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Modelling of seismic guided waves at the Dead Sea Transform
ChristianHaberland�, Amotz Agnon
�, RadwanEl-Kelani
�, Nils Maercklin
�, Issam
Qabbani�, Georg Rumpker
�, TrondRyberg
�, FrankScherbaum
�, andMichaelWeber
�
Shorttitle: GUIDED WAVESAT THE DEAD SEATRANSFORM
�GeoForschungsZentrumPotsdam,Germany
�Hebrew University, Jerusalem,Israel
�An-NajahNationalUniversity, Nablus,PalestineTerritories
�NaturalResourcesAuthority, Amman,Jordan
�Instituteof Geosciences,UniversityPotsdam,Germany
2
Abstract.
On severalrecordingsof linearseismometerarrayscrossingtheAravaFault (AF) in
theMiddle East,we seeprominentwave trainsemerging from in-fault explosionswhich
we interpretaswavesbeingguidedby a fault-zonerelatedlow-velocity layer. TheAF
is locatedin theArava Valley andis consideredtheprincipalactive fault of themainly
N-S striking DeadSeaTransformSystemin this section.Observationsof thesewave
trainsareconfinedto certainsegmentsof thereceiver linesandoccuronly for particular
shotlocations.They exhibit largeamplitudesandarealmostmonochromatic.We model
themby a 2D analyticalsolutionfor the scalarwavefield in modelswith a vertical
waveguideembeddedin 2 quarterspaces.A hybrid searchschemecombininggenetic
algorithmanda local randomsearchis employedto explorethemultimodalparameter
space.Resolutionis investigatedby synthetictests.Theobservationsareadequatelyfit
by modelswith a narrow, only 3 to 12 m wide waveguidewith S-wave velocity reduced
by 10 to 60%of thesurroundingrock. We relatethis verticallow-velocity layerwith the
damagezoneof theAF sincethelocationof receiversobservingandof shotsgenerating
theguidedwaves,respectively, matchwith thesurfacetraceof thefault. Thethicknessof
thedamagezoneof theAF, at leastat shallow depths,seemsto bemuchsmallerthanin
othermajorfault zones.Thiscouldbedueto lesstotal slip on this fault.
3
1. Introduction
In thelast few yearstheanalysisof trappedseismicwaveshasbecomea powerful
tool to studythe structureof lithosphericshearzones[e.g.,Houghet al., 1994;Li
and Leary, 1990;Li et al., 1998,1999,1994;Malin et al., 1996;Lou et al., 1997].
Similar to light beingtrappedandvery efficiently guidedby a glassfibre (owing to its
higherrefractive index), seismicwavescaughtby a low-velocity layer cantravel as
characteristicwave trainsover long distances.Due to strongvelocity contraststhey
arefrequentlyobserved in coal seams[e.g.,DresenandRuter, 1994],oil-reservoirs
[Chonet al., 1996],andalsoin tectonicallydominatedsettingssuchassubductionzones
(low-velocityoceaniccrustdescendinginto theuppermantle[Fukaoet al., 1983;Abers,
2000]). In lithosphericfault zones,thestructuraldamagezonerelatedto thedeformation
is consideredto form a low-velocity layerin whichguidedwavescandevelop.
Becausetrappedwavespropagatein theselayersfor considerableportionsof the
propagationpath,they containvaluableinformationon propertiesof thenarrow zones
itself, namelygeometry(connectivity, width, spatialorientation)andphysicalproperties
(velocitiesandattenuation).Dueto thenarrownessof thestructureson theonehand
andthe integrative characterof seismictraveltimesandattenuationon theotherhand,
this informationis usuallynot obtainedby conventionalseismicinvestigations(seismic
tomography, refraction).
The fault zoneguidedwaves(FZGW) studiesup to now includedthe pure
identificationandgeometricalmappingof waveguides,exemplarystudiesof principal
wave propagationin 2D [Ben-ZionandAki, 1990;Ben-Zion, 1998]or 3D structures
4
[Igel et al., 1997;Li andVidale, 1996;Huanget al., 1995; Igel et al., 2001;Jahnke
et al., 2002],andthemodellingof observedtrappedwaveforms[e.g.Li et al., 2000].For
theanalysisbothearthquakesandexplosions[Li et al., 1997b,1998,1999]areusedas
sources.
Most quantitative studiesattemptto derive subsurfacemodelsby waveformor
dispersioncurve matchingof guidedwave observationswith syntheticdata.Many of
themsearchthemodelspacesystematically, andsomestudiesquantify thegoodness-
of-fit of themodelsandpresentequivalentmodels[e.g.Penget al., 2000]. In orderto
accountfor thecomplex influenceof certainparameterson theappearanceof guided
waves,Michaeland Ben-Zion[1998b] proposedthe useof geneticalgorithm(GA)
to searchthe large parameterspace.GA is a very robust global searchalgorithm
[e.g. Goldberg, 1989] that proved to be useful in waveform fitting [Sambridge and
Drijkoningen, 1992;SenandStoffa, 1992;LomaxandSnieder, 1995;Levin andPark,
1997].
In this studywe presentdataof explosiongeneratedhigh-frequency guidedwaves
at theDeadSeaTransform(DST),a 1000km long,prominentshearzonein theMiddle
Eastexhibiting a total slip of � 100 km during the last 20 Myr. Theanalysisis part
of the interdisciplinaryresearcheffort DESERT (Dead Sea Rift Transect)in which
severalgeophysicalmethods(reflectionandrefractionseismics,gravimetry, magnetics,
electromagnetics)togetherwith geologicalstudiesandmodellingaim to resolve the
structureanddynamicsof thetransformat differentscales.Backboneof thestudyof the
small-scalefault structurewas2D and3D controlledsourcehigh-resolutiontomography
andreflectionseismics.In orderto derive subsurfacemodelsthat bestexplain the
5
observations,we modeltheguidedwavesby ananalyticalsolution[Ben-ZionandAki,
1990]andsearchthemodelspaceusinga hybrid schemecombiningGA anda local
randomsearch.
2. Geological setting
TheSSW-NNE striking DST separatestheArabianplatefrom theSinaimicroplate
(seeFigure1). It stretchesfor approximately1000km from theRedSeaRift to the
Taurus-Zagroscollision zone.Formedin theMioceneandrelatedto thebrake up of the
Afro-Arabiancontinentit accommodatesthelateralmovementbetweenthetwo plates.
The total amountof left-lateraldisplacementis � 100 km, recentrelative motion is
between3 and4 mm yr � � [Klinger etal., 2000]. Figure 1.
BetweentheGulf of Aqaba/EilatandtheDeadSea,thesinistralstrike-slipArava
Fault (AF) constitutesthemajorbranchof theDST [Atallah, 1992;Garfunkel et al.,
1981], taking mostof the slip. In the centralArava Valley the (straight)fault trace
(striking 15 - 20�E) is outlinedby scarps,pressureridges,small rhombgrabens,and
waterholes.Recentactivity is indicatedby offsetgulliesandalluvial fans[Klinger etal.,
2000]. Four stronghistoricearthquakesreportedlyhit theAF: 1068A.D., 1212A.D.,
1293A.D., and1458A.D. [Ambraseyset al., 1994;Amit et al., 2002;Klinger et al.,
2000].Theseeventswerecorroboratedin sedimentaryrecords[Ken-Tor etal., 2001].By
contrast,thecurrentseismicactivity alongthesouthernsectionof theDST is rathersmall
[Salamonet al., 1996].Theregion eastof theAF is segmentedinto numerousblocksby
additional(W-E andNW-SEstriking) faults(someof themnormalfaults). In thestudy
area,Neogenemarl, Cretaceouslimestone,andMioceneconglomerates(in thenorth
6
Precambriangraniteoutcrops)arein partcoveredby youngalluviumandaeoliansands.
3. Data and observations
In a specificallydesignedcontrolledsourceexperimentwe deployed5 seismiclines
crossingtheAF at about30�30’N (seeFigure1). Theroughlywest-eaststriking lines
1, 2 and3, which wereapproximately5 km apart,hadlengthsof about9 km. Spacing
betweenthe4.5 Hz geophonegroups(SM-6, verticalcomponent)on lines1, 2, and3
was100m. On theselong linessignalswererecordedby a SUMMIT datalogger(line 1,
250samplespersecond)andPDAS-100dataloggers(lines2 and3, 200Hz persecond).
Lines4 and5 wereshorter(ca. 200m) andhadreceiver spacingsof 10 m. They were
equippedwith REFTEK dataloggersrunningwith 200samplesper secondandwith
Mark L4-C-3D 1 Hz threecomponentseismometers[DESERTTeam, 2000;Maercklin
et al., 2000].
The fault traceis clearly visible in satelliteimagesover long portions,andit
is feasibleto identify it in the field at certainsegmentswith an accuracy of better
than100m. However, to enhancetheprobabilityof hitting the fault (andto generate
guidedwaves)we placed4 groupsof 3 individual shotseachat locationswherewe had
indicationsof the fault tracefrom geologicalsetting,satelliteimages,or topography.
Distancebetweenshotswithin a groupwasbetween20 and50 m. At eachshotpoint
45 kg of chemicalexplosivesweredetonatedin 20 m deepboreholes.Dueto theuseof
differentialGPS,all positionsandheightsof shotsandreceiverscouldbedetermined
with anaccuracy of � 1 m.
Weobserveprominenthigh-amplitude,high-frequency wave trainson receiver lines
7
2, 3, 4, and5 for two shots,101and102. Theobservationson line 4 and5 areshown
in�
Figure2. They arebestdevelopedon line 4 for shots101and102,andon line 5 for
shot101. In generaltheobservationsshow a seriesof characteristics,giving evidenceof
beingguidedwaves.Thesewavesoccuronly at certainreceiversfor certainshots.The
correspondingreceiversareconfinedto narrow sectionsof thelines(for positionsrefer
to Figure1 andTables1 and2). Shots101and102andtheobservingreceiverson line 4
andline 5 match(within thegivenaccuracy of independentgeologicalinformation)with
thesurfacetraceof theAF. All othershotsdid notgeneratesuchphases.As indicatedby
barsin Figure2 theguidedwavesshow very high amplitudes,which areup to 10 times
larger thanthesignalsat similar timeson otherreceivers.Offsetsbetweensourcesand
receiverswere2.3 (line 4) and1.1 km (line 5). Guidedwavesobservedat line 5 show
higherfrequenciesandashorterduration(ca.0.2s insteadof 0.3s)ason line 4, which is
expectedfor shorteroffsets. Table 1.
Table 2.
Figure 2.Comparedto otherreportedFZGW theguidedwavesat theAF show ratherhigh
frequencies(between20 and50 Hz). However, thedominantfrequenciesarecontrolled
by thegeometryandphysicalproperties,andsimilar high-frequency guidedwavesare
known for examplefrom coalseams[e.g.DresenandRuter, 1994]. As clearlyvisible
in thetime series,thewave trainsherearealmostmonochromatic.Lines4 and5 were
equippedwith 3 componentsensorswhich allowedthedeterminationof thepolarization.
Thephasesareverticallypolarized,thusonly verticalcomponentdatais shown in Figure
2. This factsuggeststhatthesephasesareLove-typechannelwavesasdescribede.g. in
DresenandRuter [1994].
8
4. Modelling and Inversion
Although influencedby many factors,guidedwavesareprimarily controlledby
a 2D structure:a waveguideof ’some’extentwith a reducedseismicvelocity, anda
sourcewithin or closeto thewaveguide.Factorsinfluencingdevelopmentandshapeof
guidedwavesaretheamountof velocity reductionwithin thewaveguide,thewidth of
thewaveguide,attenuation,andthepropagationlength.Furthermore,thedevelopmentof
guidedwavesdependson thepositionof theseismicsourcewithin thewaveguide.3D
variationsof the2D waveguidestructure,which mayconcernthewaveguidegeometry
(flexure,branching,bending,interruption,shape,heterogeneities)aswell asphysical
propertiesof bothhostrock andwaveguide(velocity, gradients),arealsoknown to alter
theappearanceof guidedwaves[Jahnke et al., 2002;Li andVidale, 1996;Igel et al.,
1997,2001].
In additionto puremappingof thewaveguidewe intendto derive quantitatively
someof themodel-describingparametersfrom theobservedwaveforms.Accordingly,
wecalculatesyntheticseismogramsfor variousmodels,comparethemwith theobserved
waveformsandinfer themostprobablemodelfrom thebestfitting dataset. Bearing
in mind well-known trade-offs amongcertainparameters[Ben-Zion, 1998] andthe
limitation of our dataset,we restrictourselvesto 2D models.This allows theestimation
of effectiveparametersaveragedover thewholepropagationlength.
We calculatedsyntheticswith a 2D analyticalsolutionfor thepropagationof waves
generatedby a � line sourcein a single layer �� �� which is embeddedwithin
two quarterspaces�� �� and �� �� [Ben-ZionandAki, 1990;Ben-Zion, 1998]. The
9
modelsaredefinedby thewidth of thewaveguide � andseismicvelocities ��� , seismic
attenuationfactors � � ���� � anddensity � of all threelayers. Sincewe intendto model
Love-type(shear)guidedwaves, � � areshearvelocities(i.e., � ��� � ). As in Ben-Zion
[1998] attenuationwasincorporatedfollowing Aki andRichards [1980]. Thereceiver
canbeplacedanywherein themodel,andthesourceanywherewithin thesinglelayer.
Thechosendepthof thesourceis usedasa proxy for theoverall propagationlength.
Syntheticvelocity seismogramswereband-passfiltered(1 or 4.5 to 90 Hz, respectively)
accordingto instrumentresponseandsamplingrate.
Thegoodness-of-fitbetweenobservedandsyntheticwaveformswasestimatedby
usingtheweightedmeanof thesemblance[NeidellandTaner, 1971]of windowsof 0.4s
containingtheprospective guidedwave train of eachobservedandsynthetictracepair
(for a givenparametercombination).We invertedsimultaneouslyfor up to 11 tracesof
a shotgather. Theuseof semblanceandthe inversionfor many tracessimultaneously
considerthedistribution of guidedwave energy acrossthewaveguideandin thehost
rock (leaking)asa majorattributeof theobservations(in additionto theamplitudeand
frequency behaviour of thewaveforms),thusstabilizingtheinversion.SeeAppendixA
for detailsof theappliedobjective function.
To efficiently searchthis multimodalparameterspaceandto derive anacceptable
model(or models)we employ a geneticalgorithm(GA). Imitating biologicalevolution,
GA is considereda sturdyoptimizationtechniquewith thepotentialof finding global
extremaandto follow-up multiple maxima[e.g. Goldberg, 1989]. It proved very
successfulin many optimizationproblems[e.g.Carroll, 1996;GibsonandCharbonneau,
1998],especiallyin seismic(waveform)inversion[SambridgeandDrijkoningen, 1992;
10
SenandStoffa, 1992;LomaxandSnieder, 1995;Levin andPark, 1997].SeeAppendixB
for!
detailsof basicGA.
As in othergeophysicalapplications(with noisepresent)we areinterestedin
(ideally: all) modelsequallywell explainingthedata(within a givenaccuracy), which
would allow thespecificationof valid parameterbounds.Accordingly, we tunedtheGA
for a broadsamplingof theparameterspaceratherthanfor fastconvergence:we used
a largepopulationsizeof 50, appliedniching(by phenotypesharing)[seefor example
Goldberg, 1989]andturnedoff theforcedreproductionof thebestmodel(no elitism).
Furthermore,we combinedGA andconsecutive local randomsearchesaroundthebest
individualsof eachgenerationforming a hybrid scheme.Thepurposeof this phenotype
manipulationis two fold: Assumingoptimain theobjective functionstretchingover
severalneighboringparameterbins,thereis a goodchanceof finding bettermodelsin
thedirectvicinity of analreadyspottedgoodmodel. Thesecondbenefitconcernsthe
enhancedexplorationof regionswith large(however, potentiallysub-optimal)valuesof
theobjective function(i.e. well fitting models).In eachgenerationwetestfour randomly
chosenmodels(that is 8% of thepopulation)in thevicinity (within a region of 5% of
theallowedparameterbounds)of 10%of thebestfitting models,subsequentlyreplacing
less-fittingindividualswith betterones.
5. Resolution
In orderto studytheperformanceof thesearchandto exploretheresolutionof the
obtainedmodelswe conductedsynthetictests.Dataweregeneratedfor thesamesource
andreceiver geometry(samestationspacingetc.) asin our experiment,andparameter
11
settingsasshown in Table3. We addedrandomtime shiftsof at most " 0.005s and
random# noise(maximumsignal-to-noiseratio of 5) to thesynthetics,which we then
invertedin thesamewayastherealdata.Synthetictimeseriesareshown in Figure3. Table 3.
Figure 3.We invertedfor 4 freeparameters:waveguidewidth � , velocity ratio � ��� �%$ � ��� � , host
rock velocities � �&� � and � �&� � (which we setidenticalexceptfor a smallperturbationto
avoid unrealisticsymmetryeffectsin thesynthetics)andanoverall attenuationfactor
( �'� �� (� � �� �� � �� (� � �� ). The lateralsourcepositionwassetfix to oneinterface
betweenwaveguideandhostrock. Furthermore,thepositionof thereceiver observing
thelargestguidedwaveamplitudewasfixedto thecentreof thewaveguide.
Figure4 A - D shows valuesof thefitting function( ) ) of all in theGA run tested
modelsasa functionof thefour freeparameters.In our implementationof GA search
we ran 300 generations(approximately15,000testedmodels)until we achieved a
satisfactoryfit andabroadsamplingof theparameterspace.As expected,theGA search
revealsasuiteof modelswith anacceptablefit ( )+*-,/.1032 ). Thebesttestedmodelreaches
)4 +,/.1065 , which is thesamevalueasthevalueassociatedwith theoriginal synthetic
model(however, it is not thesamemodel).Thedistributionof acceptableF-valuesgives
estimateson the resolutionof the particularparameter. The thresholdof acceptable
F-valueswasdeterminedby visual inspectionof the fit for somemodels. Table3
summarizestheserangesof theindividualparametersandthebestretrievedmodel.The
parameterof thesyntheticinput model(blackstarsin Figure4 A-E) plot well within
theseallowed-parameterlimits indicatingthat thesyntheticmodelis well recovered.
However, for particularparameters(i.e. � �&� �%$ � ��� � or � � �� ) theselimits areratherlarge
suggestingassociatedlow resolutionand/orstrongtrade-offs. Largestsemblancevalues
12
of individual tracesreach� 7,/.8539 . Figure 4.
An alternative representationof theacceptablemodelsanda crossplotshowing all
well fitting modelsasa functionof � and � ��� �%$ � ��� � , unveils a strongtrade-off between
thesetwo parameters(Figure4 E andF). Thewaveformscanbeequallywell fitted by
certainmodelswith narrow waveguidesandlargevelocitycontrastsor wider waveguides
andsmallervelocity contrasts.All otherparametercombinationsexhibit no such
dependenciesbut ratherrandomscatterin our synthetictest. Independentconstraining
informationononeof thesetwo parameters(for examplefrom independentseismological
or geologicalstudies)coulddrasticallyreduceambiguities.It is noteworthy thatgentle
variationsof � imply (petrophysically)significantvariationsof � �&� �%$ � ��� � .In therecoverytestpresentedaboveweinvertedfor four freeparameters,andseveral
parameterswerenot consideredin theinversion.Furthertestswith anindividual �'� �� of
thewaveguide(both in thesyntheticmodelandasa free inversionparameter)showed
thatthis parameteris not resolved(for thegeneralmodelandobservationgeometryused
in our test). For syntheticmodelsexhibiting anelevatedwaveguide-� � �� (what is for
examplediscussedfor damagezonesof faults)theGA searchfoundevenwell fitting
modelswith reducedwaveguide-�'� �� .
Furthermore,thelateralsourceposition :<; within thewaveguide,which generally
influencestheshapeanddevelopmentof guidedwaves,wasnot includedin thesearch.
Sourcesoffsetfrom thewaveguideinterfaceresultin generallylesstrappedwaveenergy
andproducea characteristichigh-frequency phasesuperposedon the low-frequency
guidedwave mode[Ben-Zion, 1998,Figure5 (left)]. Sincethelatter is not observedin
theseismogramswe skippedthis parameterin the inversion,reducingcomputational
13
burdenandavoiding furtherambiguities.
6. Results
Basedon theexperiencewith thesyntheticdataset,we invertedtheobserveddata
for thesame4 parameters.Figures5 through7 show thebestfitting modelsthatresulted
from theGA searchesof datafrom shots101and102observedalongreceiver line 4,
andfrom shot101observedalongreceiver line 5. Dueto weaksignal,dataof shot102
observedon line 5 werenotassessedquantitatively. Figure 5.
Figure 6.
Figure 7.
The bestmodelsreachfitting valuesaround )= >,/.@?62 . However, singletraces
reachfrequentlymuchhighersemblancevalues( A�B,C.10D2 ). Table4 summarizesall
derivedparametersandpermittedparameterlimits. Theestimateof accuracy wasderived
from thedistribution of all modelswith F-valueslarger than98%of the ) -valueof the
bestmodel.Remarkableis thenarrow waveguidewidth of between3 and30 m, which
appearsto bewell resolved. Thedensityplot (Figure8) shows thatmostwell fitting
models(for observationson line 4) arecharacterizedby a4 to 6 m widewaveguide.Very
similar to thesynthetictest,we noticea pronouncedtrade-off between� and � ��� �E$ � �&� �(Figures5 through7 E). Althoughlessresolved, � � is for all measurementslarger than
50. Table 4.
Figure 8.Theresultsof bothshotsfor line 4 andalsobetweenthetwo linesareveryconsistent.
For shot102many goodmodelswith a larger � ��� � above1800m/sareobserved.For the
observationsalongline 5 we derivea slightly smaller � ��� � which wouldbein accordance
with thesmallersource-receiver offsetand,in turn,a smallerpenetrationdepth(smaller
velocities). It seemsthat the observationson line 5 arebetterexplainedby smaller
14
velocitycontrasts(above0.6).Nevertheless,weshouldkeepin mind thattheobservation
alongline 5 have only poorsignal-to-noiseratio. Figure9 shows thesynthetictraces
calculatedwith arbitrary”best” modelsoverlaidon theobserved time seriesof shots
101and102observedat line 4, andof shot101observedat line 5, showing thegood
agreementbetweenobservationsandsynthetics. Figure 9.
Our syntheticsarecalculatedfor a � linesource.In orderto checkthewarrantyof
this assumptionwe appliedanapproximate2D to 3D transformationto thesynthetics
for someof theinversionsby convolving thetime serieswith � $GF H with H beingthetime
[Vidale et al., 1985;Igel et al., 2001;Ben-Zionet al., 2002]. However, we noteonly
minor changesin thewell fitting modelsandtheestimatesof valid parameterranges.
On line 3 we observedsimilar high-frequency wavetrains(not shown) for shots101
and102on a ratherbroad( �JID,6,LK ) receiver line segmentslightly offset from theAF
(seeFigure1). Theseobservationsaremostlikely associatedwith a SW-NE running
fault branch.However, we couldnot modeltheseobservationssatisfactorily with 2D
analyticalsynthetics.In principal, variationsof our simplemodelgeometrysuchas
low-velocity layerson top of a verticalwaveguideor wideningof thewaveguidetoward
thesurfacecouldexplain a spatiallybroaderradiationof high-frequency guidedwave
energy (generalstudiesof theseeffectsarediscussedin Jahnke et al. [2002], Igel et al.
[2001], Igel et al. [1997], andLi andVidale [1996]). In fact,shallow high resolution
tomographicimagesof the studyarearevealeda numberof superficiallow-velocity
featuresassociatedwith sanddunesandmarl [Maercklin et al., 2000]. However, the
requirednumerical(3D) modellingof theseobservationsis beyond the scopeof the
presentpaperandwill bepartof futureresearch.
15
7. Discussion
We interpretthehigh-energy latearrivals in our seismicrecordingsaswavesthat
have beentrappedin a sub-vertical low-velocity channelassociatedwith theAF. The
strongestargumentsupportingthis interpretationis thefactthatwe observe thesewaves
only at distinct receivers,andthat thesewavesaregeneratedonly by certainsources.
Sowe canrule out puresourceor receiver siteeffectsasvalid explanations.Recently,
Rovelli et al. [2002] andBen-Zionet al. [2002] reportedon shallow low-velocity
structures(maybebetterreferredto asreceiver sitestructures)insteadof deepcoherent
waveguideswhich canefficiently trapseismicwaves.
Thefact,thatmostpositionsof thesourcesandreceiversgeneratingandobserving
guidedwaves,respectively, matchwith the surfacetraceof theAF, suggest,that the
waveguideis formedby the damagezoneof the fault. Studieson exhumedfaults
discriminatethreemajorentitieswithin themesoscopicstructureof brittle strike-slip
faults[e.g.Chesteret al., 1993;SchulzandEvans, 2000]: the (undeformed)protolith
(host-rock),thedamagezone,andthefaultcore.Thefaultcore(centimetresto decimetres
thick) with highly deformedrock is theplacewheremostof theslip is accommodated.
Thedamagezonesurroundingthecoreconsistsof anincreasedconcentrationof faults,
fissuresandveins. Largefault zonesmight form a complex network of faultsof many
sizes[WallaceandMorris, 1986].
It waspossibleto modelmostof theobservationsquantitatively. The inversion
especiallyof thesehigh-frequency phasesis highly non-uniqueandcanonly beapplied
undercertain(restrictive) assumptions(seediscussionon constraintsabove). The
16
uppermostvelocity structure(weatheringlayeretc.) cancauseseveredistortionsof the
highM
frequency waveforms,which cannotbeaccountedfor by our simple2D models.
This holdsalsofor general3D variationswhich couldbiasbothour estimatesof thebest
fitting modelsandof theacceptableranges.Moreover, wenotethattheobjectivefunction
asrevealedby thesystematicGA searchis characterizedby many broadandnarrow
local maximaof similar amplitudeandcomplex shape[seealsoMichaelandBen-Zion,
1998a].This meansthattheobserved(noisy)datacanbealmostequallywell explained
by many differentmodels[seee.g.MichaelandBen-Zion, 1998a]thusyielding in part
quitelargeconfidencelimits of certainparameters.Webelievethattheseambiguitiesand
limits arestronglydependentontheexperimentgeometry, predominantfrequencies,used
frequency band,etc. in relationto thewaveguidegeometryandproperties.Nevertheless,
theparametersearchesgavea narrow effective waveguidewidth of about3 to 30 m (for
theobservationson line 4). We favour a very narrow waveguide(3 to 12 m) sincein
theaccompanying high-resolutioncontrolledsourcetomographyexperimentwe found
no evidencefor a wider subverticallow-velocity structureat shallow depth.Moreover,
trappingefficiency is strongerfor largervelocitycontrasts,andtheseare,accordingto the
trade-off curves(Figures5 to 7 E), allowedfor narrow waveguides.Finally, thesearches
of all independentmeasurementsendedup with bestmodelsfeaturing � between3 and
12 m.
The apparentnarrownessof the AF waveguide(andthe deduceddamagezone
width) putsit in markedcontrastto othermajor fault zones,at which thewaveguide
width hadbeendeducedby FZGW. For example,Li et al. [1990] andLi et al. [1997a]
reportwidthsof waveguidesof theSanAndreasfault (SAF),California,of between100
17
and170m. In theNorth AnatolianFault System,Ben-Zionet al. [2002] derivedfault
zonewidthson theorderof 100m. Thelow-velocity zoneof theNojima fault, Japan,
haswidth of 30 - 60 m [Li et al., 1998]. In general,thedamagezonethicknessseems
to beproportionalto thetotal slip alonga fault [e.g.WallaceandMorris, 1986],with a
constantof proportionalityof between�N,O� � and �P,O� � [Scholz, 1987].
Althoughthewholesystemof theDSTexperienced� 100km of cumulativerelative
movementsincethelast20Myr, thereareindicationsthatseveralsub-parallelfaultswere
active duringthattime, thusdistributing thetotal movement.Eyal et al. [1981] showed
that in easternSinai thetransformsplaysto numerousparallelstrands,someof which
hadslippedseveralkilometresandareinactivenow. They haveestimatedthathalf of the
total 100km aredistributedin easternSinai. It is conceivablethattheremaining50 km
aredistributedbetweentheactive AF andparallelstrandssuchasZofar andor Quaira
faults.At thesurfaceandin satelliteimagesseveralsub-parallellineamentsarevisible in
thestudyarea,andit is possiblethatwe might have imagedonly oneof severalstrands.
However, dueto thegivensourceandreceiver spacingcoveringa largerangeof scales
(meterto kilometre),we rule out theexistenceof low-frequency guidedwaves,and,in
turn, largerwaveguidewidthsona largerscalefor thestudyarea.
Anotherreasonfor a narrow shallow damagezonecould lie in thepeculiaritiesof
thetwo geologicalunitsatbothsidesof thestudiedAF segment.While thedeeperpartof
theeasternblock is mainly formedby PrecambriangranitesandCretaceouslimestones,
thewesternunit (down to a depthof severalkilometres)is mainly formedby sediments
of theHazevaformationandDanaconglomerates,whichwere- in partsyn-kinematically
- depositedduring theMiocene. Also the easternunit is partly coveredby layersof
18
Hazeva formationstrataandyoungersediments.However, structuraldetailsarestill not
knoQ
wn to date.Owing to thefactthatwe sampledtheuppermostpartof theAF segment
by FZGW (correspondingbodyP wavespenetrateto approximately300m depth),we
mighthave imagedthesuperficialdamagezone(severalhundredsof metersdepth)of the
AF thatexperienced- dueto youngerageof the involvedshallow geologicalunitsand
syn-depositionalfaulting- a reducedtotal slip.
Theinversionprovidesvaluesfor theeffectiveshallow hostrockshearwavevelocity
of between1740and1850m/s.They areslightly smallerfor theshort-offsetobservation
at line 5 (1570to 1780m/s). Togetherwith theobservedP wavearrival timesthis yields
a realistic � R $ � � velocity ratio of theshallow rocksof about1.8. We noticea wide range
of possiblevelocity reductionwithin thewaveguideof about10 to 60%of thevelocity
of the hostrock. We think that smallerratiosaremorerealistic,sincethe trapping
efficiency is larger for thesevalues(seealsonoteabove). Similar large valueswere
obtainedfor examplein a conventionalseismicexperimentat theexhumedSanGregorio
Fault (California),wherebrecciaandfoliatedrock form thedamagezone[Gettemyetal.,
2001]. FZGW analysisat othermajorstrike-slipfaultssuggestedvelocity reductionsin
theorderof 25 to 50%relativeto thesurroundingrock [e.g.Li etal., 1997a,1994;Li and
Vernon, 2001].Accordingly, thereducedvelocitiescouldbeinterpretedby damagedhost
rock materialwithin thefault zone.Salinewatersarepresentat thesurfacetraceof the
AF (isolatedwaterholes),andwe speculatethataqueousfluids arealsopresentat greater
depthof thefault zone.Thesefluidscouldalsocontributeto thevelocity reductionof the
waveguide. Nevertheless,magnetotelluricstudiessuggestthat thefault planeis rather
impermeablesinceit separatesdifferently resistive domainsat differentdepthlevels
19
[Ritter et al., 2001].
Thesizeof thedamagezoneis determinedby a competitionbetweenlocalization
anddelocalizationprocesses.Theformerarerelatedto thebrittle instabilityof damagable
media[Lyakhovsky et al., 1997],whereasthe lattermayberelatedto the long term
dynamicsof the fault zone[Lyakhovsky et al., 2001]. During the organizationof a
systemof faultsto form a planarfault zone,somefault strandsdominateandtake over
theslip at theexpenseof othersub-parallelstrands.If therateof healingof distributed
damageis high comparedto the loadingrate,theorganizationis slow. Furthermore,if
healingsaturatesover theperiodof a seismiccycle, theseismicityis clustered,andno
characteristicearthquakedevelops.Geologicstudiesof theDST indeedsuggestongoing
organization[Rotsteinet al., 1992]. Thehistoricalseismicityis clusteredasapparent
from the quiescencesince1458,the yearof a fourth earthquake in four centuries.
Paleoseismicstudiesindicatefurtherclusteringof activity over periodsof thousands
[Marco andAgnon, 2003] to tensof thousandsyears[Marco et al., 1996;Amit et al.,
2002]. High resolutionarchaeoseismicreconstructionof two historicaldevastating
earthquakesshow strongvariability of slip, at oddswith thecharacteristicearthquake
model[Ellenblumet al., 1998]. By contrast,theSAF shows characteristicearthquake
behaviour [SiehandJahns, 1984]thatis consistentwith low healingto loadingratio. The
SAF zonedoesnot healcompletelyon thetime scaleof theseismiccycle,andruptures
tendto repeaton thesamesmoothtrend[Wesnousky, 1994;Stirling etal., 1996].TheAF
seemsto healover thelongerseismiccycle, sothetraceis not assmooth.It remainsto
beseenwhetherthenarrow gougezoneindicatedhereis a relic of thelastearthquake,a
productof ongoingcreep,or aprecursorof thenext one.
20
Theapparentnarrownessof thedamagezonegivesevidencethat thedeformation
alongthis largestrike-slipfault is confinedto a narrow region. This is furtherevidenced
by conventionalseismicexperiments.Thesestudiesrevealedablockedvelocitystructure
beneaththestudyareashowing theAF separatinga westernlow-velocity block andan
easternhigh-velocityblock by ratherlargehorizontalgradients,andshowedindications
for reflectionsfrom sub-vertical structures[Maercklin et al., 2000]. The localized
deformationalongtheDST asimagedby this studycouldsupportthesuppositionthat
theDSThasoriginatedin (andis cuttingthrough)a relatively coldandstablecontinental
lithosphereasproposedfor exampleby DESERTTeam[2002].
We revealeda waveguidealonga 4 km segmentof theAF. We werenot successful
in observingguidedwavesat largeroffsetsandfor 9 othershotsfiredwithin theassumed
fault trace.After all, this is not surprisingwhenkeepingin mind thenarrownessof the
waveguideandthegivenaccuracy of a priori informationonthefault trace.Furthermore,
low-Q in thenarrow waveguideattenuatesthehigh-frequency wavesquickly. However,
this fact andtheslight differencesbetweentheobservationson line 4 and5 suggest
a variablestructure(positionof waveguides,continuity, etc.) alongthe studiedAF
segment.
8. Conclusions
With a specificallydesignedactiveseismicexperimentin theArava Valley, Jordan,
we wereableto recordwave trainswhich weretrappedin a sub-vertical, low-velocity
waveguide. The locationsof sourcesgeneratingandreceiversobservingtheseswaves
correspondto thesurfacetraceof theArava Fault, implying that this waveguideis the
21
damagezoneof this prominentfault.
Themodellingof theguidedwaveswith a2D analyticalsolutionin conjunctionwith
thesystematicGA searchfor thebestmodels(includingproperevaluation)provedto be
successfulin obtainingimportantgeometricalandpetrophysicalparametersof theAF.
We deriveda rathernarrow shallow waveguidewidth of between3 and12 m. Although
lessconstrained,thereductionof thewaveguidevelocity relative to thehostrockvelocity
is in therangeof between10 and60%.
Thevelocity reductionwithin thewaveguidecouldbecausedby damagedrock
materialandsaturationwith fluids which characterizethe wearzoneof this fault
accumulatedover time. Accordingto scalinglaws, the apparentnarrownessof the
damagezone(closeto thesurface)pointstowardatotalslip of severalhundredsof meters
to several tensof kilometresalongtheAF fault at theshallow depthscale.Regarding
the total DST slip of about100 km, this canbe understoodconsideringa possible
distribution of theslip on severalfaultsin time andspace(QuairaandZofar faultsetc.).
Furthermore,rockscloseto thesurfaceeastandwestof theAF might havebeenformed
syn-kinematicallyand,asa result,experiencedlessrelativeslip.
Theverynarrow low-velocitystructurerevealedby this studycouldnot bedetected
directly by otherseismicexperimentscarriedout in the samearea(reflectionand
refraction).In orderto derive someof theparametersin similar experimentswith high
accuracy, wesuggestto usea largenumberof sourcesandreceivers(in-fault,cross-fault)
andto useabroadfrequency range(e.g.,highsamplerate).
22
Appendix A: Objective function
Our fitnessfunction )TSR , which we maximizein theinversion,is calculatedfrom a
weightedmeanof individual semblancevaluesU<SR � V [NeidellandTaner, 1971]of each
observedandsynthetictracepair W ( X is numberof traces)for a givensetof model
describingparametersYZ \[ Z �%] .^._. Za`cb ( d is numberof parameters):
)TSRe fgVih � � V UaSR � V . (A1)
IndividualsemblancesUaSR � V arecalculatedfrom all samplesj within thetimewindow
of interestof observedandsynthetictraces( k V and lGSR � V , respectively) of tracepair W :
UaSR � V m1n [ok V^� nqp l Vr� SR � n b �
� m1n [s[ok V^� n b � p [tl Vr� SR � n b � b . (A2)
Semblanceis 1 if tracesarecorrelated,0.5 if uncorrelated,and0 if anti-correlated.
Theweight � V increasestheinfluenceof traceswith highsignalenergy in theinversion:
� V m n [tk Vr� n b �fm� h � m1n [tku� � n b � . (A3)
In orderto accomplishsmalldeviationsof the true3D subsurfacestructurefrom
thesimple2D modelswe allowedtime shiftsof " 1 sample( " 2 samplefor dataof
line 5/shot101)betweenneighboringsynthetictraces.Beforecalculatingtheobjective
function,we applieda uniform tracescaleaccordingto themaximalsignalamplitudein
thecorrespondingshotgather. Calculationswerealsoconductedfor reversedsignof the
syntheticamplitudes.
23
Appendix B: Genetic Algorithm
Developedby JohnH. Holland, [e.g.Holland, 1975],geneticalgorithms(GAs)
searchamultimodalparameterspacefor (global)maximaby usingmechanicsof natural
selectionandnaturalgenetics[Goldberg, 1989]. Model describingparametersof a
particularproblemarefirst codedinto binarystrings.In a standardGA, a populationof
binarystrings(that is a randomlychosensetof models)is modifiedby threeoperators,
namelyreproduction(selection),crossover andmutation. In the reproductionstep
individual stringsarecopiedto thenext generationaccordingto their objective function
valuesin a sensethathighervalueshave higherprobabilitiesto becopied. In thenext
step,offspringsarecreatedfrom this matingpool by assemblingsubstringsof parent
binarystrings.Substringscanbecut at oneor morecrossoverpositions.Finally, random
mutationsof singlebits areperformedon thepopulationwith achosen(low) probability.
This procedureis appliedthroughmany generationsyielding a broadsamplingof
the parametersetwhile revealingoneor moremaxima. Sincethe inventionof GA,
modificationsof andadditionsto this principal GA outline formedpowerful search
algorithms[e.g.Goldberg, 1989]. We useda populationsizeof 50,mutationprobability
of 0.02,a (uniform) crossover probabilityof 0.5,anda creepmutationprobabilityof
0.01.For in-depthdiscussionof GA andthesettingspleasereferto Goldberg [1989] and
Carroll [1996].
24
Acknowledgments.
For thisanalysisweuseddataof theControlledSourceArray (CSA)experimentaspartof the
DeadSeaResearchProject(DESERT, http://www.gfz-potsdam.de/pb2/pb22/projects/deadsea/ds-
home.html). DESERT wasfinancedby the DeutscheForschungsgemeinschaft(DFG), the
GeoForschungsZentrumPotsdam(GFZ) andtheMinerva Foundation.TheNaturalResources
Authority, Jordan,provided substantiallogistical support.We thankK. Abu-Ayyashfor his
efforts. Furthermorewe thanktheSiteGroup(Jordan)andChemical& Mining (Jordan)for
their efforts with drilling andexplosives. We gratefulacknowledgethework of all field groups,
in particularR. Ribhy, K.H. Jaeckel, S. Grunewald andG. Haim. Thanksto J. Mechiefor
supervisingpart of thedrilling activities, andJ. Bribachfor technicalassistance.Thanksto
YossiBartov for fruitful discussionson thegeologyaroundthestudiedDST segment.We are
indebtedto theAssociateEditorandreviewersYehudaBen-ZionandJohnVidalefor theircritical
remarksandhelpful suggestionson themanuscript.We usedinstrumentsfrom theGeophysical
InstrumentPoolPotsdam(GFZ) andtheFR Geophysics(FreeUniversityof Berlin). All figures
weremadeusingthegenericmappingtool (GMT) [WesselandSmith, 1995,1998]. Thanksto
David L. Carroll for makinghis GA codeavailable.We took advantageof theCWP/SUseismic
dataprocessingpacket [CohenandStockwell Jr., 1999].
25
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potsdam.de�A. Agnon, Instituteof EarthSciences,The Hebrew University, Jerusalem91904,
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Received-; revised-; accepted-.
To appearin theJournalof GeophysicalResearch
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33
Figure Captions
Figure 1. (left) Sketchshowing the tectonicsettingof the Middle East. (middle) Site map
of the active seismicexperimentat the Arava Fault (AF) aspart of the DeadSeaTransform
(DST).Fault trace(darkgrey line) asinferredbeneathsuperficialdeposits.Shotsaredenoted
by stars.Verticalsensorsonlines2 and3 (spacing100m) areshownby triangles,3-component
sensorsalong lines 4 and 5 (spacing10 m) are shown by squares. (right) Close-upof the
region displayedin themiddlepanel. Filled symbols(stars,triangles,andsquaresasbefore)
indicateshotsgeneratingandreceiversobservingguidedwaves,opensymbolsindicateshots
and receivers without suchgenerationor observation, respectively. Geologyadoptedfrom
Rabb’a[1994] (NL: Na’ur limestone,LM: Neogenemarl).
Figure 2. Observationson receiver line 4 (left) andline 5 (right) for thethreeshots101(top),
102 (middle), and103 (bottom). For eachgather, normalizedmaximumenergy (bars,top,
within time windows of 1.2 to 1.6 and0.6 to 0.8 s, respectively), time series(middle) and
spectra(bottom)for eachtraceareshown. Notethehigh-frequency wavetrainsfrom shots101
and102 on easterntracesof both lines between1.3 and1.6 s (line 4, left) and0.6 and0.8 s
(line5, right), but no suchphasefor shot103(andall othershots;seetext). For positionsrefer
to Figure1. Shown areunfilteredverticalcomponentdatacontainingpresumedguidedwaves.
Pwaveonsets(notshown) arriveat around0.7s (line 4, left) and0.4(line 5, right).
Figure 3. Waveformscalculatedfor syntheticmodel (for parametersrefer to Table3). We
addedrandomstaticshiftsof at most " 0.005s andrandomnoise(maximumsignal-to-noise
ratio of 5) to the synthetics.Shown areraw synthetics(thin line) andsyntheticswith noise
(thick line) whichweusedin therecovery test.
34
Figure 4. A-D: Fit of all in the GA searchtestedmodels(syntheticrecovery test)displayed
for the 4 free parameters.Grey dotsandblack crossesindicate ) ��,/.80D2 and ) *�,/.1032 ,respectively. Theparametersof thesyntheticinput modeltogetherwith its associated) value
aredenotedby black star. The dashedline marksthe ) level of the bestmodel found. E:
Cross-plotof all acceptablemodels( ) colour coded;red denotehigh values,purpledenote
low fit values)asa function of � and � ��� �E$ � ��� � illustrating thestrongtrade-off betweenthese
two parameters(syntheticrecoverytest).Thesyntheticinputmodelis representedby theblack
star. Dataweresortedaccordingto ) valueprior to plotting. F: Cross-waveguidevelocity
distribution of acceptablemodelsfor thesyntheticrecovery test. Grey (black) linesrepresent
modelswith ,/.10���)���,/.80D2 ( )�*�,C.10D2 ). Thesyntheticinput modelis representedby thered
line.
Figure 5. Searchresultsfor shot101observedat line 4. Notationsasin Figure4 exceptthat
grey dotsandblackcrossesindicate )J��,/.1560L�u)���� ��� and )+*-,/.1560��P)���� ��� , respectively.
Figure 6. Searchresultsfor shot102observedat line 4. Notationsasin Figure4 exceptthat
grey dotsandblackcrossesindicate )J��,/.1560L�u)���� ��� and )+*-,/.1560��P)���� ��� , respectively.
Figure 7. Searchresultsfor shot101observedat line 5. Notationsasin Figure4 exceptthat
grey dotsandblackcrossesindicate )J��,/.1560L�u)���� ��� and )+*-,/.1560��P)���� ��� , respectively.
Figure 8. Cross-waveguide velocity distribution of acceptablemodels( ) * ,/.1?6� ) of the
observationson line 4 (shots101and102). Dif ferentshadingindicateshow oftena particular
modelcomponentwasfound in the searches(from light to dark increasingfrequency). The
distinctblackvertical linesshow thatmostwell-fitting modelsarecharacterizedby a 4 to 6 m
wide waveguide.
35
Figure 9. Syntheticsof thebestmodels(thin line) andcorrespondingdata(thick line) of shot
101(top)and102(middle),line 4, andof shot101observedat line 5 (bottom).Observedtraces
havebeenshifted( " 1 or 2 samplesrelative to theneighboringtraces)accordingto thevalues
derivedin theinversion.
37
Table 1. Positionsof shotsgeneratingguided
waves
id latitude(� d ) longitude(
�E�) altitude(m)
s101 30.57800 35.33440 33.0
s102 30.57800 35.33311 21.7
38
Table 2. Positionsof receiver line segments
recording# guidedwaves
id latitude(� d ) longitude(
���) altitude(m)
412 30.55746 35.32787 31.0
413 30.55745 35.32798 30.9
414 30.55743 35.32808 31.3
415 30.55742 35.32818 31.4
416 30.55741 35.32828 31.6
504 30.58718 35.33677 36.3
505 30.58724 35.33669 36.7
506 30.58730 35.33660 36.7
507 30.58734 35.33652 36.9
508 30.58738 35.33638 34.2
509 30.58742 35.33629 33.8
510 30.58747 35.33621 33.2
39
Table 3. Parametersusedfor synthetictestand
searchresults
Parameter valueusedin rangeof values bestvaluefound
forwardcal- revealedby the in search
culation search
� ��� � (m/s) 1750 1710- 1775 1713
� ��� �%$ � ��� � 0.6 0.4- 0.9 0.43
� (m) 5 3 - 18 3.31
�'� �� 0.005 0 - 0.013 0.011
� (kg/m�) 2500 - -
: � at interface - -
Table 4. Parametersderivedby inversionof datarecordedalongline 4 and5. For each
parameterrangesandbestvaluesaregiven.
Parameter shot101/line4 shot102/line4 shot101/line5
range bestvalue range bestvalue range bestvalue
� ��� � (m/s) 1685- 1870 1742 1694- 1850 1847 1570- 1780 1710
� ��� �%$ � ��� � 0.4- 0.95 0.43 0.4- 0.62 0.44 0.45- 0.95 0.84
� (m) 3 - 35 3.70 4 - 7 4.47 2 - 27 6.02
�'� �� 0.005- 0.025 0.013 0.005- 0.015 0.006 0 - 0.015 0.0014
100 km 1 km 1 km
30N3430N
Taurus
35N
DS
T
SeaDead
ArabianPlate
35E
Line 5
Line 4
Line 3
30N34
Line 2
LM
35E20
Line 1
Line 3
NL
Line 5
AF
LM
35E20
S 103
S 101
S 102
SinaiPlate
SeaRed
Med
iter
ran
ean
Sea
AF
Line 2
Line 4
1.2
1.4
1.6
0
40
800 50 100 150 200
1.2
1.4
1.6
0
40
800 50 100 150 200
1.2
1.4
1.6
0
40
800 50 100 150 200
0.6
0.8
1.0
0
40
800 50 100 150 200
0.6
0.8
1.0
0
40
800 50 100 150 200
0.6
0.8
1.0
0
40
800 50 100 150 200
time
(s)
time
(s)
time
(s)
f (H
z)f (
Hz)
f (H
z)
line 4 (m) line 5 (m)
Fig. 2
shot 102shot 102
shot 103 shot 103
shot 101 shot 101
W EEW
0.70
0.75
0.80
0.85
fit
1650 1700 1750 1800v1(m/s)
A
0.70
0.75
0.80
0.85
fit
0.4 0.5 0.6 0.7 0.8 0.9 1.0v2/v1
B
0.70
0.75
0.80
0.85
fit
0.00 0.01 0.02 0.03Q1
-1
C
0.70
0.75
0.80
0.85
fit
0 10 20 30 40 50width (m)
D
0.4
0.5
0.6
0.7
0.8
0.9
1.0
v 2/v
1
0 10 20 30 40 50width (m)
E 0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0v s
(km
/s)
-20 -10 0 10 20x-fault position (m)
F
Fig. 4
0.60
0.65
0.70
0.75
0.80
fit
1650 1700 1750 1800v1(m/s)
A
0.60
0.65
0.70
0.75
0.80
fit
0.4 0.5 0.6 0.7 0.8 0.9 1.0v2/v1
B
0.60
0.65
0.70
0.75
0.80
fit
0.00 0.01 0.02 0.03Q1
-1
C
0.60
0.65
0.70
0.75
0.80
fit
0 10 20 30 40 50width (m)
D
0.4
0.5
0.6
0.7
0.8
0.9
1.0
v 2/v
1
0 10 20 30 40 50width (m)
E 0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0v s
(km
/s)
-20 -10 0 10 20x-fault position (m)
F
Fig. 5
0.60
0.65
0.70
0.75
0.80
fit
1650 1700 1750 1800v1(m/s)
A
0.60
0.65
0.70
0.75
0.80
fit
0.4 0.5 0.6 0.7 0.8 0.9 1.0v2/v1
B
0.60
0.65
0.70
0.75
0.80
fit
0.00 0.01 0.02 0.03Q1
-1
C
0.60
0.65
0.70
0.75
0.80
fit
0 10 20 30 40 50width (m)
D
0.4
0.5
0.6
0.7
0.8
0.9
1.0
v 2/v
1
0 10 20 30 40 50width (m)
E 0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0v s
(km
/s)
-20 -10 0 10 20x-fault position (m)
F
Fig. 6
0.60
0.65
0.70
0.75
0.80
fit
1550 1600 1650 1700v1(m/s)
A
0.60
0.65
0.70
0.75
0.80
fit
0.4 0.5 0.6 0.7 0.8 0.9 1.0v2/v1
B
0.60
0.65
0.70
0.75
0.80
fit
0.00 0.01 0.02 0.03Q1
-1
C
0.60
0.65
0.70
0.75
0.80
fit
0 10 20 30 40 50width (m)
D
0.4
0.5
0.6
0.7
0.8
0.9
1.0
v 2/v
1
0 10 20 30 40 50width (m)
E 0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0v s
(km
/s)
-20 -10 0 10 20x-fault position (m)
F
Fig. 7