuch longerat MAJO andTATO thanat ANMO Next we examinethe frequencydependenceofand LON, the amplitude ratios of R3 to R2 are theasymmetryof multiple orbit surfacewave am-

271

plitudes. We filtered the long-periodsurfacewave the R5 to R4 phaseappearin the rangesbetweenrecordsin four different passbands(50—150 s; 150 and250 s andbetween200 and300 s, but not100—200s; 150—250 s; 200—300 s). in the rangebetween100 and200 s. At MAJO the

Figure 4 shows thefiltered surfacewaves(verti- R3 amplitude is equal to (200—300 s) or evencal component)from the recordsat SCP, GAC, larger than (100—200s) that of the R2 phase.AtANMO, CTAO, MAJO, and TATO for the 1983 TATO, the R3 amplitude is also substantiallyCostaRica earthquake.At GAC (4) 90), the R3 larger than what is expectedfrom the intrinsicamplitude is larger than that of R2 in all these attenuationif Q 100 to 200 is appropriate(seefrequency ranges. Such amplitude reversalsare also Fig.11). The amplitudereversalof the R5 toobservedalso for the R4 and R5 phases. AtSCP R4 phaseis observedin the ranges150 to 250 sthe amplitudereversalsof the R3 to R2 phaseand and200 to 300 s. At ANMO no suchanomalies

1983 CostaRica

SCP CTAO

(50—150)I $~*I4J~2~I!*h~! —— ~ . - .0

(100-200).s4444~ ~0 ~ -~, .

R6 (1 50-250)R6 _____

(200300)

ANMO MAJO

__________________________________ —

•~t - I

R2111 ~.a R4 R5 R2 R3i R R•uW,. .‘~ ~.141~21IM .• .• ••• •4~~4**’h1 ~

GACTATO

~

2W~

R2 Rq~1 A4 A5 R6 R2 R3 R~ A5~ •+• ? ~ •~y.•.*~•* .•••• ~• •~.• -•

0 5 0 5I I I L_____ iI

hourhourFig. 4. Band-passfiltered long-periodsurfacewavesof the 1983 CostaRicaearthquake.Note that the R3 to R2 ratios vary fromband to bandas much asbetween stations.

272

are observedin any of thesefrequencyranges.At and 200 s while no suchanomalyis observedinthesefive stations,a substantialovertonephaseis the band between200 and 300 s. As is showninobservedaroundthe X3 phasein the period range Fig. 1, the 1982 Ometepecand 1983 Peru—Ecua-between 50 and 200 s. The band-passfiltered dor earthquakeshave very similar great-circlerecordsof the 1983 Akita-oki eventat LON and paths to MAJO and TATO. These great-circleANMO, which approximatelycover thereciprocal pathsare somewhatsouthwardof that betweengreat-circlepaths for the 1983 CostaRican event the CostaRica eventand MAJO or its reciprocalthroughMAJO and TATO, are shown aswell as path (e.g., between the Akita-oki event andat COL and HON in Fig. 5. At stations ANMO ANMO). The band-passfiltered records(Fig. 6)andLON, no amplitudeanomaliesare observedin show that the R3 to R2 ratios are different be-the rangebetween50 and250 s. At stationHON, tween the two events. No substantialovertonethe amplitudeanomalyof R3 to R2 is significant phaseX3, as wasobserved betweenR2 andR3 atin all four bands.At COL the R3 amplitude is MAJO or TATO for the CostaRica event, arelarger than thatof R2 in the bandbetween100 s notedhere.

1983 Akita—oki

R2 R3 ( LON

~~T~6°( 1O0~2OO~1 670

2 ~ I I~$~/. 900 •i~11iI~,•~ 470

...~1,4 ••.,,•••

COL ANMO

-~1 ‘0 ~ •

I ~I 340 I~i 490i_Il 1 • -~~,‘-- •

R2~ R3 R4 R2 R3 A4~2.~ “~ •‘~~‘~“~•• *© w,”i~~- .,- —•.• . ~ . •.

~,.••I,,.. ~‘ ~ v ~ ~ ,,.

0 5IIII

hourFig. 5. Same as in Fig.4 for the 1983 Akita-Oki earthquake.

273

A—i ~ spondingphaseis obviousin the vertical compo-4-318° nent. For the stations NWAO,CTAO, TAU, and

Peru-Ecuador SNZO, the first minor arc passageis throughold(MAJO)

(50—150)•~,~, , ocean. Figure7c shows theamplitude anomalies

of the multiple orbit Love waves. The amplituderatios of G3 to G2 show substantialvariationamongthe stations.The tendencyis moreor lesssimilar to that observedfor the R3 to R2 ratios

250) ~3 but notquite the same.Figure 8a shows theverti-cal componentof the Akita-oki event. Because ofthe station distancefrom the epicenter, the sep-

(200-300) arationof X3 phasefrom the R2 phaseis not

good at some stations. However, comparedwiththe radial component (Fig. 8b), no substantialovertonephase(— X3), which was observedfor

A—123°Ometepec the CostaRica eventat TATO and MAJO, exists.4-316°(TATO) Instead,the overtonephasearoundX4 is substan-

tial at TATO. A similar phaseis observed atstation GAC. In the transversecomponentthe G3

to G2 ratio is equalto or greaterthanoneat GAC,ANMO, GRFO, KONO,andCOL.

Ru

3. Ray tracing experiments

We have observedsome amplitude anomaliesof long-periodsurfacewavesfrom the eventsthatIIoccurredin the circum-Pacific region. As is dis-

0 4cussedby Lay and Kanamori(1985), the geomet-

hour rical effects of the global lateral heterogeneityFig. 6. Comparisonof bandpassfiltered long-periodrecordsof seem to be the major cause of theamplitudethe1983 Peru—Ecuadorand1982 Ometepecevents. Thegreat- asymmetry of fundamental modes. Lay andcircle pathsfor theserecordsare very similar. Kanamori performedraytracingexperimentswith

the Nakanishi and Anderson(1984) model andpresented some successfulpredictions of am-

To summarizeour observationsabovewe dis- plitude asynmietriesshowing focusingor defocus-play the 100 s low-passfiltered recordsectionsof ing of rays. Schwartzand Lay (1985) comparedthe two earthquakesin the vertical, radial and the results of ray tracings with the model oftransversecomponents(Fig. 7a—candFig. 8a—c). Nakanishi and Anderson andthat of WoodhouseThereis anunexpectedlylargevertical component and Dziewonski(1984) and pointed out that theassociatedwith the X3 phaseat certain stations; results are strongly model-dependent.While theTATO, MAJO, COL, LON, GAC andSCP.Com- phasepredictions agreereasonablywell betweenparedwith the radial component,the arrival time the models, matching the amplitude asymmetriesof the peak amplitude of thesewave trains is remainsunsatisfactory.delayed.Thesestations havethe first minor arc The global phase velocity distributions ob-passagethrough the North American continent. tamedby Tanimoto(1985) aredescribedwith 10thAlthough the overtonephaseX3 is substantialin order spherical harmonics.The long-wavelengththe radial componentat other stations,no corre- features of this model are consistent with the

274

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V

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Q~ _•_•-~_•-t_•U

N I —

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5 --—— 5-Vu

o ~ a ~3- Q IC 3- . . —

(Sep) V1~]0 S

275

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(LL ~Hh’1I ~ 1 1

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V ilIL —p -~--- — I

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276

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(!~ ~ Cl

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-~ S 55 ° -,

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~ ~ IS~—f—_-~ I

2< ~ HIS ISI, -

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S

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IS ~ ~ -~. S

IS ~ ~=~———~—— ~

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(Sap) ~-~çj

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CC

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(Sap) Villa

280

previous two models, but Tanimoto determined son usinga formulation for ray tracingderivedbythe resolution of this data set more rigorously. JobertandJobert(1983).Resolvingkernel widthswere on theorder of 2000 Figure 9a—c shows theray paths for R1, R1,km. Here, we carry out ray tracing experiments R3 and R4 phasesof the CostaRica eventat thewith the model ofTanimotofor anothercompari- periodsof 250 s. 200 sand 154 s, respectively.The

a bCosta ~Jc9_ P1 250 rofa ~ca P 200 s

Fig. 9. (a) Ray tracings withthc phasevcIocit~model ol’ Tanimoto (l9~5)(or the 19X3 CostaRicaevent at 2500. (h) Samea~(a) at2000. (c) Sameas (a) at154s.

281

c of R3 to R., at SCPand GAC are not explainedI. st~P1cc Ri 134 —- with theseray tracings.

Figure lOa—c showsthe resultsfor the Akita-oki~ earthquake.In the surfacewave records of this

_________ event the amplitude anomaliesof R3 to R, are

__ a...—‘~ Akita—0k~ P1 250 s

P2

P2

P3 /5

R4

Fig. 9. (continued)

amplitudeasymmetriesof R3 to R., at MAJO andTATO are well predicted with the ray tracingat250 s. The relativefocusingof the R, phaseanddefocusing of the R3 phase at CTAO, SNZO, •.. -. .1

NWAO, and TAU are alsoconsistentwith the Fig. 10. (a) Sameas Fig. 7a for the1983 Akita-Oki event. (h)observations.On the other hand,the asymmetries Sameas (a) at200 s. (c) Same as (a) at154 s.

282

b CAkitC,—0kI Ri 200 s . L- I Ri 15

Fig. 10. (continued)

4. Useof great-circle Q measurementfor a test ofreciprocity

most significant at COL. HON. SNZO. NWAO To assess theattenuation of surface waves,and CTAO. The focusing and defocusingof the great circle Q has been measuredignoring theraysare consistentfor stationsCOL andCTAO. effectsof interactions withthe laterally heteroge-

283

0—measurement neous Earth.We calculated greatcircle Q fromthe R2 and R4 amplitudesaccordingto the for-mula (Lay andKanamori,1985)

2~ — ¶1— (i)U1T ln ~:? ~~osta Pica the period, U1 is a great-circlegroupvelocity and

where 1 is the length of a great-circlepath, T is

TOTO a1 is the spectralamplitudeof the i th ordersurfacet1~t -

cTm~su wave. The great-circle Q’s measured fromthe

50-1983 CostaRicaearthquakerangesfrom 50 to 150

III in the period rangebetween150 and 230 s (Fig.3.5 4.0 4.5 5.0 5.5 6.0 6.5 ha). At some stations, Q exceeds250 at periods

Frequency(mHz) around250 s. Owing to the effectsof amplitudeasymmetries,Q measurementswere unstableinsome records.In Fig. lib, c, theamplitude ratios

983 Costa Rica

of R3 to R2 which wereobtainedfrom thelow-pass1.0 -

filtered records(see Figs.2 and3), versusdistanceMAJO

0.1=250 sec) the calculatedratios of R3 to R2 for a certain Qare plotted. Three solid linesin eachgraphshowand periodas afunction of distance.The ratios at

05 c~10= 103 1-250 sac) stationsMAJO andGAC for theCostaRica event

are higherthan the calculatedvalues.The ratiosatCC (0=100 1= loOsed ANMO, GRFO, SNZO and TAU are lower.The

013-0. ~ NW 0ccc anomaliesthat are indicated by this graph are

3 II consistentwith the observationin Figs. 2 and 7a.5’ 30 80’ 90’ 125’ 155’ 180’

DISTANCE Figure 1k also indicates anomalous observation

at COL, HON, LON, ANTO, CTAO, NWAO and1983 Akita-oki SNZOfor the1983 Akita-Oki earthquake.

Now that the ray tracing experimentsdemon-HON strate focusing or defocusing effectsof surface

1.0 - waves arisingfrom the interactions withthe lateralheterogeneityof theEarth,somecorrections shouldbe appliedto the Q measurement;we follow the~ 250 sect

procedurefor such correctionsdescribedby Layand Kanamori(1985).

N 80NO~ (0 100 1 250 sect The intrinsicattenuationQ0 is definedby05- LON

ST1ANTO _____________ (2)

CTAO SNZO

NWAO I 80~ (0 i0O,T 100 sod = — L.~Tln ~C0’ 30’ 60’ 90’ 120= ISO’ 180= for a uniform Earth. Thenthe ratios of the actu-

DISTANCE

ally measuredamplitudesto thosefor the uniformEarthare definedby

Fig. 11. (a) Q measurementfrom severalstations of the 1983 E. = a1/a10 (3)

CostaRica earthquake.(b) The amplitude ratiosof R3 to R2phases whicharemeasured fromthe seismogramsin Fig. 2 are E. = a,+ 2/a,+ 2,0 (4)plotted.Calculated amplituderatiosfor specifiedQ andperiod We then,obtainarealsoshownas afunctionof distance.(c) Sameas (b) fortheseismogramsin Fig. 3. E1/E1~2. (5)

284

Neglectingdifferencesof groupvelocitiesbetween betweenthe events.For the reciprocal path theLIS~,for the homogeneousEarthand U1, we obtain amplitudesof the ith, i + ith and i + 2th surface

ln ~ waves aredenotedas b,, b,+~ and b.+ 2~Then the

Q Q1. 1__~.i. Q1. [i + (ln E1/E1~2/lnii)] ratiosof the actuallymeasuredamplitudesto those

0 (6) for the uniform Earthmay be describedasb,/a,0=E1 (7)

for the assessmentof an intrinsic attenuation. The b / = E (8i±lf i+1,o j+1

ray-densityanomaly (E1) can be calculated from b — E 9the ray-tracingexperiment. i+2/~~i+2,o— i+2

Yet, the patternsof ray tracingsshow substan- Thismeans,obviously, that the amplitude ratiostin! variations frommodel to model at thepresent of multiple-orbit surfacewavesshouldbe the samestage (Schwartz and Lay, 1985) suggestingthat betweenevents whichprovide precisereciprocalestimationof a proper value for E1 may not be paths.As we notedin the examinationof filteredvery realistic. Also,this approachshouldbe valid GDSN records,the amplitude asymmetryof thefor reciprocalpaths.Thus weexaminesome wave R3 to R2wavesis significant at HON for the 1983forms and Q alongreciprocalpaths.First we find Akita-Oki event. This asymmetryhas not beena pair of events that providesa reciprocalpath, predictedby the ray-tracingexperiments.i.e., the sourceand stationlocationsareexchanged To examine this asymmetryalong a shorter

120°E 1800 120°W

~i 45°N

TATO (3) 11/16/83

(2) —~ ~00

5.-

- 12/30/84 —

SNZO -45°S

I I

Fig. 12. Two pairs of epicentersandstation locationswhichprovide reciprocalgreat-circlepaths(1) and(2) areshown.

285

path,we usesmallerevents(6.4 ~ M~s~6.7) which R2 to R1 and R3 to R2, obtained from theoccurrednearthe 1983 Akita-Oki earthquakesince band-pass filteredrecords(Fig. 13) are differentin21 March 1983 when stationHON becamefully each pair. The surface waves of someTaiwanoperational.To providerecordsfor the reciprocal events (6.1 ~ M~~ 6.9) recorded at HON werepath, thereis an adequateevent,the 16 November examined,but the signal-to-noiseratio was poor1983 Hawaii earthquake(M5 = 6.7). We also ex- and not usable for this study. As is discussedamine two more paths, one betweenHON and above, if thereciprocity is valid along apath,thenTATO andthe otheronebetweenHON andSNZO the Q measurementshould be identical in each(see thestation locationsand the hypocentersof pair of the regionalpaths.However,Fig. 14 showsthe eventsin Tables II and III). The epicenters, that Q measuredas a function of eigenperiodthe station locations and their great-circle paths variesevenbetweenreciprocalpaths. Along pathare shown in Fig. 12. Here, we label the path (2), Q measuredat SNZO has a peak value ofbetweenHON and MAJO as (1), that between about400 at around150 s while Q at HON hasaHON and SNZO as (2) and that betweenHON peakvalueof about300 at around180 s. Since weandTATO as(3), respectively, calculateQ from themultiple-orbitRayleighwaves

Clearly each pair of paths is not strictly re- R1 and R3, the propertiesextractedreflect onlyciprocal,but theseare the closestamongavailable the average along thegreatcircle (Knopoff, 1969).eventsand records. Yet,the amplitude ratios of At thismoment,we haveno specificexplanations

- for theseobservations.

(1) (2)

______ -- -• —+ ~ ~ 4

- MAJO ~.. R~ 1983 Hawaii ~4~R2SNZOR3

1984 Hachijo 1984 New Zealand—i,. ~ • 18*

R1 HON R1 ii R3V C’ C C C ‘ • S’4.1114L. .50 . C.’ A CC .CV.C.53 ..

4—~_~-—~(hour)

Fig. 13. Band-passfiltered (50—150,100—200, 150—250s) long-periodvertical surfacewavesof the1983 Hawaii earthquakeobservedatMAJO andTATO andthoseof the1984 Hachijo and1984 NewZealandobservedatHON which providereciprocalpathsfor (1)and(2), respectively.

286

0 Measurement through the North American continentthe over-400 tonephase(— X3) is substantialevenin the verti-

cal component.This wave train arrives slightly300 later than the X3 phasewhich is clearlyidentified

in the radial componentand canbe explainedby200 - the sourceexcitation (Okal and J0, 1985). Such

100 amplitude asymmetriesof overtonephasesbe-tweenthe verticaland radial componentsare not

48 5.3 5.8 6.3 6.8 explainedby the geometricaleffects. Conversions(1O”~Hz) from fundamentalto higher modesthrough inter-

actionwith the structuremay needto be consid-__________________________ ered. As Park (1986) demonstratedwith syn-

200 MAJO(1) .thetics, mode coupling is an importantcause of

150 - amplitude anomaly,too. To explain someresidu-als of Love wavesobservedin the verticalcompo-

100 TATO(3) nent, mode conversionfrom Love waves to

50 - HON(1) Rayleigh waves, which iscausedby the Coriolisforce, is alsopointed out (Park, 1986). On the

44 4.9 5.4 ~ 6.4 6.9 other hand,our preliminary determinationsof Q

(iOu Hz) suggest that surface wave propagationon theFrequency laterally heterogeneousEarthon nearlyreciprocal

Fig. 14. (a) Q measurementfor the path(2). (b) Q measure- pathsis very sensitiveto receiverandsourceloca-ment for thepaths(1) and(3) tions. This sensitivity is not expectedin smooth

Earthstructures.Wetentativelypropose thattheremust be heterogeneityon a scalecomparabletothe wavelengthsusedin this study.

5. Discussion While this study examinesthe geometricalef-fectsof lateralheterogeneityon surfacewave am-

We have examined amplitudeasymmetriesof plitudes,it is hopedthat this type ofapproachwilllong-periodsurfacewavesusingGDSN recordsof eventually be applied to invert for the lateralsome recentevents. Atpresent,this phenomenon heterogeneityof the Earth. Promising results ofis primarily explained by the focusing and de- Gaussian beam syntheses were presented byfocusing effects of surfacewave rays causedby Yomogida and Aki (1985) and Jobert(1985), butinteractionwith the lateralheterogeneity(Lay and at the presentstage, thevariation of ray tracingKanamori,1985).To examinethiseffect, wetraced patternsis too large amongthe models to makerays using the phase velocity distribution of themusefulin such aninversion.Accordingly,justTanimoto (1985) for the 1983 Costa Rica and pursuingforward problemswith ray tracing may1983 Akita-Oki earthquakes.The resultsare simi- notbe efficient. In general,representingthe prop-lar to those ofthe previousexperiments(Lay and agationof surfacewave modes asuncoupledscalarKanamori,1985; SchwartzandLay, 1985) in that potentialswould be adequateon an Earth withsome observedamplitude asymmetrieswere pre- smoothly changing characteristics(such as onedicted in terms of ray density, whileotherswere representedby an 1= 10 spherical harmonicex-not. The superposition of prominent overtone pansion).Thiskind of representationhasprovidedphasesover the fundamentalmodesmayat times us with goodpreliminarymodels,but the evidencebe acause ofamplitudeasymmetriesas discussed indicatesthat the determinationof more detailedby Roult and Romanowicz(1984).We havenoted modelswill require the inclusionof the effectsofthe path dependencyof suchovertonephases.At mode-to-mode coupling. Complete variationalsomestations thathaveasimilar great-circlepath methodsof calculating normal modes can im-

287

mediately assess suchmode conversion effects Kanamori, H., 1970. Velocity and Q of mantlewaves. Phys.

(Tsuboi,1985;Tsuboiet a!., 1985). Buttheseseem Earth Planet.Inter., 2: 259—275.

to beinefficient for short wavelengthpropagation Kennett,B.L.N., 1984. Guidedwave propagationin laterally

modeling. A different approachmight be to ex- varying media—I. Theoreticaldevelopment.Geophys.J.R.Astron. Soc., 79: 235—255.

tend the notion of lateral propagationoperators Knopoff, L., 1969. Phaseand group slownessin inhomoge-

beyondtheir currentdevelopment(Kennett,1984). neous media.J. Geophys.Res., 74: 1701.

Our continuingstudywith moreavailabledatafor Lay, T. and Kanamori,H., 1985. Geometriceffects of global

reciprocalpathsas well asexaminationof mode lateral heterogeneityon long period surface wave prop-

conversionsor couplings will be presentedin a agation.J. Geophys.Res.,90: 605—621.Nakanishi,I., 1979. Phasevelocity and Q of mantleRayleigh

subsequentstudy. waves,Geophys.J.R.Astron. Soc., 58: 35—39.

Nakanishi, I. and Anderson, D.L., 1984. Measurementsofmantlewavevelocitiesandinversionfor lateral heterogene-

Acknowledgements ity and anisotropy,II. Analysis by thesingle-stationmethod.Geophys.J.R. Astron.Soc., 78: 573—617.

Okal, E. andJ0, B.G. 1985. Dispersionof higherordermantle

We thankN. Jobert,T. Lay, E.Okal, G. Roult, Rayleighwaves. Phys.Earth Planet. Inter., submitted.B. Romanowicz,T. Tanimotoand K. Yornogida Park,J., 1986. Syntheticseismogramsfrom coupledfree oscil-

for sendinguspreprints.T. Tanimotosent us the lations: effectsof lateralstructureandrotation.J. Geophys.

spherical harmonics coefficients of his phase Res.,91: 6441—6464.Roult, G. and Romanowicz,B., 1984. Very long period datavelocity model. The program to calculate great from the Geoscopenetwork: Preliminary resultson great

circle Q has been made available to us by I circle averagesof fundamentaland higher Rayleigh and

Nakanishi.We thank S. Cardimonafor his assis- Love modes.Bull. Seismol.Soc. Am., 74: 2221—2243.

tance in producingFigs.7 and 8. The comments Schwartz,S. and Lay, T., 1985. Comparisonof long-period

by the anonymousreviewers helped clarify the surfacewaveamplitude and phaseanomaliesfor two mod-manuscript.S. Cardimonaand W. O’Brien read elsof global lateralheterogeneity.Geophys.Res. Lett., 12:231—234.the manuscriptandprovideduswith helpful corn- Tanimoto, T., 1985. The Backus—Gilbert approachto thements. This researchwas partially supportedby three-dimensionalstructurein theupper mantle: 1. Lateral

NSF GrantsEAR83-12890and EAR84-10352. variationof surfacewavephasevelocity with its error andresolution. Geophys.J.R. Astron.Soc., 82: 105—123.

Tsuboi,5., 1985. Variational Calculationof theNormalModesof a Laterally Heterogeneous Earthandits Application to

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