Physicsof theEarth and PlanetaryInteriors, 21(1980)83—96 83© Elsevier ScientificPublishingCompany,Amsterdam— Printedin TheNetherlands

THE FATE OF THE DOWNGOING SLAB: A STUDY OF THE MOMENT TENSORS FROM BODY WAVESOF COMPLEX DEEP-FOCUSEARTHQUAKES

RICHARD A. STRELITZ

Lunar and PlanetaryInstitute,3303NASARoad1, Houston,TX 77058(U.S.A.)

(ReceivedDecember8, 1978;revisedandacceptedApril 4, 1979)

Strelitz, R.A., 1980.Thefateof thedowngoingslab:astudy of the momenttensorsfrom body wavesof complexdeep-focusearthquakes.Phys.EarthPlanet.Inter.,21: 83—96.

Twolarge,complexdeep-focusearthquakesareanalyzed,usingbody waves,to determinetherelativelocationsandequivalentforcesof thecomponentevents.Detailsof thesourcemechanismdeterminationaregiven,withspecialemphasison themeansof comparingresultsfor double-coupleandmoregeneralmodels.Theformalismincludesadescriptionof amethodfor calculatingthe confidenceellipsesaroundthe principalaxesof the momenttensor.Aninterpretationof theresultssuggeststhat themechanismof deep-focusearthquakesis controlledby thebuoyancyof theslabandthechangein viscosity atthe650km discontinuity.

1. Introduction Sasatani,1974,1976;Furumoto,1977;Koyama,1978),or the sourcemechanism,asdeterminedby

The sourceof deep-focusearthquakeshasbeenof long-periodsurfacewavesor free oscifiations(Gilbertinterestsincedeep-focuseventswere first discovered, andDziewonski,1975;FurumotoandFukao,1976),It wasthe adventof theplatetectonicshypothesis andthereforea mechanismaverageoverthesub-which gavemeaningto thedistribution of these events.If, ashasbeencommonlyassumed,a largeevents,while thethermalandmechanicalmodels eventis only a successionof shearingmotionsprop-further clarified ourunderstandingof theclustering agatingerraticallyalongthe sameplane,then thereis

of earthquakesat certainpointswithin the descend- no difficulty in the long-periodapproach;however,ingslab. thereis goodevidencethatmotionin deep-focus

Previousstudiesof deep-focusearthquakeshave earthquakestakesplacealonga varietyof planesconcentratedon therelationshipbetweensubevents (GilbertandDziewonski,1975,particularlytheirof complexdeep-focusearthquakes(Fukao,1972; fig. 27 (Fig. 6 here);Strelitz, 1975).

TABLE I

Epicentralparametersof thetwo earthquakesstudied.ThesearethestandardUSCGSvaluesandhavenotbeenredeterminedforthis work

Location Date Time Latitude Longitude Depth Magnitude(°) (°) (km)

Colombia 7/31/70 1708 : 5.4 1.45S 72.55W 651 7.1SeaofOkhotsk 8/30/70 1746:9.0 52.38N 151.49E 645 6.6

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To bestunderstandthecomplexitiesof multiple long-periodcomponentsthat theyhad to be con-events,the compressionalwave arrivalsof theP, PcP sideredof little or no use.Agreementimprovedand pPphaseswere decomposedinto a sequenceof markedlyafterrectification,indicatingthe needtopulseswhich were analyzedin termsof arrival time, makemeasurementsfrom processeddigital data,andamplitudeand zerofrequencylevel. Thesevalues not rawseismograms.were usedto determinethe relativepositionsof the Following digitization,the recordswerefiltered byeventsand theuncertainties;thenthelatter two amoving-window matchedfilter to removetheeffectresultswereusedto determinetheprincipalaxesand of the seismometer,andthusto convertthe seismo-theuncertaintiesof themomenttensorcorresponding gram into a sequenceof pulseswithout instrumen-to botha double-couplesourceand a generalreforma- tally inducedbackswingsandbroadening.tion sourcewithout volumechange. The applicationof this filter thusgenerateda

Analysesof theseresultsshowthat thetwo large groundmotionsectionof 55 records,eachaboutfiveandcomplexdeep-focuseventsstudiedhere(the to sevenminuteslong(to thePParrival,generally)for8/30/70Seaof Okhotskand7/31/70Colombia the Okhotskeventand25 recordsaboutfour to fiveevents— seealso Table I) consistof a numberof minuteslongfor theColumbiaevent.Thesesectionsdistinct episodesof motionalonga fault planethat were plottedout in orderof increasingdistanceto aidbecomesprogressivelysteeperasthe eventsdescend in identification of bothmajor(P, pP,PcP,sP)andinto the slab, minor (pMP, a bouncefrom theundersideof the

Moho,andpPcP)phases,which couldotherwisebemisinterpretedasarrivals from a multiplet.Finally,

2. Data recordswere groupedby azimuthto facilitateidenti-

fication of individualsubeventarrivals,an essentialThe raw dataconsistof a numberof long-period buthighly subjectiveaspectof this study.Only by

WWSSNseismogramsfor eachevent.In somecases correlatingrecordsfrom nearbystationscanonetheverticalcomponentswereoff scaleandwere decideon thenumberandorderof the subeventsthatunsuitablefor detailedstudy,butwheneverpossible, compriseeachseismogram.At this stagealone canverticalcomponentswere used.In caseswhereall complications,suchaschangein theorderof arrivalthreecomponentswere available,comparisonswere of theeventscausedeitherby supersonicrupturemadebetweeneachcomponentto verify the accuracy (VR > ui,) or by alack of connectionsbetweentheof measurementsof the incomingcompressionalwave events,or nodalarrivalsfor somesubeventsbe con-by horizontalinstruments.In mostcases,therewas sidered.Pulseshapesarea useful but notnecessarilysufficient similarity betweenthe recordsto justify the diagnostictool for this identification.useof all three,butneverthelessthesemeasurements Oncethecorrelationshavebeenmade,andadeci-were given lessweight in the inverseproblems.No sion aboutthenumberandform of the subeventsattemptwasmadeto apply polarizationfilters or any reached,the remainderof the analysisis moreauto-otherform of automaticshearwavesuppression.This matic. Eachrecordandtheassociatedgroundmotionwasunnecessaryfor theOkhotskevent,while for the wereplottedon aninteractivedisplay device,alongColombiaevent,thedatawerenot of sufficient with arrival timesof thephasesof interestcalculatedquality to permit theapplicationof suchafilter, from aJB model.Eachphasewasthenseparatedout

Recordswere digitized andrectified to removethe from thetotal recordanddecomposedinto a seriesofeffect of the non-orthogonalityof penmotionand pulses.The definitionhere for a pulse is the groundthe baseline.In mostcases,therewas little uncer- motioncausedby the arrival of energyfrom one sub-taintyaboutthelatter becausea minimumof two event.It wascharacterizedby threecoordinatepairsminutesprior to visible onsetwere also digitized and (see Fig. 1): thearrival timeor onsetand the baseline;usedto determinethebaseline.During digitization, thepeakamplitudeandtime; andthedecayslope,arrivalsof “glitches”, or sharpbreaksin the first continuedto thebaseline.arrival wave form,weretabulated.However,there Following this characterization,the triangularwas so muchvariationin thesetimesamongthethree figure definedby thesethreepointswassubtracted

85

8a“4

2ORIGiNAL RECORD

0’

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GROUND MOTION H II ,~ N C ~,O— — “0 ‘fi ~‘ C ~o ~ N d~ N ~O C’~ Os 00I ~

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~ ~00N00OsN©00OsN m “000 ‘.0 ‘ 00 C m C~..~ ,~ I.o I I I I I~ ~ I_-._-————---‘~i~f”’’--’.._~_.~P3 U110.6 © © ©C 1’3 N ~ 1’~~ N 05

= ~ ‘~ N N C4~ 00 N ~‘ ~‘ N ~‘

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C C C C C C C C C CCSTU1~74.30 335.24 24 1755 P © — ~ 00 CI

Fig. 1. Exampleof thestrippingprocedureusedto measuretheamplitudeandarrivalof thesubevents.To theright ofthelowerfour tracesarenumberscorrespondingto thesub-eventnumber(P1,P2 etc.),thearrivaltime relativeto the ~ Z m m m c”~~ r”~m ~

Cstartof digitizationandtheareaof the pulseremoved(shownon theleft) in digital units.At thebottom,thefile being ,fl ,,., ,,‘0 ~

analyzedis given. C designatestheevent,andis followedby .~ . ~‘ ~ ~i °~~ 0’~~ ‘.~

thestationcodeandthecomponent.Also givenarethedelta ‘— © “~ “0 N Os — 05 ~n N ~‘.0 ‘I’ ‘r, ‘1) — ‘,~ ~ N N N0 ~ — —

azimuth,atwo-digit instrumentcode,the time at thestartofa

therecordandthephasename.U

m 05 Q N N 00’ Os 0500

N

— cq, r4~m ,.-~ ,-.~ — ~‘4-.

point by point from the record,andthe resultdis-C m m 0 ‘i~v’. .,~~

0 N —4 Os”0 ‘.0 ‘.0 0505 Osplayed.~Subsequentpulseswere strippeduntil alleventshadbeenaccountedfor. Thus,at theend,the ,~

original groundmotion(b) couldbe reconstitutedbysummingarithmetically,point by point,tracef andthe total amplitude.During eachroundof stripping,asubjectiveweighting or quality factorwasentered.Thesec~atawere thenstored,providing atableof sta- ~ ~ u <

00~~tions,phases,predictedandobservedarrival times, I- ~ o ~ ~ z z ~

86

ray parameters,observedpulsewidths,andheights enhancedability to resolvethe depth,as expected,andareasfor eachsubevent,alongwith a subjective anda betterconditionnumber.estimateof thequalityof thephase(FableII). Despite thiseffort to accuratelycalculatethe

Theremaybe somedoubtsaboutthestripping relativelocations,experiencehasshownthat theprocedureandthecharacterizationof thearrival by scatterin thepoints is largerthan might beexpected3 points. It is not inconsistentwith sourceinversion from the0.5 s readingaccuracy.Whetherthis is duestudieswith syntheticseismograms(Burdick, 1977), to bad data,poormeasurementsor inadequaciesofandsimple modelsof rupturewhich predictpara- the first-order perturbationmodelandrelativeloca-bolic-typepulses(atriangularpulsewhich is, in turn, tion technique,is neitherknownnorimportant(here).mandatedby thequality of thedata).It doeshow- Nonetheless,the solution is controlledby readingsatever precludeconsiderationof possibleovershoot a few stations.The effect of this leverageis to skeweffects(Kikuchi andFukao,1976) andcrustalcon- the results.Consequently,in the interpretationbelowtaminationof thewave train.The suddencessationof lesssignificanceis given to the absolutelocationsenergyfollowing the pulsearrivalsprovidessomejus- (savefor the depthvariation,which is less question-tification for discountingtheeffectsof crustalcon- able)than to therelativemechanisms,which aretamination. seeminglymorerobust.

Thereareseveralpossiblesourcesof error in theinversionsfor location andmechanism.Onemajor 3.2. Mechanismsfactor is possiblelateralheterogeneity,especiallynear Usingthevaluesfor theareaandheight of thethe source.Althoughit is commonpractice(Engdahl pulsefoundin the strippingprocedure,the sourceet a!., 1977)to neglecttheeffectsofheterogeneityfor mechanismsweredeterminedby aninversionfor theeventsin the lowermostslab,despitesomeevidence elementsof the momenttensor.Following Strelitzthat the slab doespersistbelowtheseismicallyactive (1978), the inversionswere performedfor thegeneralzonenear650 km (Jordan,1977),onecannotsimi- triple couplewithout volumechange,and for thelarly ignore thepossibilityof near-sourcecontamina- ordinarydouble-couplesolution,againwithouttion for upwardrays(pP).Thusrelativedatawere volume change.Insteadof absoluteamplitudesorusedwhereverpossible,comparingmeasureddatato a areas,it was foundpossibleto userelativevaluesin alocal reference,as opposedto a standardEarth manneranalogousto thatembodiedin relativeloca-model.For thelocationproblem,this is awell estab- tion schemes.fishedprocedure,but for sourcemechanismstudies,it Thebasisfor this procedurelies in thetreatmentis a novelandlesscertaintechnique.Detailsof these of theseismogram[a(r, w)] asaproductof simple

procedureswill be givenbelow, Section3. filters (Ben Menahemet a!., 1965)correspondingtotheeffectsof thecrustHCR(W), geometricspreadingG(i~),attenuationHQ(w),orientation,magnitudeand

3. Calculations effectof sourcefIniteness,H5(P, w), andthe record-3 1 Relativelocations ing instrument [HINS(w)] or otherdetailsof interest.

In the frequencydomain,the termsexcludingthe

Epicentrallocationswerecalculatedusinga variety sourcecanbe combinedinto a simple factorof datasubsetsto testthe leverageat someof the [c(~, w)], andin thetime domain,especiallyfor longpartitionsof thewhole set.Themethodusedwasthe periodsor zero frequency(the so-calledscalarmo-standardTaylorexpansion(Bolt, 1960).Minor varia- ment),a similarcontractionof termsis possibletionsto accommodateindirect phasessuchaspPwere a(r, ~o)= HINS(w) ‘Hç~(~)‘HcR(C~))included.Also, in orderto removesomeof thedepthof focusvs. origin timetrade-off, thedataset ‘G(~) ‘HsQ~,~.‘) (1)includedpP—Ptimes.Theselatterpointswere givenagreaterweight than theindividualpoints.Compari- H~(P,w) = M0 M(w): Ffr) (2)sonsof the resultsof this calculationwith thoseinwhich relativetimeswereexcludedshowedan a(r, w) = c(A, u.,) ‘Hs(#, ‘.‘) (3)

87

whereM isthemomentratetensorandF~f~is an TABLE IIIexcitationtensordefinedby Strelitz (1978). Polesof fault planesolutionsof referenceeventfor each

Thestandardprocedureis to calculateeachterm earthquakestudied.0 ismeasuredfrom vertical(00 isdown);in eq.1 separately,or neglectthem,asthesituation 0 ismeasuiedfrom north.X andYarethepolesof the greatwarrants.Exceptnearcausticsor othersimilarpatho- circleof the fault planelogic points,it shouldbe true thatc(~,w) doesnot Event X yvary muchif the recordingstationis fixed andone ______________ _______________

considersonly nearbyevents.Of course,“nearby” is o odefmedoperationallyin termsof a smoothandwellbehavedderivativeofc; anyway,theerror from a 7/31/70 58.0 58.0 32.0 —105.0changein c(~,w), dueto a smallchangein ~, should .

be lessthan theuncertaintyin calculatinganyone ofthe componentfilters basedon someidealizedandsmoothedEarthstructure.Thus,definingc in termsof a referenceeventwith a “known” source,should Certainnaivemeasuresof the robustnessof theleadto highquality results. solutionwill be discussedbelow in Section4,where

In practice,oneuseseithertheratio of peakam- thereis a moreformaldiscussionof how to calculateplitude,or the ratio of zero frequencyspectrallevel, the errorsin theorientationof theprincipal axes.from an unknowneventto that of a knownevent.As This is of interestbecauseof thepossiblelargevaria-mentionedin Section3.1.,this formalism permitsone tion of theeigenvectorsdueto relativelysmalltousedatawhich might otherwisebe discarded(such changesin thevaluesof theelements.asindirectphasesandhorizontalrecordingsof com- Consideringthat themomenttensoris onlypressivephasesanddiffractedwaves),albeitwith second-order,thereis no barrier,eitherpracticalorprogressivelylargera priori uncertainties, computational,to determiningthevarianceof the

The sole remainingquestionlies in thechoiceof a eigenvectorsusinga MonteCarlo technique.referenceevent.Forthesemultiple events,the logical If M is the solutiontensorcomposedof the ele.choiceis tousethefirst event.It is at this point that mentsdeterminedin x~or x~,it canbe decomposedthemostproblematicaspectof therelativesource into principal values:mechanismproceduresarises:namely,how doesone M = UTAU or Mu = Au (4)modelthe sourceof thereferenceevent?Giventheunderstandingthatat no point in this procedurewill whereu arethe normalizedeigenvectorsof M andA,,it be possibleto try to determinetheexistenceof an istheassociatedeigenvalue.isotropic component,becauseof the lackof coverage Usingonly thediagonaltermsof E (seeAppendix,in somequadrants,it becomesamatterof somecon- eqs.A7a,b for definition of E), one canfind a newcern thaterrorsin the referencemodel maypreclude tensorM’ with elementsm1,determinationsof certainfeaturesof interest.How-

m,.—m1/+6m1/g~ever,to permit theuseof indirectphases,honzontalcomponentsanddiffractedphases,this problemmust —

— mgJ+L~kkgkbe accepted.The sourcemodelneededasa referenceeventwas thatgivenby thevery well constrained whereEkkrefersto thevarianceof elementrn,1 andfault planesolutionsdeterminedfrom first motions is a standardrandomvariable,independentof k.(seeTableIII). Thentheeigenvectorsof this newmatrix are u1.

Resultswere calculatedfor bothrelativeexcitation The angularseparationbetweenthe perturbedandof peakamplitudeof the pulse,andfor the pulse unperturbedvaluesis givenbyarea.Forthelatter dataset,the resultsweremore 0 = cos’~(u‘u’ 7stable,althoughnot somarkedlyasto precludethe ~1 1 /useof oneform overanother.The realquestionof whereO~is the anglebetweenthe1” axis andtheinterestlies in theaccuracyof thesolution. directionof thej~I~vector. It is quite easyto calculate

88

themeanof andthusto determinethesepointson The termsof interestarethoseinsidetheexpectedtheconfidenceellipse. valueoperatorE(6mzm~mst).Expandingthesein

A problemwith this methodis that it doesnot termsof the probabilitydistributions(eq.11), it isoffer a wayto include theeffectsof thecoupling clear that only for thosetermswhereif = Ic! or if = 1kbetweentermsindicatedby the off-diagonalelements is thevaluenon-separableinto two independentof the variancetensorE (seeeq.12), or in the real integrals.Wherethe variablesare all independent,physicsof the problem. then only in thesecaseswill theexpectedvaluebe

A morerigorousderivationmay be obtainedby non-zero,becauseE(6m11)is zero.For this situation,

applyingfirst- (andif necessaryhigher)orderpertur- the expressionbecomesbationtheory. Firstly, considerthe casewherethe E(!a ~I)elementsof &M are constantordeterministic. kjRealizingthat theeigenvectorsmaybe consideredas = ~ ~u,~~m)

2/(A — A1)

2]1”2 (13)basisvactors,theperturbationof the/ eigenvector itcanbewritten in termsof alinear combinationof the However,for the caseat hand,thereare off-dia-othertwo eigenvectors(5u

1 = ak/uk).Then,the per- gonal termswhich indicatea lack of independenceorturbationof thefth eigenvectorin the directionof covariancebetweenthe terms.Forthis case,thethekth eigenvectoris (MathewsandWalker, 1964,p. expectedvalueof cross-termssuchasE(öm~J~mkl)is287. Notethatakk= 0,to first order.) in genera!non-zero.

This expressioncanbe simplified by goingto aak,= (u~. &Muk)/(Ak — A1) (8) tensornotationandthevectorproductmatrix U, in

termsof theeigenvectorsu1,I = 1, 2, 3

= ~ ~II~UflU~8?fl1p~/(X~ç— (9) ulyK= L~f~’. = UKN (14)

The statisticalcaseisattackedin the fashionof andrecognizingthat the usualvariancematrix E (eqs.Girshick(1939),althoughboththeintent andtheno- A7a, b) from the inversioncanbe consideredatationarequitedifferenthere.The quantityof inter- fourth-ordertensorwith elementsE(~3mq~mk,)=

est is theexpectedvalueof ak/I E11 . Therefore,

E(Iak/I) E[~ak, ak/)’] (10) ak/= ~ Ui~Mim/(Ak— A1) (15)

E~x)f xF~x)dx (11) E~ak/~ak/)”2

whereP~x)is thedistribution function. = — (16)By thedefinitionof the varianceof eachelement

~5mjj,P is a gaussianfunction of zeromeanandstan- = [(UKJ)TEUKJ/(Ak— A1)

2]~2 (17)darddeviationdm

11.The squaringleadsto termsofthe form ~m11 ~mk1, a fourth-ordertensorwhose21elementsare thoseof the variancematrix from the 4. Resultsinversion,includingthecouplingbetweentermsdesignatedby the off-diagonalterms.Expandingthe The earthquakesstudiedwere two largeevents,productof the sumsin eq.9 into the sumof products one in the Seaof Okhotsk(8/30/70)andtheotherinleadsto an expression Colombia(7/31/70)(seeTableI). Both eventshave

beenstudiedin detailby otherinvestigatorsusingaE(Ia,~jI) variety of methodsanddatasets.The mostsignificant

— 2 1/2 differencesin interpretationareprobablytheresult

— lm~t sI.~/t~’1/~~m1m1m&mst~~”tuc— ~‘1~ of theobservers’decisionsaboutcertain issues,most(12) importantandsubjectiveof which is thatconcerning

89

the numberof subeventsinto whichthe sourcemay thesepossibilities,thenatureof the seismicityis notbe decomposed.However,without a seismogramor as straightforwardassimplemodelsof slab dynamicsseismogramanalysisof how andwhereeacharrival indicate.was pickedandhow eachsourcewasdescribed,it is Thereis evenlessinformation aboutseismicityinnearlyimpossibleto comparethe resultsof different theColombiaregion (Fig. 2).The recordsshowthreeauthors.(Worksheetsfor eachstationandphaseused othereventsthat maybe associated,but thesedataareavailablefrom the author.) arecertainlyinsufficient to explainor indicateanyof

The Seaof Okhotskeventlies in a nestof deep- theslab dynamics.It may be significantthat all offocusactivity (Fig. 2). The patternof seismicity theseprior events(Table V) are reportedto be ofinsidetheslab is of a confusingnatureas regardsthe largemagnitude(~7).orientationof the faultplanesand to a lesserextent Both eventswerewell recordedon WWSSNtheprincipal axes(Fig. 3 andTable IV). Thereare instruments.The Seaof Okhotskeventwasin bothtwo classesof events,thosewith dip slip mechanisms locationandmagnituderangesthat favoredunim-(Fig. 3, eventsa,b, e,f) and thosewith thrustmecha- pededrecordingby a largenumberof stationswhilenismswithnearlyvertical “P” axis (eventsc, d). coveragewaspoorer for theColombiaevent.Thereseemsto be no correlationof mechanismtype Following theselectionof recordssuitablefor analy-with locationoreventdepth,althoughbothhave sis,andtheir digitization anddeconvolution,recordstrikessuggestiveof thetrenchorientation.Thevaria- sectionsbasedon bothazimuthanddistanceweretion maybe due to chance,or differencesin the loca- usedto correlatearrivalsandto determinethe num-tion within theslab (upperor lowerpart,or proxim- berof subeventsthat mostplausiblycharacterizedtheity to a bendor tear)or couldbe the resultof the arrivals.Forthe Okhotskevent,four distincteventsdatasetsavailableto the different observers.Despite werechosen,while eight were chosenfor theColom-

biaevent.Thereis muchgreateruncertaintyin thislatternumber,andbecausetheidentificationof eacharrival dominatesthelatteranalysis,oneshouldbe

~ I4~. ~ ~O•E awareof the potential for errors.~ ,~~ 60°N Locationsof the subeventsarelistedin TableVI

andshownprojectedon the focalspherein Fig. 4.~ The focalmechanismsare thoseobtainedby first-

°“~ \‘~‘ motion studies,andwere corroboratedby those~ST~

S5.W$0° —7r~~N

4Of~ ..J~ - ~) ~*~0

I ( L1—~.

~ ~..‘ I3O~- - ~ - 30

______ -t--P - 4 DEPTH OP FOCUS

ZO.NL4 - ~-~2O°N

I3c$E 14ø• 150 I6O~E ____j — .±_____ 10•3

Fig. 2. Left: mapof seismicityin the Seaof Okhotskregiontakenfrom USCGSmap. Right: map of deepseismicityneartheColombianevent.

90

N N seemto indicatethat theeventscanbe confidentlya 9/1/55 d placednear thesolutionlisted.Forthemost part,subeventlocationsfor both

earthquakesare in the lowerhalfplane,implying rup-500km

ture downwards.Forthe Okhotskevent,the evidencepointsto rupturebeing into theslab,if it is assumed

560km —““ that thefirst eventoccursin the upperedgeof theslab,aspredictedby theoreticalmodelsof subducting

N N platerheologies(Toksozet a!., 1973).For the South

~y50km

a slab,althoughthe motionis morehorizontaltowardsb 7/22/59 ~ Americanevent,thereis almostno informationabout

T otheractivenests.Without a firm knowledgeof theorientationof the presumedslab, for example,whetherit is dipping andintact but seismicallyinac-tive for much of its length andbreadth,orwhetherit580 kmis detachedand falling, it is difficult to speculate

N N further on therelevanceof the locations.It shouldbe

~ 645 km 1/29/71 pointedout that thedirectionof the subeventsistowardsthe next zoneof deepseismicactivity to thesouthin thePeru—Boliviaregion(fig.2). Indeed,con-

C 8/30/70sideringthe separationbetweenthe first and lastevents(‘-‘lOO km), it is notunreasonableto considersucha connection.Otherstudies,suchas the520 km

Fig. 3. Faultplanesolutions(shownin thestandardlower Dopplershift phasework of Mendiguren(1972)havealso led to theconclusionthat rupturepropagated(or

halfsphereprojection)for somelargeeventsin the SeaofOkhotsk.Lettersin the upperright-handcornerof eachdia- moreconservatively,that seismicactivity migrated)gramreferto eventsnotedin TableIV. southeastwardtowardsthePeru—Bolivianest.

More importantthanthe locationsin under-standingthe relationshipbetweentheseismicityandthe dynamicsof the slab,arethe sourcemechanisms

determinedby a constrainedmomenttensorinver- of thecomponentevents.Solutionswere determinedsion. Thesimilarity betweenthe first-motionand for two cases:sourcemodelsáorrespondingto apulse-amplitudeandpulse-areamomenttensorsolu- double couple;andonecorrespondingto a generaltionsfavoredthe useof theseeventsasreferencesfor deformationwithout volume change.It may seemmechanismstudies, odd to limit theresultsto this set of alternatives,con-

While thereis no precisecoincidenceof locations sideringthat interestin non-standardsourcemecha-of subeventsand fault planesfor the first event,there nismscenterson isotropic sources,especiallyfor theis a suggestiveclusteringof locationsin one quadrant. Colombiaevent.However,if phasechangeswereim-Theseresultsare compatiblewith thoseof Furumoto plicatedin thatevent,then thereis no goodreason(1977)who alsostudiedtheseevents.The apparent why volumechangesshouldnot accompanyotherrupturetime (which is definedasthequotientof the largedeep-focusevents.Thechoiceof possibledistancebetweentwo events,andthedifferencein modelswas madeon the basisof the natureof theorigin times)is well within theboundscommonly data:all thedataare from Pphases,andnotmoreacceptedforplausible rupturevelocitiesless than v5, than 5% of theseare of a non-compressivetype.Withthe shearvelocity.Oneproblemis that the locations that asa constraint,it wasimpossibleto meaningfullyarein thosesectorswhich havethemost sparsecover- determineanyisotropic component.age,a failure commonto somelocation algorithms Residualsfor eachdataset from eachmodel typeusingnoisy data.However,the errorlimits would were comparedaccordingto the statisticsthatdeter-

91

TABLE IV

List of large(M ~ 5.5)earthquakesin the SeaofOkhotsk.Dataarefrom theEnvironmentalDataCenterEpicenterTape.Thoseeventsdesignatedwith a letter in thefirst columnarethosewhosefault planesolutionsareshown in Fig. 3

Date Time Latitude Longitude Depth Magnitude(Mb)(°) (°) (km)

8/14/22 1141 : 13.0 53.000N 150.000E 530 6.805/28/24 951:59.0 48.000N 146.000E 500 7.001/ 1/28 1843 : 27.0 53.000N 15 1.000 E 530 6.504/22/28 455 : 1.0 47.500N 145.000E 350 6.505/ 8/28 446 : 2.0 50.5 00 N 149.500E 570 6.508/23/28 117 : 53.0 50.000N 147.000E 620 6.253/10/30 1627: 26.0 50.000N 149.000E 620 6.506/ 3/30 1809 : 28.0 50.500N 149.000E 650 6.252/23/31 215 : 2.0 50.000N 148.000E 600 6.008/ 2/31 2329 : 45.0 5 1.500N 15 1.500E 400 6.50

10/25/32 1702:12.0 46.750N 144.000E 410 6.5011/ 6/32 1247:53.0 51.000N 150.000E 520 6.001/18/33 1715 : 1.0 51.000N 149.000E 570 6.505/24/33 435 : 48.0 47.500N 145.500E 420 6.00

12/ 4/33 1933:55.0 47.000N 144.000E 360 6.757/26/35 803 : 39.0 48.000N 145.500E 480 6.257/27/35 1013 : 9.0 48.750N 146.500E 490 6.25

11/11/35 1855 : 29.0 50.000N 147.000E 590 6.005/26/39 1218 : 17.0 47.000N 144.000E 420 6.005/19/40 1517:55.0 51.000N 149.000E 580 6.75

12/13/42 842: 40.0 53.000N 152.000E 530 6.002/23/50 831 : 23.0 49.200N 147.800E 477 6.00

a 9/ 1/55 2240 : 0.0 52.700N 154.900E 500 6.007/ 3/58 1248 : 4.0 48.080N 147.270 E 412 6.10

b 7/22/59 1924 :18.0 53.030N 152.840E 650 6.2511/22/66 629 : 53.1 48.000N 146.800E 452 5.70

c 8/30/70 1746 : 9.0 52.380N 15 1.597 E 645 6.60d 9/ 5/70 752 : 27.2 52.280N 15 1.490 E 560e 9/ 5/70 752 : 32.4 52.320N 151.460E 580 5.70f 1/29/71 2158 : 5,4 51.721N 150.946E 520 6.10

8/21/72 623 : 48.9 49.506N 147.036E 578 5.90

mine thebehaviorof constrainedandunconstrained consistencyof thesolutions,regardlessof whether

inversions.In no casewasthe resultfor thegeneral thedataconsistedof absoluteamplitudes,relativecasearguablysuperior.It wasencouragingto seethe moments,or anyof theother formats.Evenmore

TABLE V

Othereventsnearthesiteof the7/31/70Colombiaearthquake.Datafrom two contiguousregionsareincluded.DataarefromEnvironmentalDataCenterEpicenterTape

No. Date Colombia Latitude Longitude Depth Region Magnitudetime (°) (°) (km)

1 4/28/11 952 : 54.0 0.00S 71.00W 600 103 7.25PAS2 12/18/21 1529:35.0 2.50S 71.00W 650 111 7.9OPAS3 1/17/22 350:33.0 2.50S 71.00W 650 111 7.60PAS

92

TABLE VI

Therelativelocationsanduncertaintiesin determinedquantitiesfor the subeventsof the Okhotsk and Colombia events. dT, doetc.refer to the formal error in theparameter

EventNo. T (s) dT 0 (°) do (°) 0 (°) dO (°) r (km) dr(km) z (km) dz (1cm) a2 (s)

Seaof Okhotsk2 2.8 0.03 20.0 0.6 31.7 25.0 3.5 0.2 3.3 0.2 0.873 5.9 0.03 29.4 0.4 33.0 9.9 8.9 0.4 7.7 0.4 0.774 8.6 0.05 36.9 4.3 110.0 8.9 7.7 0.4 6.1 0.6 1.2

Colombia2 6.1 0.27 17.6 8.9 —56.3 27.8 20.4 5.0 19.4 3.2 1.43 10.4 0.20 93.3 12.7 103.0 6.3 23.3 2.4 —1.4 2.4 1.14 21.6 0.40 105.0 3.6 123.5 2.1 85.3 3.1 —22.1 4.9 2.15 27.9 0.70 106.9 3.0 143.6 1.8 104.0 3.5 —30.3 8.3 3.56 36.9 1.0 84.6 6.7 144.8 2.6 78.5 3.6 7.3 12,1 4.07 44.0 1.0 77.8 3.8 138.3 2.6 77.7 3.8 16.4 12.2 4.08 58.5 0.80 38,2 2.6 125.6 4.1 119.8 5.6 94.2 9.4 5.8

than theconfidencelimits for eachprincipalaxis, theefficacyof themethodused.The usefulnessofwhich in mostcaseswere aslargeasthe PandT sym- this sortof analysislies not in showingthat the

bols in Fig. 5(B), this consistencyof mechanism, double-couplesourceis inadequate(which it is not),independentof dataor constraint,further indicated but ratherthat it is necessaryto considerboth mecha-

nismsandcompareresults.It is not enoughto solve

for thegeneralsolution,but in somecases,it is per-

~ missible to discardthe isotropicpartof the tensorandclaim that the remainderrepresentsthe truedouble-couplesolution. However,numericalexperi-mentswith syntheticdatahaveshownthis to be an• incorrectprocedurein somecases.In bothearthquakes,thereis a markedprogressionof mechanismfrom low-anglethrustto near-verticalfaulting astheeventsdevelop(Table VIla, b; Fig. 5).

LOCATION OF SUBEVENTS 8/30/70

N 5. Interpretation

The systematicvariationof themechanismsof

complexdeep-focusearthquakesadvocatedhere isnota new idea. Studiesof the sourceof theColombiaeventusingsurfacewaves(FurumotoandFukao,1976)and freeoscillationshavebothsuggestedsuchmotion; indeed,the “path” of thePaxisdetermined

Lower Upper by Gilbert andDziewonski(1975)is remarkablycloseLOCATION OF SUBEVENTS 7/31/70 to thatmeasuredhere,althoughthetime scalesare

somewhatdifferent (Fig. 6). In addition, theapparentFig. 4. The locations of subeventsof the Okhotskevent(top) andthe Colombiaevent(bottom).Confidenceellipses steepeningof the fault planesis akin to that observedareshownprojectedon the fault planesolution for the first for the9/5/70Seaof Okhotskearthquake(Strelitz,event. 1975).

93

B~D

w

~-2

~ 4

Fig. 5. Faultplanesolutionsasdeterminedfrom theconstrained inversionof the moment tensorusing relative pulseareadataforthe Okhotskevent(A) andthe Colombiaevent (B). Error bars are shownfor the principalaxesof all Okhotsksubevents;for theColombiaevent,they areonly shownfor thelastsubevent,becausemost of theellipsesareapproximately thesamesize.

Attemptsto link thesefindingsto thedynamicsoftheslab mustbe relegatedto thespeculativerealm,becauseof the lack of any realinformation abouttheTABLE VIInatureof the slab at thesedepths.It is assumednot

Sourcemechanismsof thesubeventsin termsof thepolesofthe nodalplanesandthe amplituderelativeto the first, refer- only thatseismicityimpliestheexistenceof the slab,enceevent butalso that suchactivity occurssolely on the upper,

coldersectionof the slab.In the two regionsof inter-Event X Y Relative esthere,thereis doubtaboutthe geometryand con-No. amplitude tinuity of theslab becauseof the patternof seismic-

0 0_________________________________________ity.a Seaof Okhotsk The existenceof metastableelasticconditions

whichculminatein largeearthquakesrequiresthree2 35.79 145.85 55.60 —63.19 0.833 40.18 101.00 58.96 —61.66 1.82 conditions:4 26.75 124.49 63.32 —56.78 1.73 (1) a sourceof stress;

b Colombia (2)rheologyableto accumulatestrain;

2 72.56 39.15 20.23 —172.42 0.51 (3)a stressrateexceedingthecreeprate.3 76.43 39.59 26.07 159.14 0.92 It is primarily dueto (2) that seismicactivity ispre-4 59.71 86.78 39.91 —47.51 2.34 cludedin boththeunperturbedmantleandthe lower5 65.88 71.83 24.15 —105.35 1.80 boundaryof theslab.However,if thestrainrateis6 72.92 71.53 19.58 —138.74 2.80 greatlyincreasedby motionon anearbyfault, for7 73.07 73.02 18.83 —133.82 2.568 89.20 54.71 15.70 147.54 1.67 example,it is not impossibleto believethat faulting

may takeplace in regionswherethe rheologyor stress

94

restof the slabasshown in Fig. 7 (2). The work of

partof theslab ismovingupwardswith respectto theFukao(1972)on thePeru—Brazilmultiple eventcon-curswith this interpretation.Also, if oneassumes~P ~1IIIIII~ buoyancy,encountersa zoneof increasedviscosity,P thatplane fracture is occurringat eachpoint, albeit

40 on differentplanes,one is led to the conclusionthat

theslab,movingunderthe influenceof its negative

andfracturesalonganarcuateline which leadsto

~

detachment.From thetravel-timeanomalyinformation of ScS(Jordan,1977),whichwas corroboratedin partofseveralobservationsof PcPhere,it would seemthatthenow-detachedslab falls throughtheboundarylayerandis eventuallyabsorbed.Thispartof the des-cent takesplacewithout seismicactivity, becauseof aprobablelack of sourcestressin the detachedpiece.This is not to saythat theslab is stressfree, butFig. 6. Motion of the principalaxesof the moment tensor forrather,that thestrain rateis well within thecreep

the Colombianevent. (A) Inversion basedon absolutemoments.Eventusfirst arrival(T = 0); event3 is at T = regime.10.4 s;5 is atT= 27.9 s; 7 is at T = 44.0s. (B) Inversion Otherpointsof significancein thishypothesisbasedonrelativemoments.Event8 isnot shownbecauseitfailed to converge.(C) Solutionof Gilbert andDziewonski(1975),basedon freeoscillations.Numbersbesideeachpointreferto time (s) relativeto first P wavearrival.

SLAB

activity. Consequently,in thecaseat hand,thereis DISCONTINUITY

field would otherwisehindernucleationof seismicno reasonto limit theregionof activity to a cold and _________________brittle upperlayer.

It could similarly be arguedthat thefractureneednotbe limited to the slab andmay extendto thenearbymantle,althoughevidencefor this is certainlylacking. Finally, the locationof the secondaryeventsindicatesthat, if thefirst eventis locatedin theupper ___________________surface,then the secondaryeventsoccurwithin theslab,regardlessof whethertheslab hasthesamedipangleasthe sectionsaboveit, or a near-verticalface. 2//

The nextpartof the problemconcernstheorienta-tion of theprincipalcompressivestress,which variesfrom verticalto an anglewhich pointsup the slab.This observationis morecertainfor theOkhotsk Fig. 7. Schematicrepresentationofthe processesthat seem

event— the structureof the slab in northernSouth to occur in the lowermostportion of the slab. (1) showsthe

Americais muchmoreproblematic.Identificationof patternof seismicityin slaband possiblefracture of slab. (2)showsdetachedslabfalling independentlyof upper portion.

the fault plane(asopposedto the auxiiary)withthe Jaggedline in both diagrams representsthe 650 km discon-planemostcloselyassociatedwith thelocationof the tinuity separatingregionsof differing densitiesand viscosities

secondaries,leadsto theconclusionthat thebottom (p andv).

95

include theobservationsof Billington andIsacks unknownsrn,1. Combiningthe termsfor Ck andFk,,(1975),who notedthe existenceof faultzonesor eq.Al becomesplanesovera time-periodof severalmonthsin the —ak— CkfFiji—Tonga deepseismiczone,andan inferredbendin the slab towardsthehorizontalfrom studiesin that Fora suiteof observations,a canbewritten as a vec-regionusing theJHD method.Anotherpoint is that tor A andc asamatrix C(the designmatrix).Okhotskactivity subsequentto this major“slab- Dependingon theproblem,xcan be subjectedtosplitting” eventoccurredabovethe zoneof inferred linearconstraintsD suchthatfracture.Onepossibleexplanationfor thedifferences ~ = (A3)in modesof seismicreleasebetweenthe SeaofOkhotsk,Seaof JapanandSouthAmerica regions, whereZ containstheprescribedvaluesthat the lincarwhereearthquakesare largeandsporadic,and the combinationofunknownelementsx musttake,Fiji—Tongaregion,whichhasa muchmoreactiveand usuallyzero.Finally a weightingschemeembodiedinconsistentpatternof energyrelease,might lie in the thesquarematrix Wmay be included.ageand compositionof thematerialbeingsubducted, Following Martin (1971)we will considerthetwoandin differencesbetweentheoceanicandcontinen- casesfor theunconstrainedx~and constrainedcasestal lithosphereinto whichit is introduced.Thesedif- x~.ferenceswould be manifestedin a differencein Defining furtherbuoyancyandhencein the body forcesin the two = A — Cx~ (A4a)regimes.

andsimilarly for R~

(A4b)

6. Conclusions= (CTW~~CTWA=ff~CTWA “A5The source mechanismsof the componentevents 4. ~ a

of complex,deep-focusearthquakesmaybe studiedin detailby exploitingthelinearity of the moment x~’= x~+ (Z — cx~)T(DH~Dl)_lDH_l (A5b)tensor.Suchwork canbe of greatuse in increasingour understandingof theforcesactivein the lower- whereH is thecovariancematrix (C

7’WC).most reachesof slabs.Result,s,mainly from the study Estimatesof a~ando~aremadeas follows:of two suchevents,indicatethat thedowngomgslab 2 Tau=L

4WR~/(fl-.-p) (A6a)fracturesuponencountennga regionof increasedrigidity at about650km depth,whereit separates 2 = RTWR +/ \THI

from the restof the slab. U U — X~pj 4.Xc — Xu)14.,fl — P — 1)(A6b)

A wheren is the numberof datapoints,p is thenumberppen X of parameters(six) and1 is thenumberof constraints

Before investigatingthe problemin detail it would app eMore importantly,one canwrite down anexpres-

be appropnateto makethe following definitionsin ~ for theerrormatrixEtheinterestof notationalconsistency.Consideragaineq.3 E~= a~H” (A7a)

ak=ckM:F(Pk,l) (Al)E~= a~[H~— H~DT(DHlDT)~DH~] (A7b)

whereak is theexcitationat thektn stationof thewave type1, andM is thestandard3 X 3 symmetric In standardpractice,errorsin the ~th unknownaresecond-ordertensorwith elementsrn,,. quotedasE•,.

To simplify notation,let x bea 6 vectorof the

96

Acknowledgements greatdeepshocks.Phys.EarthPlanet. Inter., 11: 352—357.

I would like to thank F.A. Dahlenand T. Jordan Gilbert,F. andDziewonski,A., 1975. An applicationof

for their advice,R. ParkerandT. Onstottfor their normalmodetheoryto theretrievalof structuralpar-ametersandsourcemechanismsfrom seismicspectra.

assistancein locatingsomeof thereferences,andT. Phios.Trans. R. Soc.London,Ser. A, 278: 187—269.Jackson,L. Mager,andP. Davis for theirhelp in pre- Girshick,M.A., 1939.Onthe samplingtheoryof therootsof

paringthis report.Thiswork was supportedby NSR- determinantalequations.Ann. Math. Stat.,10: 203—224.EAR 75-15209AOl (atPrinceton),and by the Lunar Jordan,T.H., 1977.Lithosphericslabpenetrationinto the

lower mantlebeneaththe SeaofOkhotsk. J. Geophys.,andPlanetaryInstitutewhich is operatedby the Uni- 43: 473—496.versitiesSpaceResearchAssociationunderContract Kikuchi, M. andFukao,Y., 1976.Seismicreturnmotion.

No. NSR09-051-001with theNationalAeronautics Phys.EarthPlanet. Inter., 12: 343—349.

and SpaceAdministration.This paperconstitutesthe Koyama,J., 1978. Seismicmomentof the Vladivostokdeep

Lunarand PlanetaryInstituteContributionNo. 359 focusearthquakeof September29, 1973,deducedfrom PwavesandmantleRayleighwaves.Phys.EarthPlanet.Inter., 16: 307—3 17.

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Furumoto,M., 1977. Spatio-temporalhistory of thedeep models.Geophys.J. R. Astron.Soc., 52: 359—364.Colombiaearthquakeof 1970.Phys.Earth.Planet.Inter., Toksoz,M., Sleep,N. andSmith,A., 1973.Evolutionof the15: 1—12. downgoinglithosphereandthemechanismof deepfocus

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