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Adaptive mesh refinement applied to tsunami modeling: TsunaFLASH [Elektronische Ressource] / Widodo Setiyo Pranowo

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Adaptive Mesh Refinement Applied to Tsunami Modeling: TsunaFLASHWidodo Setiyo PranowoA dissertation submitted in partial fulfillment ofthe requirements for the degree of doctor in engineering (Dr. Ing)Supervisors:1. Prof. Dr. Wolgang Hiller (Alfred Wegener Institute)2. Prof. Dr. Jorn¨ Behrens (Universitat¨ Hamburg)Submitted on June 28, 2010Colloquium on July 29, 2010Program Authorized to Offer Degree: Fachbereich 3 Mathematik und Informatik,Universitat¨ Bremen2010AbstractAdaptive Mesh Refinement Applied to Tsunami Modeling: TsunaFLASHWidodo Setiyo PranowoThe devastating Sumatra-Andaman tsunami of December 2004, is a milestone for the internationalcommunity striving to introduce measures to prevent hazards from (future) tsunamis. One of themeasures is numerical modeling which plays a key role for predictions as well as inundation map-ping developments.Numerical modeling has been used as a tool for analyzing and reconstructing tsunamis foralmost 40 years. Nowadays, many tsunami codes are available as open-source or free-ware andwidely used in the tsunami modeling community. Many numerical methods have been applied suchas finite difference, finite element and finite volume. The same applies to gridding methods, such asstructured and unstructured non-adaptive types.This thesis introduces a new triangle-based adaptive mesh finite element model for tsunamipropagation (and inundation) simulations.

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Publié par
Publié le 01 janvier 2010
Nombre de lectures 45
Poids de l'ouvrage 31 Mo

AdaptiveMeshRefinementAppliedtoTsunamiModeling:TsunaFLASH

WidodoSetiyoPranowo

Adissertationsubmittedinpartialfulfillmentof
therequirementsforthedegreeofdoctorinengineering(Dr.Ing)

Supervisors:1.Prof.Dr.WolgangHiller(AlfredWegenerInstitute)
2.Prof.Dr.J¨ornBehrens(Universit¨atHamburg)

201028,JuneonSubmitted

201029,JulyonColloquium

ProgramAuthorizedtoOfferDegree:Fachbereich3MathematikundInformatik,
Universit¨atBremen
2010

Abstract

AdaptiveMeshRefinementAppliedtoTsunamiModeling:TsunaFLASH

WidodoSetiyoPranowo

ThedevastatingSumatra-AndamantsunamiofDecember2004,isamilestonefortheinternational
communitystrivingtointroducemeasurestopreventhazardsfrom(future)tsunamis.Oneofthe
measuresisnumericalmodelingwhichplaysakeyroleforpredictionsaswellasinundationmap-
elopments.vdeping

Numericalmodelinghasbeenusedasatoolforanalyzingandreconstructingtsunamisfor
almost40years.Nowadays,manytsunamicodesareavailableasopen-sourceorfree-wareand
widelyusedinthetsunamimodelingcommunity.Manynumericalmethodshavebeenappliedsuch
asfinitedifference,finiteelementandfinitevolume.Thesameappliestogriddingmethods,suchas
structuredandunstructurednon-adaptivetypes.

Thisthesisintroducesanewtriangle-basedadaptivemeshfiniteelementmodelfortsunami
propagation(andinundation)simulations.TsunaFLASHcombinesanumericalmethoddevelopedin
theframeworkoftheunstructuredtriangularelement,yetnon-adaptive,tsunamimodelTsunAWI
withadaptivemeshrefinementcapabilitiesprovidedbythelibraryamatos.Themethodsarewell
suitedforaccurateresolutionoflocalizedfeatures,maintainingcomputationalefficiencyintermsof
thenumberofcomputationsandtherequiredmemory.

InthisfirstdevelopmentsofTsunaFLASH,anumberofexperimentshavebeenperformedfor
testing.Thereare:Anexperimentsonvariousinitialconditions,fromananalyticalsourceuptoa
couplingtothesophisticatedrupturegeneratorRuptGen;experimentswithdiverseerrorestimators
fortestingrefinementcriteriaandadaptationalgorithms;benchmarkexperimentsusinganalytical
solutionsandfieldobservationswheretheanalyticalsolutionisderivedfromthefirstbenchmark
problemfromTheInternationalLongWavesreference;andtheseasurfaceelevationinthefielddata
experimentisusedfromthesatellitetracksofJason-1andTopexforverificationoftheSumatra-
Andamanmega-tsunami2004event,whilethewaterlevelreadingofDART23401isusedforthe

verificationoftheAndamanminortsunami2009.

Someadditionalstudieshavebeenconductedtoassessthephysicalbackgroundoftsunamis

simulationandtestpropersupportingtoolsforTsunaFLASH.Thereexperimentscomprisesource

modelreconstructionsandsimulationsbasedupontheseinthecontextofaprobableworstcase

tsunamisimulationforPadang;experimentstotesttheinfluenceofdifferenttypesoftopographies

ontheinundationbehavior;andaninvestigationofthemostrepresentativesourcemodelforthe

Andaman-Sumatramega-tsunamiof2004.Finally,theambiguityofthearrivaltimeoftheJava

minortsunami2009isexperimentallyinvestigated.

Keywords:tsunami,numericalmodel,finiteelement,unstructuredmesh,adaptivemesh

Zusammenfassung

AdaptiveGitterVerfeinerungangewandtaufdieTsunamiModellierung:TsunaFLASH

DerverheerendeSumatra-Andamanen-TsunamivomDezember2004isteinMeilensteinf¨ur
dieinternationaleGemeinschaftbeiderErgreifungvonMaßnahmen,Gefahrenzuk¨unftigerTsunamis
zureduzieren.F¨urdieVorhersagevonAnkunftszeitenderWellenunddieEntwicklungvon¨Uberflungs-
kartenspieltnumerischeModellierungeineSchl¨usselrolle.
NumerischeModellierungwirdseitfast40JahrenzurAnalyseundRekonstruktionvon
Tsunamisverwendet.VieleTsunami-CodessindOpenSourceoderFreewareundweitverbreitet
inderTsunami-Modellierungsgemeinschaft.VerschiedenenumerischeMethodenwerdenange-
wandt,wiez.B.dieFinite-Differenzen-,dieFinite-Elemente-oderdieFinite-Volumen-Methode.
BeiderGittergenerierungwirdzwischenstrukturiertenundunstrukturiertensowienichtadaptiven
undadaptivenVerfahrenunterschieden.
IndieserArbeitwirdeinneuesFinite-Elemente-ModellzurBerechnungderAusbreitungs-
und¨UberflutungsphasevonTsunamiwelleneingef¨uhrt,welchesaufadaptiverGitterverfeinerung
basiert.TsunaFLASHverbindetdasVerfahrenderadaptivenGitterverfeinerung(mitHilfederBib-
liothekamatos)mitdemnichtadaptivenFinite-Elemente-ModellTsunAWI.BeideMethodensind
f¨ureinehoheAufl¨osunglokalerGegebenheitensehrgeeignet,wobeidienumerischeEffizienzin
BezugaufdieAnzahlderBerechnungenunddenben¨otigtenSpeicherplatzerhaltenbleibt.
IndererstenEntwicklungsphasevonTsunaFLASHwurdenzahlreicheUntersuchungendurch-
gef¨uhrt:UnterschiedlicheAnfangsbedingungenwurdengetestet,voneineranalytischenQuellebis
zueinerkomplexenDeformationdesMeeresbodens(generiertdurchdasProgrammRuptGen).
VerschiedeneFehlersch¨atzerf¨urVerfeinerungskriterienundAlgorithmenzuradaptivenGitterver-
feinerungwurdenverglichen.BenchmarkexperimentemitanalytischenL¨osungenundFelddaten
wurdendurchgef¨uhrt.DieanalytischeL¨osungistvomerstenBenchmarkproblemderInternational
LongWaves-Konferenzabgeleitet.ZurValidierungdesModellswurdenSatellitentracksvonJason-
1undTopex,welcheDatenderMeeresspiegelauslenkungdesSumatra-Andamanen-Megatsunamis
von2004lieferten,verwendet.DerWasserstandderBojeDART23401dientederValidierungder

ModellergebnissedeskleinerenAndamanen-Tsunamisvon2009.

Zus¨atzlicheStudienwurdendurchgef¨uhrt,umdenphysikalischenHintergrundvonTsunami-

simulationenzuuntersuchensowiediekorrekteFunktionsweisederunterst¨utzendenWerkzeugef¨ur

TsunaFLASHzutesten:ZumeinenbeinhaltendieseExperimenteRekonstruktionenvonAnfangsbe-

dingungenundSimulationenimKontexteinesm¨oglichenworst-case-TsunamisvorPadang,Suma-

tra.DabeiwurdederEinflussvonverschiedenenTopographiedatens¨atzenaufdas¨Uberflutungs-

verhaltenuntersucht.Zumanderenwurdedasammeistenrepr¨asentativeQuellmodellf¨urden

Andamanen-Sumatra-Megatsunamiermittelt.SchließlichwurdendieUnklarheitenbeiderBes-

timmungderAnkunftszeitendesJava-Tsunamisvon2009n¨aherbetrachtet.

Stichw¨orter:Tsunami,numerischesModell,Finite-Elemente-Methode,unstrukturiertesGit-

ter,adaptivesGitter.

CONTENTSOFABLET

ListofFigures..........................................

ListofTables..........................................

Glossary.............................................

Chapter1:Introduction..................................
1.1Tsunamiintheworld.................................
1.2TsunamiModeling..................................
1.3Motivationandobjective...............................
1.4Thesisoverview....................................

Chapter2:TheModel..................................
2.1Shallowwaterequation................................
2.2Unstructuredfiniteelementmethod..........................
2.3Leapfrogscheme...................................
2.4Inundationboundarycondition............................
2.5Manningsroughnessandviscosity..........................

Chapter3:AdaptiveMeshRefinement..........................
3.1amatos........................................
3.2Meshrefinementandcoarsening...........................
3.3Spacefillingcurve..................................

Chapter4:NumericalDevelopment...........................
4.1Spatialdiscretization.................................
4.2Timedescritization..................................
4.2.1Physicalandnumerical(wave)mode....................
4.2.2Robert-Asselintimefilter...........................
4.3Timestepcontrol...................................

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15151717

212123242626

4.4Inundationscheme..................................
4.5Bottomfriction....................................
4.6Smagorinskyhorizontalviscosityterm........................

Chapter5:Tools.....................................
5.1Visualizationtools..................................
5.1.1tsunaflashplot.m.............................
5.1.2tsunaflashmovie.m............................
5.1.3rgb2bmp.sh.................................
5.2Analysisandverificationtools............................
5.2.1tsunamifft.m................................
5.2.2tsunamimagnitude.m...........................
5.2.3tsunaflashtseries.m...........................
5.2.4tsunaflashcomparerunupbeach.m...................
5.2.5tsunaflashcomparesattrack.m.....................
5.3SeaBottomDeformationGenerator.........................
5.3.1tsunamirupdimslip.m...........................
5.3.2SeaBottomDeform.f90..........................
5.3.3tsunamiprojection.m...........................
5.4Initialgridgeneratorforscenarioofrunupinachannel...............

Chapter6:Modelsetup,NumericalExperimentResultsandDiscussion........
6.1Modelsetup......................................
6.1.1Bathymetryandtopography.........................
6.1.2Initialcoarsemesh..............................
6.1.3Hardwareandsoftware............................
6.2Experimentonthediverseinitialconditions.....................
6.2.1Cosinebell..................................
6.2.2Ellipticsource................................
6.2.3Couplingwitharupturegenerator......................
6.2.4Faultparameters...............................
6.3Experimentonthediverseerrorestimators......................
6.4Bechmark:Runuponaslopingbeach........................
6.5Experimentonthediverseadaptationalgorithm...................
6.6Computationalspeed.................................
6.7TestcaseonSumatra-Andamanmegatsunami2004.................

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353636363939394041444650556264

6.8TestcaseonAndamanminortsunami2009.....................

Chapter7:MiscellaneousResults............................
7.1ExperimentonthePadang(next)futuretsunami...................
7.1.1Reconstructionofthesourcemodel.....................
7.1.2ComparisononthetopographyofSRTMandHRSC............
7.2ExperimentonfilteringgaugesdataofJavaminortsunami2009event.......
7.3ExperimentonthediversesourcemodelofSumatra-Andamanmega-tsunami2004
event..........................................

Chapter8:ConclusionsandFuturework.........................
8.1Conclusions......................................
8.2Futurework......................................

AppendixA:HowtorunTsunaFLASH...........................
A.1Introduction......................................
A.2Buildingamatoslibrary...............................
A.3BuildingandExecutingTsunaFLASH.........................
A.4Filesinclude......................................
A.5CouplingwithRuptGen................................
A.6Filesoutput......................................
A.7Outputvisualization..................................
A.8Useagerestrictions..................................
A.8.1Copyright...................................
A.8.2License....................................
A.8.3Warranty...................................

AppendixB:SourceParametersofPadang(Next)FutureEarthquake...........

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129

FIGURESOFLIST

agePNumberFigure1.1Themaintypesofaplateboundariesthatfeaturingbyacontinentalriftzonesas
youngboundaries,convergentboundaries,divergentboundariesandatransform
boundaries[KiousandTilling,2008].........................3
1.2Theillustrationofthesubductionfault(dip-sliptype)istriggeringtsunami.Itshows
bysequelsfromleftpanel(theinitiationofoceanicplatesubductstotheterrestrial
plate),middle(theterrestrialplateissqueezedinthemeantime),andrightpanel(a
leadingedgeoftheterrestrialplatebreakreleasesaverticaldislocation).[Atwater
etal.,2005].......................................3
CN2.1(a)Conforming(P1),and(b)non-conforming(P)shapefunctionbasedonHanert
1etal.[2005]......................................11
2.2WettinganddryingconceptbasedonLynettetal.[2002];(a)runupandrundownin
aslopingwall/beachwherethedotsrepresenttheextrapolationnodes;(b)schematic
sketchofthelinearextrapolationfromtwowetnodes(black)toadrynode(red)in
theshadedelement...................................14
3.1Thephasesoftheadaptivealgorithminamatos.Numericalcalculationsinvec-
tors(aftergatheringdatafrommesh),andmeshmanipulations(afterscatteringnew
valuestomesh).[Behrens,1997,2006].......................16
3.2(a)Bisectionoftrianglesmarkededgeand(b)refinementtree[Behrensetal.,2005;
Behrens,2006]....................................19
3.3Space-fillingcurvesinadaptivetriangularmeshrefinement[Baderetal.,2008]..19
3.4TheoriginalSFCconceptofSierpi´ensky[Sagan,1994]..............20
ˆ4.1Flowchartofthetimestepformeshadaptation.hisabasisfunctionofelevation,
andvˆisabasisfunctionofvelocity.Alocalcriterionisdenotedbyη.CFLstands
τforCourant-Friedrichs-Levy.TORisatoleranceofrefinementforthemesh.....27
6.1Bathymetry(shownincolour,max.depthof9,923meters)andTopography(shown
inwhite,max.heightof7,833meters)fromtheGlobalETOPO-5[NOAA/NGDC,
1988]..........................................37
6.2IGGproduceforcreatinganinitialcoarsemesh.Thecompletesequenceisnot
shownhere.(a)level01,(b)level04,(c)level17,(d)level20withpunchedoutland.38
6.3ExperimentusingcosinebellinitialconditionsinSundaStrait...........40

iv

6.4Constructionofellipticsourcefromtwosinefunctions...............
6.5EllipticsourceappliedinTsunaFLASH........................
6.6RuptGenpatchesmapalongtheSundatrench,150patchesare(parallel)alongthe
trenchand15patchesareperpendiculartothetrench,inoverallare2250patches
[Babeyko,2007]....................................
6.7ThedeterminationofNodalPlanes(NP)inthefocalmechanism;(a)Whenseismic
stationsdetectanearthquake(seeintheleftpanel:thesignalofgroundmotionsil-
lustratedaswhiteandblackdots,andthesymbolofcrossproductistheepicenter),
someofthestationswillreceiveasignalofthefirstgroundmotion(compressional,
blackdots)andsomeotherstationswillreceivesecondgroundmotion(rarefac-
tional,whitedots).Thedistributionofthefirstmotioncanbeusedtodefinethe
twonodalplanes,thefirstwouldbetheFaultPlane(NP1)andthesecondshouldbe
AuxiliaryPlane(NP2);(b)Inthis3-dimensionalillustrationofdip-slipearthquake
thetwonodalplanesareclearlyrepresented;(c)Imaginaryfocalspherearoundthe
faultepicenterisusedforprojectionofthegroundmotionsdirectionswhichrep-
resentedbythetwonodalplanestobeafocalmechanismdiagramknownasbeach
ball.[CoxandHart,1986;USGS,2009a].Forbeachballcasesseefigure6.8....
6.8Thesimplecasesofpurenormaldip-slip,reversedip-slip(thrust),andstrike-slip
motiononafault.Theupperimagesshowblockdiagramsillustratingthefault
motion;andthelowerimagesthecorrespondingfaultplanesolutionwhichiscom-
monlyrepresentedasbeachball,theblackareaispushingthetensionawayfrom
thefocalarea(compression,[+]),whilethewhiteareaispullingthetensiontoward
thefocalarea(rarefaction,[-]).[USGS,2009a]....................
6.9Faultplane(Σ)geometryoftypicalinterplatesubductioninanearthquakezone
belowtheseafloor;Qisanepicenter,Pishypocenter;Faultlengthisparalleltothe
Strike-axis(y-direction);Faultwidthisparalleltothedip-axis(x-direction).(a)3D
profileshowsthecontourofslipdistribution(δ(ξ,y))inthefaultplane.(b)Cross-
sectionalviewoftherupturezonetypeofdip-slip(a≤δ≤b)wherevariableslipis
definedasδ(ξ)≡[δ+−δ−],whileαisthedipangle.[GeistandDmowska,1999].
6.10ExperimentswiththediverseerrorindicatorsusingBengkulu2007minortsunami.
(a)Inhomogeneousinitialupliftattimestepno.0000;(b)Gridattimestepno.
9975,using(ητ=∇h);(c)Gridattimestepno.9975,criterion:(ητ=h−h¯);
(d)Gridattimestepno.9975,criterion:(ητ=h).................
6.11Experimentresultsusinggradientvalueofseasurfaceheightatelement(ητ=
∇h)asanerrorindicator..............................
6.12Experimentresultsusingaveraging(ητ=h−h¯)asanerrorindicator......
6.13Experimentresultsusingthemaximumabsolutevalueofseasurfaceheightatele-
ment(ητ=h)asanerrorindicator........................
6.14Sketchofslopingbeachcomputationaldomainforbenchmarkcase.Maximum
depthis5kmatthedistanceof50kmfromthecoastline.MSLismeansealevel..

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6.15Waveformof(a)equation6.8[Carrieretal.,2003],(b)initialconditionforTsuna-
FLASH[Liuetal.,2008]................................
6.16ThebenchmarkresultsofTsunaFLASHusingthefirstproblem-setofIWLRM[Liu
etal.,2008]:runupontheplanebeachtotheanalyticalsolutionthatperformsa
goodagreement.Blacksolidlinerepresentsbeach1/10slope,reddotisthemodel
simulationresult,whilebluesolidlineistheanalyticalsolution.Thissimulation
usesfollowingparametersFGL=10CGL=9TOR=0.07TOC=0.05,errorindicator
ητ=h,andadaptationalgorithm(6.5.1)......................
6.17CorrelationbetweenTsunaFLASHsimulationandanalyticalsolutionfordifferent
adaptationalgorithmsandgridlevels.........................
6.18ThebenchmarkresultsofTsunaFLASHusingthefirstproblem-setofIWLRM[Liu
etal.,2008]:runupontheplanebeachtotheanalyticalsolutionthatperformsa
goodagreement.Blacksolidlinerepresentsbeach1/10slope,reddotisthemodel
simulationresult,whilebluesolidlineistheanalyticalsolution.Thissimulation
usesfollowingparametersFGL=9CGL=9TOR=0.07TOC=0.05,errorindicator
ητ=h,andadaptationalgorithm(6.5.1)......................
6.19TsunaFLASHverificationforrunupontheplanebeachtestcase.Comparisonto
theanalyticalsolution,usinganerrorindicatorofητ=h,andalgorithm6.5.1,
theresultof(c)FGL=10CGL=9TOR=0.07TOC=0.05showsgoodagreement.
EachpanelshowsT=160sec,T=175sec,T=220secrespectivelyfromlefttoright;
blacksolidlinerepresentsbeach1/10slope,reddotrepresentsthemodel,while
bluesolidlineistheanalyticalsolution........................
6.20TsunaFLASHverificationforrunupontheplanebeachtestcase.Comparisontothe
analyticalsolution,usinganerrorindicatorofητ=h,andalgorithm6.5.2,the
resultof(c)FGL=10CGL=9TOR=0.07TOC=0.05showsgoodagreement.Each
panelshowsT=160sec,T=175sec,T=220secrespectivelyfromlefttoright;black
solidlinerepresentsbeach1/10slope,reddotrepresentsthemodelresults,while
bluesolidlineistheanalyticalsolution........................
6.21TsunaFLASHverificationforrunupontheplanebeachtestcase.Comparisontothe
analyticalsolution,usinganerrorindicatorofητ=h,andalgorithm6.5.3,the
resultof(c)FGL=10CGL=9TOR=0.07TOC=0.05showsgoodagreement.Each
panelshowsT=160sec,T=175sec,T=220secrespectivelyfromlefttoright;black
solidlinerepresentsbeach1/10slope,reddotrepresentsthemodelresults,while
bluesolidlineistheanalyticalsolution........................
6.22Experimentresults,usingabsolutemaximumbasedcriterion,(ητ=h)asanerror
estimator,FGL=9CGL=2,TOR=0.007TOC=0.001,onAceh2004forthetestcase.
Thesealevelcolorscaleusedisforbettervisualization,whereactualmaximumup-
liftis5.87metersandmaximumdepressionis-2.16meters.Inheretherefinement
isclearlyshownwhilecoarseningdoesnotoccur...................

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6.23Experimentresults,usingabsolutemaximumbasedcriterion(ητ=h)aserror
estimator,FGL=9CGL=2,TOR=0.007TOC=0.005,Smagorinskyconstantof0.3,
onAceh2004fortestcase.Thesealevelcolorscaleusedisforbettervisualization,
whereactualmax.upliftis5.87metersandmaximaldepressionis-2.16meters.In
here,thecoarseningisclearlyshownaswelltherefinement.............
6.24TsunaFLASHverificationforAceh2004event.(a)Satellitetrackson26December
2004;(b)ItsverificationwithJason-1;(c)ItsverificationwithTopex/Poseidon;At
(b)and(c)bluelinerepresentsobservationaldata,redlinerepresentsmodeldata..
6.25WavepropagationfollowedbygridevolutionduringsimulationforAndamanminor
tsunami10August2009event.Theinitialconditionhasmaximumelevationof
0.1480mandminimumelevationof-0.2448m....................
6.26(a)ComparisonofTsunaFLASHsimulationresultsfortheAndamanminortsunami
10August2009eventtotheobservationdataofDART23401andTsunAWImodel
results.(b)AsmallbumpisshowninthesimulationresultwhenusingSmagorinsky
constantof0.001,(seethered-dash-circledarea)...................
7.1ThereliablecouplingandslipdistributionforthesourceofPadangearthquakefor
the(next)futureproposedbyNatawidjaja[2008]afterChliehetal.[2008]which
locatedinfrontofPadangregionwithmomentmagnituderangeofMw8.8-8.9,
see(a);Thereconstructionresult,usingRuptGen[Babeyko,2007;Babeykoetal.,
2008],oftheinterseismiccoupling(b)andslipdistributionandthecontourofex-
citation(c)withouttheBengkuluearthquake12Septemberistakingintoaccount,
totalmomentmagnitudeisMw8.92353........................
7.2(a)Mw8.92353;(b)Mw8.87359afteromitthemomenmagnitudeofBengkulu12
September2007earthquake,seethedetailsofthesourceparameterintableB.1and
B.2...........................................
7.3Theexampleoftheprofilesnapshotofthetopographydataof(a)HRSC[DLR/RSS
GmbH,2007];(b)SRTM[DLR,2003].ItshowsthattheHRSCprofileismuch
differenttotheSRTM,whereattheLatitudeof0.950◦Shasdifferencesabout10
metersatthecoastalarea................................
7.4Inundationresultsofthesimulation,basedontheslipdistributioninfigure7.1(c),
scenarioofMw8.92353,usingtopographydataof(a)HRSC[DLR/RSSGmbH,
2007];(b)SRTM[DLR,2003].............................
7.5Shake-mapofMw7.0earthquakeeventinsouthernJava[USGS,2009b].PAMEis
gaugestationatPameungpeukandPELAisgaugestationatPelabuhanratu.....
7.6Amapofatidegaugestations(indicatedbyyellowpin)andearthquakeepicen-
ter(indicatedbyyellowcircle).ThestationslocatedinsouthernJava,Indonesia,
fromwesttoeastrespectivelyare:PelabuhanRatu,Pameungpeuk,Cilcap,Sadeng,
Prigi2.Fortheexperiment,thestationofCilacapandSadengareexcludedsince
nosignificanttsunamiwavesignaldetectedthere.Thereisonegaugestation,also
used,atChristmasislandofAustralia.........................

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777880818384

7.7TimeseriesofwaterlevelthePameungpeukstation(a)Waterlevelrecorded,(b)
Residual,(c)Powerfrequency,(d)Periods......................85
7.8TimeseriesofwaterlevelthePelabuhanRatustation(a)Waterlevelrecorded,(b)
Residual,(c)Powerfrequency,(d)Periods......................86
7.9TimeseriesofwaterlevelthePrigi2station(a)Waterlevelrecorded,(b)Residual..87
7.10TimeseriesofwaterleveltheChristmasislandstation(a)Waterlevelrecorded,(b)
Residual........................................87
7.11The5initialconditionsaregeneratedfortheexperimentoftheSumatra-Andaman
2004eventfrom8scenariosintable7.1........................89
7.12Theparedwithsimulationthesatellite(red-solid-line)tracksofthe(Sat-tracks,Sumatra-Andamanblue-solid-line)megofatJason-1sunamiand2004Topecom-x
on(left-(a)andLayetal.right-panel,[2005]inScenariorespectivA,ely,(b)eachTaniokafigure),etal.using[2006],the(c)initialHirataconditionetal.based[2006].90
7.13Theparedwithsimulationthesatellite(red-solid-line)tracksofthe(Sat-tracks,Sumatra-Andamanblue-solid-line)megofatJason-1sunamiand2004Topecom-x
(left-andright-panel,inrespectively,eachfigure),usingtheinitialconditionbased
on(a)Banerjeeetal.[2007],(b)Hoechneretal.[2008]ScenarioC.........91

A.1TheDirectorystructureofTsunaFLASH.......................122

viii

ABLESTOFLIST

agePNumberableT1.1Tsunamiwavecharacteristicsindeepoceanandshallowwater[Gonz´alezetal.,2007].4
2.1TheManningsroughnesscoeffient(n)whichiscommonlyusedinthetsunami
modeling.......................................13
5.1Theempiricalrelationamongtsunamimagnitude,maximumwaveheightandthe
damagepotentialcharacteristics,afterLisitzin[1974]................32
6.1Highestlocalgridresolutioncorrespondstoadaptiverefinementlevel.......37
6.2Computationalspeedresultsofthebenchmarkproblemset-1(600sectime)simulation64
6.3Computationalspeedresultsofthebenchmarkproblemset-1simulationdoneby
otherauthors.....................................65
6.4FaultparametersoftheexcitationforAndamanminortsunami2009simulationfrom
anearthquakemagnitude(Mw)of7.5........................70
6.5Thecomputationresultsoftheasinglerupturedimension,anaveragedislocation
20andshearrigidity,totheMw7.5(USGS)orMo2.239x10N.m[Kanamori,1977;
HanksandKanamori,1979],basedonvariousempiricalformulas(seesection5.3.1)71
7.1Totalmomentseismic(Mo),momentmagnitude(Mw)andshearrigidity(µ)ofthe
diversesourcemodelfortheexperimentofSumatra-Andaman2004event.....92
B.1SourceparametersofPadang(next)futureearthquake:faultdimensionanddislocation129
B.2SourceparametersofPadang(next)futureearthquake:focaldepth,dip,strikeand
rigidity.........................................135

ix

ABBREVIATION,ACRONIMANDGLOSSARY

amatos:AdaptiveMeshGeneratorforAtmosphericandOceanographicSimulations.

AWI:AlfredWegenerInstituteforPolarandMarineServices,Head-officeatAmHan-
delshafen12,D-27570Bremerhaven,Germany.

CET:CentralEuropeanTime(UTC+1hour).

.vyCourant-Friedrichs-LeCFL:

CGL:Coarsegridlevelfortheadaptivemesh.

DART23401:Deep-oceanAssessmentandReportingofTsunamis,IDStationNumber23401,
locatedat8.905N88.540Eor600NMWest-NorthwestofPhuket,Thailand.Ownedand
maintainedbyTMD(seeGlossary:TMD)inconjunctionwithNationalDisasterWarning
CenteroftheKingdomofThailand.

EARTHQUAKETSUNAMI:Atsunamiistriggeredbyanearthquake.

ETOPO5:Adigitalbathymetryandtopographydatawhichhas5arc-minresolution.

FAULTPLANE:Theplanar(flat)alongbottomsurfacewhichhascertainslip(dislocation)dur-
inganearthquake.Afaultplanesolutionisawayofshowingthefaultandthedirectionof
sliponitfromanearthquake,usingcircleswithtwointersectingcurvesthatlookslikeabeach
ball.Itisalsocalledafocal-mechanismsolution(USGS).

FGL:Finegridlevelfortheadaptivemesh.

x

FINITEELEMENTMETHOD:Amethodforfindinganapproximatesolutionofpartialdifferen-
tialequationsbyemployingelementbasisfunctionsforaspatialdiscretization.

GFZ:Geo-Forschung-ZentrumorknownasGermanResearchCentreforGeosciences,Head-
officeinthecityofPotsdam.

GEBCO:GEneralBathymetricChartoftheOceans.

GITEWS:German-IndonesiaTsunamiEarlyWarningSystems.

HRSC:High-ResolveStereographicCamerathatusedforcaptureaspatialtopographydata.

IWLRM:The3rdInternationalWorkshoponLong-waveRunupModels.

INCOIS:IndianNationalCenterforOceanInformationServices,headquarteratHyderabad,
India.

JMA:JapanMeteorogicalServices.

LEAPFROG:Aschemeforintegratingdifferentialequations,wherethreetimelevelsareap-
pliedinthecalculation,i.e.present(t),past(t−1)andfuture(t+1).Thisschemehassecond
.yaccuracoforder

MANNINGSROUGHNESS:AbottomfrictionschemewhichwasproposedbyRobertManning
(1816-1897),itwasimprovedandintroducedasGauckler-ManningformulabyGauckler
(1867).Uptonow,itiswidelyusedforhydrodynamicscomputationandcommonlyknown
roughnessManningasformula.

MINORTSUNAMI:Atsunamigeneratedbyanearthquakewherethemaximumwaterlevel
detectedbygaugesislessthan1meters.

MO:Amomentmagnitudeoftheearthquakescale.Theunitisdimensionless.

xi

MW:Aseismicmomentoftheearthquakescale.TheunitisNm.

NEIC:NationalEarthquakeInformationCenterofUSGS.

NDBC:NationalDataBuoyCenteroftheUnitedStatesofAmerica,afiliatedtoNOAA.

NGDC:NationalGeophysicalDataCenteroftheUnitedStatesofAmerica,afiliatedtoNOAA.

NOAA:NationalOceanicandAtmosphericAdministrations,UnitedStatesofAmericaDe-
Commerce.ofpartment

NUMERICALMODEL:Atoolforreconstructingaphysicalphenomenabyusingmathematical
equationsandemployeanumericalmethodsforitscomputation.

PMEL:PacificMarineandEnvironmentalLaboratory,afiliatedtoNOAA.

RHS:Right-Hand-Side,amathematicaltermforeverythingontherightsideofanequation
.operatortestaor

RUPTGEN:ARuptureGeneratordevelopedatGFZ.

SRTM:AShuttleRadarTopographyMissionwhichisconductedtocapturetheearthsurface
data.ationvele

TMD:ThailandMeteorologicalDepartment.

TOC:Thetoleranceofcoarseningfortheadaptivemesh.

TOR:Thetoleranceofrefinementfortheadaptivemesh.

TSUNAMI:AJapanesewordforaseismicseawave.Itsconstructionoftsuwhichmeans
harbourandnamiwhichmeanswave.

xii

TSUNAMIEARTHQUAKE:Atsunamigeneratedbyaslowearthquake(longperiodsofseismic
wavesexcitation)inaveryshallowhypocenterdepthwithfaultdislocationgreaterthansev-
eralmetersandmagnitudesurface(Ms)isbiggerthanmagnitudebody(Mb),producingsmall
magnitudemoment(Mw)butsignificantrunup.

TSUNAWI:Tsunamiunstructured(nonadaptiveyet)finiteelementmodeldevelopedatAlfred
WegenerInstituteforPolarandMarineResearch,Bremerhaven,Germany.

TsunaFLASH:TsunamiunstructuredadaptivefiniteelementmodeldevelopedatAlfredWegener
InstituteforPolarandMarineResearch,Bremerhaven,Germany.

UNSTRUCTUREDADAPTIVEMESH:Ameshconstructedbytriangularelements.Thenumber
andsizeofelementschangesbasedoncriteriaduringthesimulation.

UNKNOWN(DOF):Degree-Of-Freedom,avariableorparameterwhichisdefinedinthemath-
approximation.ematical

USGS:UnitedStatesofAmerica-GeologicalSurvey.

UTC:UniversalTimeConventionorknownalsoasUniversalTimeCodewhichisexpanded
fromCoordinatedUniversalTime.ForGermanytimezoneCET=UTC+1hour(seeGlos-
sary:CET);whileforIndonesiawhichhave3timezones,e.g.WIB=UTC+7hours(see
WIB)Glossary:

WIB:WaktuIndonesiaBarat,Indonesianwesterntimezone.ThiszoneiscoveringSumatra
island,Javaisland,andProvinceofWestKalimantanandProvinceofCentralKalimantan.

xiii

WLEDGMENTSCKNOA

TheGITEWSprojectiscarriedoutthroughalargegroupofscientistsandengineersfrom
(GFZ)GermanResearchCentreforGeosciences(consortiumleader)anditspartnersfromtheAl-
fredWegenerInstituteforPolarandMarineResearch(AWI),theGermanAerospaceCenter(DLR),
theGKSSResearchCentre,theKonsortiumDeutscheMeeresforschung(KDM),theLeibnizIn-
stituteforMarineSciences(IFM-GEOMAR),theUnitedNationsUniversity(UNU),theFederal
InstituteforGeosciencesandNaturalResources(BGR),theGermanAgencyforTechnicalCoop-
eration(GTZ),aswellasfromIndonesianandotherinternationalpartners.Fundingisprovidedby
theGermanFederalMinistryforEducationandResearch(BMBF),Grant03TSU01.
TheauthorwishestoexpresssincereappreciationtoAlfredWegenerInstituteforPolar
andMarineResearch(AWI),wherehehashadtheopportunitytoworkintheComputingCen-
ter(Rechenzentrum),andtoUnitedNationsUniversity-InstituteforEnvironmentandHuman
Security(UNU-EHS)whichprovidedfellowshipwithinTheGermanIndonesianTsunamiEarly
WarningSystem(GITEWS)inCapacityBuildingframework.
MygreathonorandgratefullythanktomyDoktor-vater:(Prof.Dr.J¨ornBehrens),forall
valuableknowledges,discussions,guidance,time,andsupports.Iveneverforgethowheskind
efforttocompanyusstrugglinginordertogetaspousevisaformywifeintheAusl¨anderbeh¨orde.
ThankyouverymuchalsoforthekindhelpandsupportbeingmyworkandlivinginBremerhaven,
tocolleagues(formerandrecent)inTsunamiResearchGroupatAWI:Dr.JensSchr¨oter,Dr.Sven
Harig,Dr.AlexeyAndrosov,FlorianKlaschka,OliverKunst,LarsMentrup,Dr.StephanBraune,
Dr.EifuTaguchi,HaiyangChui,ClaudiaWekerle,Dr.NataljaRakowsky,AnnikaFuchsandSven
Steinmann.AgreathonorandthankfulalsotoProf.Dr.WolfgangHiller(DirectoroftheComputing
andDataCenteratAWI)forthesupervisionandthesupportsbeingmyworkatAWI.Thanks
alsogoestocolleaguesinComputingCenter(Rechenzentrum)atAWIwhobroughtanicefriendly
atmosphere.IwouldlikealsotoexpressmythanktothestudentsfromUniversityofBremen

xiv

whocontributingvaluableworkinTsunaFLASH,i.e.JanSchlicht,CorinnaZiemer,MariaB¨ohme,
StephanJuricke,ThomasRackow.Avaluablediscussionandtutorialonthefaultparametersand
sourcemodelingalsohavebeencontributebyDr.AndreyBabeyko,Dr.AndreasH¨ochnerandDr.
SaschaBrunefromGeo-Forschung-ZentrumPotsdam.Abriefvaluablediscussiononthemodel
benchmarkalsohavebeenconductedwithProf.YinglongJ.Zhang(ScienceandTechnologyCenter
forCoastalMarginObservationandPrediction,OregonHealthandScienceUniversity).

MyworkwasalsocheeredupbythescientificdiscussionamongtheUNUsGITEWSPhD
students,i.e.WidjoKongkowhosharinghiswideknowledgeaboutatsunamimodeling,Ade
Anggrainiforbeachballfocalmechanismtutorial,RokhisKhomarudinforinvolvingmeathis
paperintheZeitschriftf¨urGeomorphologie,PachochenkoJintasaraeinthetopicofbathymetry,
RavelosonAdrimiartowhoallowmespentthenightinhisapartmentbeforemyvisaapplicationto
theUSEmbassyinBerlinregardingAGU-FM2008,alsosomediscussiononvariousthingswith
Sumaryono,JonatanLassaandDennisChang-Seng.ThehugesupportalsocamefromDr.Fabrice
Renaud(DirectorUNU-EHS),Prof.Dr.Ing.JanosBogardi(theformerRectorUNU-VieEurope)
withtheimportantacademicofficers(Dr.ThomasSzockeandEvalyneKatabaro).Mygratitude
acknowldgealsogoestoProf.Dr.-Ing.TorstenSchlurmann(Franzius-Institut,LeibnizUniversit¨at
Hannover)whoopenmeagreatopportunityforthefellowship.

MylifeinBremerhaveniscolorfulbyfriendsincludingbythe(locally)IndonesianStudent
Association(PPIBremen),regionally(PPIJerman)andworldwide(PPIDunia).Especially,Iwould
liketothankfultoFaridHendry,SylviaRiana,FeronicaLuttmerandWalterLuttmer,Siswandi
familywhobeingmyfamilyinBremerhaven.Togrepthefellowshipopportunityalsocontributed
bytheformerandrecentsupervisorsfrommyhomeinstitutionintheMinistryofMarineAffairs
andFisheriesoftheRepublicofIndonesia,i.e.Prof.Dr.Ir.IndroyonoSoesilo,Dr.GellwynnJusuf,
Dr.AndienH.Taryoto,Dr.SugiartaWiraSantosa,Dr.SafriBurhanuddin,Dr.AgusSupangat,Dr.
BudiSulistyo,Drs.AsepD.Muhammad,andDr.GabrielTonnyWagey.Iwanttoacknowledge
alsotoDr.SubandonoDiposaptomowhogavemethefirsttsunamibook(inbahasaIndonesia)that
Ihaveeverhad.ThankyoualsogoestoProf.HamzahLatief(PusatPenelitiankelautan,Institut
TeknologiBandung)whowasvisitmeatmyfirsthalfyearbeinginBremerhavenandsharedhis

xv

knowledgeonatsunamimodeling.
Finally,Iexpressmygreathonourandgratefullythanktomyfather(BapakIr.AlriantoNo-
topurnomo,MM),mymomm(IbuSukadarmi),myfatherinlaw(BapakR.Soegondo),mybeloved
motherinlaw(IbuSoenarsiwhorestinpeaceinheaven),mybrothersandsisters(MasGatotSuhan-
dono,ST.;MbakIbin,SP.;MasTotok,SP.;VembriaRoseHandayani,ST.,M.Siandfamily;Wijaya
KukuhPrabowo,ST.andfamily;RizkyRosianaHardiati,ST.andfamily),forallwishes,blessing,
supports.and

Credits:TheTEXLaTeXeditorhavebeenusedaswordprocessorofthisthesis.Thebeautiful
sketchofslopingbeachhasbeendrawingbyFraukeThiele-Wolff(AWI-Rechenzentrum).Initial
meshofIGGisprovidedbyOliverKunst.Initialgridanddatafortheslopingbeachexperimentis
providedbyStephanJ¨uricke,MariaB¨ohme,andThomasRackow.Initialmatlaboutputtemplate
forTsunaFLASHisprovidedbyCorrinaZiemerandJanSchlicht.TsunAWImeshesareprovided
bySvenHarigandClaudiaWekerle.ThenumericalworkshavebeenconductedinIFortcompiler
andSolarisSunFire.TheGeneralMeshViewer(GMV)fromLosAlamosNationalLabsUSAand
MatlabfromMathworkshavebeenusedforvisualization.Somevaluabledataisdownloadedfrom
NOAA/PMELforsatellitetracksdataof26December2004;fromNOAA/NGDCforETOPO5;
fromNOAA/NDBCforDARTbuoy23401dataofAndamanminortsunamieventof10August
2009;andalsofromGEBCOforthebathymetry.TheLast-MileProject(Franzius-Institut,Leibniz
Universit¨atHannoverandDeutschesZentrumf¨urLuft-undRaumfahrt)alsohavebeensharingthe
HRSCofPadangTopographydata.Inaddition,DLRprovidedtheSRTMdata.

xvi

and

my

handsome

TIONDEDICA

Tomydearestwife,TriHandanariforherhugesacrifices;

son,

Meino

Rafif

owPrano

,

who

xvii

was

born

in

en,vBremerha

24

September

2009

1ChapterODUCTIONINTR

Thouseestthemountainsandthinkestthemfirmlyfixed:buttheyshallpassaway
asthecloudspassaway:(suchis)theartistryofAllah,whodisposesofallthingsin
perfectorder:forheiswellacquaintedwithallthatyedo(TheQuran,An-Naml,
(027):088)Whentheearthisshakentoher(utmost)convulsion,Andtheearththrowsupher
burdens(fromwithin)(TheQuran,AlZal-Zalah,(099):001-002).

1

ThetheoryofContinentalDriftpublishedbyAlfredWegenerinhisbookTheOriginsofThe
Continentsin1912gaveanimpacttoscientistsfordevelopingthetheoryofplatetectonicsduring
1950s-1960s[Jacoby,2001;KiousandTilling,2008;Yount,2009].Withthetheoryofcontinental
driftgeologicalfeaturesandphenomenasuchastheshapeofcontinents,rifting,drifting,faulting,
orogenesis(naturalmountainbuilding)andevolutionsofthecontinents,continentdisplacement,
earthquakeandvolcanismcanbeexplained.Figure1.1depictsthemaintypesofplateboundaries.
Thesubductionzone,seeinfigure1.1,whereconvergentplateboundariesareoverriding
onetoanother,istheplacewherethemosthazardousearthquakesappear.Earthquakeswitha
magnitudelargerthan7cantriggertsunamis.Thegenerationofatsunamiisshowninfigure1.2.
TheterminologyofthetsunamicomesfromtheJapanesewordtsuwhichmeansharbourand
namiwhichmeanswaveforaseismicseawave[Lisitzin,1974].Tsunamisarelongwaves
(gravitywaves)travelingwithveryhighvelocitiesthroughtheocean.Theymightbetransoceanic
andcauseteletsunamisinthefar-field.Duringtravelingthroughthedeepocean,thewaveheightof
atsunamiistypicallylessthan30cmGonz´alezetal.[2007].Whileapproachingtheshorethewave
heightincreasesextremelyandmaygainmorethan10meters.Thecharacteristicsoftsunamiwaves
areshownintable1.1.From2267tsunamigenicevents,tsunamistriggeredbytectonicearthquakeis
72%,bylandslideis10%,byvolcanicis5%,bymeteorologicalis2%andofunknownmechanism
is11%[IOC-UNESCO,2005].AccordingtoBryant[2005],ofthe92eventsoftsunamitriggered

2

byvolcanicevents,16.5%aregeneratedbyaneruptionassociatedwithatectonicearthquake,20%
bypyroclasticflows,14%bysubmarineeruptions,7%bycalderacollapse,5%bycoldmaterial
avalanches,4.5%byhotmaterialavalanches,3%bymudflows,1%bylavaflows.Theshock
wavesintheatmospherecontributesonlyto4.5%;and25%issuspectedlycausedbyasubmerged
eruption.Thedisasterofthetsunami,whichmayalsoincludedamagesbytheearthquakeand/orthe
volcaniceruptioncasualties,maycostlivesandmassivedamageofinfrastructure.Thedeathtoll
causedbytsunamiandrecordedsince1800:on27November1816atsunamikills10,253people
inBali[Latiefetal.,2000];on02March1856theAwuvolcaniceruptioninNorthernSulawesi
Indonesiageneratesatsunamiandcauses3,000casualties[Latiefetal.,2000];on26August1883
thefamousKrakatauvolcaniceruptioncausesatsunami,whichcaused36,000deathsinIndonesia
[Latiefetal.,2000];on13August1868aChileantsunamicauses25,000deaths[UNESCO−IOC,
2006a];on15June1896SanrikutsunamiinaJapancauses22,000deaths[UNESCO−IOC,2006a];
on2March1933atsunamistrikeSanrikuJapanagainandcauses3,000deaths[UNESCO−IOC,
2006a];on22May1964anothertsunamiinChilecauses2,000deaths[UNESCO−IOC,2006a];
on17August1976aPhilippinestsunamiclaims8,000deaths[UNESCO−IOC,2006a];on12
December1992atsunamiontheBabiislandpartofFlores/Indonesiakills1,952people[Latief
etal.,2000];on17July1998atsunamikills2,182peopleatthenorthcoastofPapuaNewGuinea
[Landeretal.,2003];andthehighestdeathtolliscausedbythe26December2004Andaman-
Sumatramega-tsunami,whichhit11countriesclaimed231,452victims,whereIndonesia,Thailand,
SriLankaandSoutheastIndiaaretheworsthitcountries[UNESCO−IOC,2006b].

1.1Tsunamiintheworld

TheGlobaltsunamidatabasefortheworld2007[ITDB/WLD,2007]hasarecordof254,462earth-
quakeeventsduring1500BCuntil2007,and1,988tsunamieventsfrom2000BC(whichstroke
theSyriancoast)until2008(whichwasaminortsunamithathitSimeulue,westcoastofnorthern
Sumatra).Thedifferencebetweenthenumberofrecordedearthquakesandtsunamieventsisdueto
thefactthatisatsunaminotalwaysgeneratedbyanearthquake,sincenotallearthquakesareunder
sea.

3

Figure1.1:Themaintypesofaplateboundariesthatfeaturingbyacontinentalriftzonesasyoung

boundaries,convergentboundaries,divergentboundariesandatransformboundaries[Kiousand

2008].illing,T

Figure1.2:Theillustrationofthesubductionfault(dip-sliptype)istriggeringtsunami.Itshowsby

sequelsfromleftpanel(theinitiationofoceanicplatesubductstotheterrestrialplate),middle(the

terrestrialplateissqueezedinthemeantime),andrightpanel(aleadingedgeoftheterrestrialplate

breakreleasesaverticaldislocation).[Atwateretal.,2005].

4

Table1.1:Tsunamiwavecharacteristicsindeepoceanandshallowwater[Gonz´alezetal.,2007].

ParametersDeepOceanShallowWater

Depth1000≤h≤5000meters10≤h≤1000meters
Period5≤τ≤60min5≤τ≤60min
Amplitude0.01≤η≤1meters1≤η≤10meters
Wavelength30≤Λ≤800km3≤Λ≤356km
Speed0.10≤c≤0.22km/sec0.01≤c≤0.10km/sec
Maxcurrent0.05≤u≤9.9cm/sec9.9≤u≤990cm/sec

Tsunamievidenceinthepast(palaeo-tsunami)canbecollectedfromsomesedimentorde-
positlayersasatsunamiindicator.ThereisadatabasecompilationoftsunamidepositbyKeating
etal.[2008].Uptotheyearof2008,thetsunamidepositdatabasehas278entriesthatcategorizes
thedeposittooriginatefrom:co-seismicevents(19%),impactsfromacretaceous/tertiaryboundary
(7%),lansliderelatedevents(9%),volcanogenicevents(6%),sourceordepositfromcontinen-
talmargins(3%),submarinetsunami(12%),meteotsunamiorstorm(10%),andunknownorigin
(34%).Anothertsunamiproxyisthegrowthofacoralreefthatgivesinformationabouthistorical
upliftanddepressioninasubductionregion,e.g.KumarandAchyuthan[2006];Natawidjajaetal.
[2006];Chliehetal.[2007,2008];Natawidjaja[2008].
Afterthedevastatingtsunamiof26December2004,scientistsfocusontheIndianOcean.
Geologiststartedstudyingpalaeo-tsunamisinordertorevealthetimeperiodofmegatsunamis.
Accordingtopalaeo-tsunamirecordsbetween326BCand2005[KumarandAchyuthan,2006;
RatogiandJaiswal,2006],80percentofalltsunamisIndianOceanareoriginatingfromtheSunda
arcregion(Indonesia)whichgeneratesaneventonceevery3years,whiletheotherregionhavea
returnperiodofapproximately10years.OtherpotentialtsunamisourcesareintheMakranaccretion
zoneofPakistan,IndusDeltaandCoastofKutchandSaurashtrainIndia,whilesomeearthquake
epicentersarenearBangladeshandMyanmar,andtheChagosridgenearDiegoGarcia.
InadditiontotheIndianOceanregion,recenttsunamieventsrelevantforIndonesiainlast

5

6yearsafter26December2004Sumatra-Andamantsunami[Ammonetal.,2005;SteinandOkal,
2005]are:28March2005inNias(westofSumatra)[Ammonetal.,2005];17July2006south
ofJava[Ammonetal.,2006];12September2007nearBengkuluaminortsunami(westcoast
ofsouthernSumatra)[Borreroetal.,2007a,b,2008,2009];andthenfivemoreminortsunami
events,17November2008inToli-toli(NorthernSulawesi)[BAKOSURTANAL,2008;Wangetal.,
2008],04January2009inManokwari(IrianJaya)[BAKOSURTANAL,2009;Kongko,2009],10
August2009inAndaman,16August2009inPadang,02September2009inSouthofJava,30
September2009againinPadang.TworecentminortsunamisareinnorthernSumatra,06April
and09May2010.Scientistsforeseeanumberofevents(willhappen)infrontofPadang(Westof
Sumatra)[StoneandKerr,2005;Natawidjaja,2008;McCloskeyetal.,2008;Behrensetal.,2009],
Bali,andsouthofJava[Khomarudinetal.,2010]inthenearfuture.Inordertobuildcommunity
preparedness,GITEWSandsomelocalgovernmentprojectsareconductinginundationmodeling
forhazardmapping,evacuationrouteplanningandtsunamidrillexercise.

ModelingTsunami1.2

Before1990tsunamimodelingscientistsfocusedonfarfieldtsunamionlywithsomeeventslikein
Japan,HawaiiandUSwestcoast[SynolakisandBernard,2006].Duringthe1990s-2000sthere
aremanyevents,withdominantlynearfieldtsunamimodelingstudies.Anear-fieldtsunamiisa
tsunamifromanearbysource,lessthan200kmaway,generatedbyasmallearthquake,alandslide
orapyroclasticflow[UNESCO−IOC,2006a].Generallynear-fieldisconsideredlessthanoneor
twowavelengths.
Themega-tsunami2004posesachallengingtaskforscientiststoreconstructtheeventfrom
thesourceusingmodels,whichcandealswithallavailabledataforverificationsuchas:runupfield
measurement,tidegauges,andsatellitetracks.AfterAmmonetal.[2005]providedthefirstsource
model,followingstudiesprovidedtimedependentormovingrupturee.g.byLayetal.[2005],
Taniokaetal.[2006];Hirataetal.[2006],Banerjeeetal.[2007],and(mostrecently)Hoechner
etal.[2008].In28march2005,theNiastsunamievent,againinnorthernWestSumatra,gavemore
topicsofdiscussionaboutthecompletepictureoftheSumatra-Andamanrupture[Banerjeeetal.,
2007].al.,etGeist2007;

6

In2006,theJavatsunamieventremindsthescientiststolookbacktotheeventsofPeru1996
and1960[KanamoriandKikuchi,1993],Java1994[Tsujietal.,1995],Nicaragua1992[Ideetal.,
1993;KanamoriandKikuchi,1993],Kuril1975and1963[KanamoriandKikuchi,1993],Aleutian
1946[Kanamori,1972],andSanrikuJapan1896[Kanamori,1972].Discussionarouseonmodeling
thesourceandinundationofthetsunamiearthquake[Ammonetal.,2006;Fritzetal.,2007;Fujii
andSatake,2006;Kongkoetal.,2008;Lavigneetal.,2007]asachallengeforthiskindoftsunami
characteristic.ThetermofatsunamiearthquakewasfirstmentionedbyKanamori[1972],where
atsunamiisgeneratedbyaslowearthquake(longperiodsofseismicwavesexcitation)withavery
shallowhypocenterdepth,withfaultdislocationgreaterthanseveralmetersandmagnitudesurface
(Ms)isbiggerthanthemagnitudebody(Mb),suchthatifproducesasmallmomentmagnitude(Mw)
butsignificantrunup.TheNicaraguanearthquake1992isthefirsttsunamiearthquakerecordedby
modernbroadband-seismicnetworks,allowingscientiststobetterunderstanditsrupturemechanism
1993].Kikuchi,and[KanamoriDuring2007-2008,themodelingofminortsunamiisdiscussedinthescientificcommunity,
(e.g.inEGU2007,AGUFallmeeting2008),asaresponsetothe12September2007Bengkulu
(westcoastofsouthernSumatra)event[Babeykoetal.,2007;Borreroetal.,2007a,b,2008;Gusman
andTanioka,2008;Hsu,2007;Loritoetal.,2008;Okaletal.,2007;PranowoandKongko,2008;
Toninietal.,2007].Thediscussionabouttheminortsunamiwillcontinue,sincetherearetwo
morerecentevents,17November2008inToli-toli(NorthernSulawesi)[BAKOSURTANAL,2008;
Wangetal.,2008]and04January2009inManokwari(IrianJaya)[BAKOSURTANAL,2009;
Kongko,2009].In2009,theSamoan(WestPacific)tsunamiof29September2009andthePadang
(WestSumatra)tsunamiof30September2009hasdrawnthescientistsattentione.g.Bhattacharya
[2009];Schiermeier[2009];Wekerleetal.[2009].
Other(hydrodynamic)tsunamisandsourcemodels,whichhavelowerfrequency,are(un-
derwater)landslidetsunamie.g.Liuetal.[2005];Bruneetal.[2008]andtsunamigeneratedby
asteroid/meteoridimpactse.g.AhrensandOKeefe[1983];Chapman[2004];CrawfordandMader
[1998];HillsandGoda[1998];Mader[1998a,b];WardandAsphaug[2000,2002,2003];Yabushita
[1994].HattaandInthisthesis,wecollectseveralinitialconditionsorsourcemodelapproachesandimple-
mentedintoTsunaFLASH,e.g.:cosinebellfunctionalformfrom[Williamsonetal.,1992];anidea

7

ofanellipticalfunctionisderivedfromGusiakov[2007];ananalyticallandslideN-waveinitial
conditionfromLiuetal.[2008]after[Carrieretal.,2003];manuallygenerationofrupturefrom
therealfocalmechanismdataofanearthquakeevent;couplingwitharupturegeneratorsoftware
RuptGenBabeyko[2007];Babeykoetal.[2008];assestovariousempiricalformulasforestimating
therupturedimension;assestheimplementationofexcitationbyslipdistributionforthesimulation;
collectsandassessofseveralsourcemodelsforSumatra-Andamanmega-tsunami2004reconstruc-
tions.

1.3Motivationandobjective

Numericalmodelinghasbeenusedasatoolforanalyzingandreconstructingtsunamisfor40years
[Aida,1979].Nowadaysmanytsunamicodesareavailableasopen-sourceorfree-wareandare
widelyusedinthetsunamimodelingcommunity(suchas:SWAN[Mader,1998a,b;Hillsand
Goda,1998;Mader,2004];COMCOT[WangandLiu,2006;Wuetal.,2008];TUNAMI[Imamura
etal.,2006;McMurtryetal.,2004;Kongkoetal.,2008];MOST[TitovandGonzalez,1997;Borrero
etal.,2009];ANUGA[Nielsenetal.,2005;Nielsen,2007;Taubenb¨oketal.,2009]).Commercial-
ware(suchas:MIKE21byDHI[Baruaetal.,2006;Gayeretal.,2008;Leschkaetal.,2008];and
3DDbyASRLtd.[Black,2002;ASRLtd,2005;Henderson,2008])alsoavailable.Manynumerical
methodshavebeenappliedandarerepresentedinthesecodes(FiniteDifference,FiniteElement,
FiniteVolume).Griddingmethodssuchasstructuredandunstructurednon-adaptivehavebeen
applied.Intheendofyear2008TsunAWI(Tsunamiunstructuredmeshfiniteelementmodeldevel-
opedatAlfredWegenerInstitute)byBehrensetal.(2006-2008)[Behrensetal.,2007;Behrens,
2008],hadbeenlaunchedasanoperationalmodelintheGerman-IndonesianTsunamiEarly
WarningSystem(GITEWS)framework.Thismodelhasbeenbenchmarked[Androsovetal.,2008]
andverifiedwith2004Sumatra-Andamanmegatsunamievent[Harigetal.,2008].
Anewdevelopmentusesadaptivemeshrefinementtoimprovecomputationalefficiencyand
accuracy,thisapproachiscalledTsunaFLASH[Behrens,2007;BehrensandPranowo,2008;Pra-
nowoetal.,2008;BehrensandPranowo,2009].Anotherablock-structuredadaptivefinitevolume
codeTsunaCLAWbyLeVequeandGeorgein2006[GeorgeandLeVeque,2006].

8

Adaptivemeshrefinement,forfluidflowwasfirst,introducedby[BergerandOliger,1984]
and[BergerandColella,1989],andwasimplementedusingafinitedifferencemethodandstruc-
turedgrid.Firstexperimentsofitsapplicationforatmosphericandoceanmodelsarestartedby
Behrens[1998],followsbyBlayoandDebreu[1999]andDebreuandBlayo[2002].In2002,
Maderetal.reconstructstheLituyalandslidemega-tsunami8July1958employingtheContinous
AdaptiveMeshRefinement(CAMR)fortheNavier-stokesequationandastructuredgridforEu-
larianCompressiblehydrodynamics;thecodesarecalledNOBEL/SAGE[Mader,2004].Thesame
CAMRisusedforsimulatingatsunamigeneratedbyanasteroidimpact[Gisleretal.,2003]and
landslideonatleast32processors[Gisler,2010].
ThisthesisshowstheperformanceofTsunaFLASH,whichrepresentsthefirsttsunamimodel
solvedonanadaptivefiniteelementmesh.Aninovationisthetriangularadaptivemesh.Inorder
toimprovetherealisticperformance,weadoptamovingboundarytechniqueforinundationLynett
etal.[2002],bottomfrictionfromProvostetal.[1995]andMeietal.[2005],andSmagorinsky
horizontalviscosityterm[Smagorinsky,1963]intoTsunaFLASH.Inadditiontotheimprovement
phase,wedefineandconductseveralnumericalexperimentsandtestcasesforvalidation.Tosupport
theseefforts,wecollectdata(e.g.bathymetry,topography,waterleveltimeseriesfromgauge/buoy,
seasurfaceelevationfromsatellitetracks)andconcepts(e.g.fourierfilterwavefrequency;empirical
relationamongearthquakemagnitudemoment,tsunamimagnitudeandmaximumwaveheightat
thecoast;empiricalrupturedimensionestimation,visualization)inordertoprovidepropertoolsfor
modelinputpreparationandfurtheranalysisofmodelresults.

1.4Thesisoverview

Inchapter1,theshortdescriptionofanearthquakeandtsunamiisstartedfromthetheoryofcon-
tinentaldrift.Ashortreviewoftsunamimodeling,thesourceaspect,anditsrelationtothewave
propagationandrunupmodelthengivemotivationtothisthesis.
Chapter2describesthegeneralconceptofanestablishedtsunamimodelnon-adaptiveun-
structuredfiniteelementgrids,developedatAlfredWegenerInstitute(AWI)andcalledTsunAWI.
Theadoptedconceptofadaptivemeshrefinementwillbedescribedinchapter3.Inhere,abriefin-
troductiontoamatos,themeshrefinementandcoarseningstrategy,aswellasthespacefillingcurve

9

optimizationandCourant-Friederich-Lewystabilitycriterionwillbegiven.Thenumericalimple-
mentationintotheadaptiveschemeisdescribedinthechapter4.Tovisualize,furtheranalyze,
verify,benchmarkandinitializethemodel,sometoolsareused,giveninchapter5.
Themodelsetupforanumberofnumericalexperimentsarediscussedinchapter6,we
consider:experimentsondiverseinitialconditions,experimentsondiverseerrorestimators,an
experimentonSmagorinskyviscosityhorizontaldiffusion,ananalysisonthecomputationalspeed,
benchmarkandtestcases.Therearetwofielddatabasedtestcases:1)thesimulationoftheSumatra-
Andamanmegatsunami2004eventandacomparisontothesatellitetracks(Jason-1andTopex).2)
thesimulationoftheAndamanminortsunami2009eventandacomparisontoDART-buoydata.
Inchapter7,weprovidemiscellaneousresultsfromastudiesduringthedevelopmentphase.
AmongtheseareanexperimentofsourcemodelreconstructionforafuturetsunamiinPadang
includingthecomparisonofdifferencesoftopographyelevationdata.Furthermore,anexperiment
onfilteringgaugesdataoftheJavaminortsunami2009andanexperimentwithdiversesource
modelsfortheSumatra-Andamanmegatsunami2004areconducted.
Conclusionsandanoutlookforfutureworkaredescribedinchapter8.
AdescriptiononhowtorunTsunaFLASHisprovidedinappendixA.Itdescribesinshort
howtoinstall,build,executeTsunaFLASHincludingsettinguptheamatosasalibraryandcoupling
toRuptGen.Informationaboutwhatkindoffilesareincludedandanoutputvisualizationmethhod
isalsogivenhere.Thesourceparametersof201faultrupturesofPadangnextfuturetsunami
reconstructionresultsisprovidedinappendixB.

10

2ChapterMODELTHE

The(Tsunamiunstructured(non-adaptiveyet)meshfiniteelementmodeldevelopedatAlfred
WegenerInstitute),knownasTsunAWIisanoperationalmodeltoproduceascenariodatabase
fortheIndonesianTsunamiEarlyWarningSystem(InaTEWS).Theworkhasbeeninitiatedand
maintainedintheGerman-IndonesianTsunamiEarlyWarningSystem(GITEWS)framework.
ThischapterpresentsabriefdescriptionofthebasicconceptofTsunAWIwhichisused
forthedevelopmentofTsunaFLASH(seeChapter4).Furtherdetailsofthemodelareavailablein
Behrensetal.[2007]andBehrens[2008],anadvanceddescriptiononthebenchmarkisprovided
inAndrosovetal.[2008]andthe2004Sumatra-Andamanmega-tsunamieventtestcaseisfurther
describedinHarigetal.[2008].

equationwaterwShallo2.1

Theshallowwaterequation,whicharemostcommonlyusedbycurrenttsunamimodelssuchas
inImamuraetal.[2006];TitovandGonzalez[1997];Hanertetal.[2005];Nielsenetal.[2005];
Behrensetal.[2007],aregivenby:

∂η∂t+∇∙(v(h+η))=0(2.1)
∂vCdv|v|
∂t+(v∙∇)v+f×v+g∇η+ρ(h+η)−∇∙(Ah∇v)=0(2.2)
Equations(2.1)and(2.2)arethecontinuityequationandmomentumequationrespectively,
where(v∙∇)visthe(non-linear)advectionterm,f×vtheCoriolisterm,g∇ηthepressuregradient,
ρC(hdv+|vη|)thebottomfriction,∇∙(Ah∇v)theviscosityterm,ggravitationalforce,ηtheelevationabove
meansealevel,andhthewaterdepth.
Fortheboundarycondition,equations(2.3)and(2.4)representtheradiationconditionsfor
openoceanboundaryandno-slipconditionforlandboundaryrespectively,whereneisthenormal

ardoutw.ectorv

11

(2.3)(2.4)

gv∙ne=h+ηη(2.3)
v∙ne=0(2.4)
Wettinganddryingorinundationboundaryadvectionaregivenbelow.
2.2Unstructuredfiniteelementmethod
Elevationnodesarelyingontheverticesofthetriangulationandvelocitynodesarelocatedat
thecenterofedgesegments.Withtheseshapefunctions,thediscreteelevationfieldiscontinuous
everywhere,whereasthediscretevelocityfieldisonlycontinuousacrosstriangleboundariesatmid-
edgenodesanddiscontinuouseverywhereelsealongtriangleboundaries.Seefigure2.1.Amajor
advantageofnon-conformingshapefunctionsistheirorthogonalityproperty.Theelevation(h)and
theDepth(H)isdiscretizedwithlinearconforming(P1)shapefunctions,asgivenin(2.5),whereas
thevelocityvisdiscretizedwiththenon-conforming(P1NC)functions2.6.

hˆ:hˆ1=1−x−y;hˆ2=x;hˆ3=y
vˆ:vˆ1=1−2y;vˆ2=2x+2y;vˆ3=1−2x

(2.5)(2.6)

(b)(a)Figure2.1:(a)Conforming(P1),and(b)non-conforming(P1NC)shapefunctionbasedonHanert
[2005]al.et

12

schemeogfrLeap2.3

Time-discretizationinTsunAWIisachievedbyapplyinganexplicitleapfrogscheme.According
toAndrosovetal.[2008]thisleapfrogtimediscretizationneedsrelativelysmalltimestepstoreach
anumericalaccuracyincomparisontoimplicitschemes,butithasadvantagestotheinundation
modelwhichoperatesincoastalareaswithahighgridresolution.Animplicitschemerequiresmore
computationalresourcesthananexplicitscheme.Howeveritproducesanumericalwave(mode)
thatcanberemovedbyusingAsselinfilter[Asselin,1972].Furtherdiscussionaboutnumerical
(wave)modeisprovidedinsection4.2.1.Time-stepsizeiscontrolledbytheCourant-Friedrichs-
Levy(CFL)conditionforstabilityoftheexplicittimescheme[Behrens,2008;Harigetal.,2008].
Thisexplicitschemeiswidelyusedinoceanandwavemodel,particularlyintsunamimodels,e.g:
TUNAMI[Imamuraetal.,2006]andCOMCOT[Liuetal.,1998]whicharefinitedifferencebased,
andANUGA[Nielsen,2007]whichisbasedonthefiniteelementmethod.

conditionboundaryInundation2.4

TherunupschemeinTsunAWIfollowstheideasofLynettetal.[2002].Oncethewavecrestreaches
theshore,thegradientoftheseasurfaceheightisextrapolatedfromwavenodestodrynodeson
land[Behrens,2007],seefigure2.2.Whenadrynodeisexcludedfromthesolutionthenthesea
surfacewaveisextrapolatedintoitfromatleast4wetnodesusinglinearleastsquareextrapolation
(2.7).see),f(

f(x,y)=a0+a1x+a2y(2.7)
f(x,y)−a0+a1x+a2y2=min(2.8)
where[a0,a1,a2]isatripletparameter,and(2.8)isusedforfindingthebestfitoffwith
respecttotheL2-norm[Androsovetal.,2008].

2.5Manningsroughnessandviscosity

TheuniformGauckler-Manningsroughnessscheme(commonlyknownasManningsroughness)
[Chanson,2004]forthebottomfrictiontermisappliedforTsunAWIfollowinge.g.TUNAMI

13

Table2.1:TheManningsroughnesscoeffient(n)whichiscommonlyusedinthetsunamimodeling

ReferencecharacteristicBottomn

0.015Concrete,rubbleafterG.J.ArcementandV.R.Schneider[1984],
[1979].FranziniandyLinsle0.020Land(farming/waste)afterImamura[2009]andKotanietal.[1998].
0.025Naturalcoast,riverandchannelsafterImamura[2009],
(goodcondition)Kotanietal.[1998],
[1979].FranziniandyLinsle0.030CoastwithforestafterImamura[2009]andKotanietal.[1998].
0.035NaturalchannelsandfloodplainsafterG.J.ArcementandV.R.Schneider[1984],
(sandy,stonyandweedy)LinsleyandFranzini[1979].
0.040NaturalchannelsandfloodplainsafterG.J.ArcementandV.R.Schneider[1984].
(bouldery)

[Imamuraetal.,2006]andgivessatisfyingperformanceinacomparisonbyHarigetal.[2008].

gn2v|v|4/3
(h+η)(2.9)
ThedimensionlesscoefficientofManningsroughness(seetable2.1)canbederivedfrom
experimentalstudyinahydrauliclaboratory[LinsleyandFranzini,1979;G.J.Arcementand
V.R.Schneider,1984;Chanson,2004]orfromremotesensingdata[Kotanietal.,1998;Imamura,
2009].TheSmagorinskyviscosityhorizontal(wave)diffusion[Smagorinsky,1963]isusedinTsunAWI
toimprovewavepropagationstability[Harigetal.,2008].Forfurtherdescriptionanditsapplication
toTsunaFLASH,seesection4.6.

14

Figure

2.2:

ettingW

and

(a)

drying

concept

based

on

ynettL

et

al.

aslopingwall/beachwherethedotsrepresenttheextrapolation

(b)

[2002];

(a)

runup

and

wnrundo

in

nodes;(b)schematicsketchofthe

linearextrapolationfromtwowetnodes(black)toadrynode(red)intheshadedelement.

3Chapter

REFINEMENTMESHAPTIVEAD

15

Thetraditionalshapeoftheunstructuredfiniteelementmeshisatriangle[Weatherill,1999].
Unstructuredmeansthatthenodeororderingcannotbeformedintoaregularneighborarrayof
theform(i,j),i=1:n,j=1:mlikeinthestructuredgrid.Atthesametimethemeshordering
needstoenablesearchesfornodesorelementsbyconnectivityinformationinafastandefficient
way.Therefore,basicdatasuchastreestructuresplayamajorroleinthegenerationofunstructured
meshes.Weadoptatriangularadaptivemeshrefinementtechniqueasanewapproachfortsunami
modeling.amatos,theAdaptiveMeshGeneratorforAtmosphericandOceanographicSimulations,
byBehrens[Behrens,1997,1998,2003,2006],isemployed.Therefinementstrategyusedisbi-
sectionoftrianglesmarkededge[Behrensetal.,2005]andmeshorderingisbasedonSierpinskis
spacefillingcurve[BehrensandZimmermann,2000].
amatoshasbeenusedinappliednumericalresearche.g.studyofthetracertransportbywind
intheArcticstratosphere[Behrensetal.,2000],windjetstreamandzonalflowoveramountain
[L¨auteretal.,2007].

amatos3.1

Originallyamatoshadbeendevelopedtoovercomeproblemsinthearisingofnumericalclimate
2005].al.,et[BehrenssimulationsTheadaptivealgorithmconsistsoffivesteps:

1.aninitialcoarsemeshisgenerated,

adaptation,meshinitial2.

3.gatherallrequireddatafromthemeshintoaconsecutivedatastructure,

16

Figure3.1:Thephasesoftheadaptivealgorithminamatos.Numericalcalculationsinvectors(after
gatheringdatafrommesh),andmeshmanipulations(afterscatteringnewvaluestomesh).[Behrens,
2006]1997,

calculations,numericalperform4.

5.scatterbackthecalculationresultstothemesh,

Thesummaryoftheproceduresisdepictedinfigure3.1.

Theuserhastoprovideaninitialcoarsemeshandthebathymetry/topographyofthemodel
domain[Behrensetal.,2005].ThesoftwareofIGG(InitialGridGeneratorforamatos)hasbeen
employedtoproduceaninitialcoarsemesh(file)basedonblack(colorofoceanicdomain)andwhite
(coloroflanddomain)domainbitmapfileinPGM(PortableGreyMap)format.Whenthenumer-
icalcomputationiscarriedoutintheoceanicdomainonly,theland-white-colorwillbepunched
out[Behrens,2003;Kunst,2009].Thecompletemeshgenerationandadaptationarecontrolled
byGRIDAPIprogramminginterface.Adescriptionofbathymetry/topographydataisprovidedin
6.1.1.section

3.2Meshrefinementandcoarsening

17

amatoscreatesaConforming−Nested−Triangle(CNT)gridtype,andusesH−adaptivity[Behrens,
2006].Therefinementstrategyusedisbisectionoftrianglesmarkededge[B¨ansch,1991;Behrens
etal.,2005].Itproducestwochildtrianglesfromoneparenttriangleelement.Forcreatinga
completemeshallelementsarecheckedforwhetheritshallberefined.Eachelementisrefinedat
itsmarkededge,ifaneighboringelementbecomesnon-admissible(i.e.containsahangingnode),
itismarkedforfurtherrefinement.Theiterationcontinuesuntilnomarkedelementsareleft.See
3.2figureInordertocoarsenabisectedtriangleelement,admissiblepatchesareconsidered.Anad-
missiblepatchisagridpartconsistingoffouradjacenttrianglesgroupedaroundanodethatbisects
arefinededge.Atleastthreeelementsofthefourneedtobeflagged,thenallfourelementsare
deletedtoobtainanewmeshsectionwithonlythetwoparenttriangles.
Thoseadaptivemanipulationsofthemesharecontrolledbyalocalelement-wiseerroras
acriterion,Themeshwillberefinedwherethecriterionisgreaterthanthethreshold(formula
3.1),otherwiseifitislessthanthethresholdvalueofthecoarseningtolerance,themesheswillbe
3.2).(formulacoarsened

∇h|τ>θrefmax(∇h|τ)(3.1)
∇h|τ<θcrsmax(∇h|τ)(3.2)
ForTsunaFLASH,insteadofusingthegradientofelevationaserrorestimators((ητ=∇h)),
thereisanothercriterion,e.g.theaveraging(ητ=h−h¯)andthemaximumabsoluteerroresti-
mators((ητ=h)).Experimentresultsusingacriteriaaredescribedinsection6.3.
3.3Spacefillingcurve

ThemeshorderingisbasedonSierpinskisspace-fillingcurve(SFC).WaclawSierpinski(1882-
1969)introducedthetheoryofthisSFContotrianglepolygonsin1912[Sagan,1994].Thismeans
thatSFCmapsa2-dimensionaldomainontoa1-dimensionalcurve,thisisillustratedinfigure3.4.
ThiskindofSFChasproventoincreaseefficiencyfortriangularmeshesinappliednumericalmod-

18

eling[BehrensandZimmermann,2000;Behrens,2006;Baderetal.,2008;BehrensandBader,

2009],seefigure3.3.AccordingtoBehrensandZimmermann[2000];GriebelandZumbusch

[2002];Baderetal.[2008];BehrensandBader[2009]thismethodhas

memory

meshes.

requirements

and

increase

cache

yficiencef

during

the

numerical

reducetoabilitythethe

computation

on

evadapti

Figure

3.2:

Behrens,

(a)

2006]

Figure

3.3:

Bisection

(a)

of

Space-filling

striangle

escurv

in

edmark

edge

evadapti

and

(b)

triangular

(b)

refinement

mesh

tree

refinement

[Behrens

[Bader

et

et

al.,

al.,

19

2005;

2008]

20

Figure

(a)

(c)

(e)

(g)

The3.4:

original

SFC

concept

of

(b)

(d)

(f)

(h)

Sierpi´ensky[Sagan,

1994]

21

4ChapterDEVELOPMENTNUMERICAL

Anadaptiveunstructuredtriangularfiniteelementtsunamimodelhasbeendeveloped.The
descritizationisdeducedfromBehrens[2008]afterHanertetal.[2005]andtheinundationscheme
isfollowingLynettetal.[2002].ThetimestepiscontroledbyaCFLcriteria[Courantetal.,
1928].Implementationofthebottomfrictionandhorizontalviscositytermisfollowingtheideaof
Androsovetal.[2008]andHarigetal.[2008].

etizationdiscrSpatial4.1

Shallowwaterequations(2.1)and(2.2)arespatiallydiscretizedbyusingRitzGalerkinsmethod.
Aconformingelement(P1)forthefunctionofseasurfaceelevation(η),depth(h),andtotalwater
depth(h+η),denotedbyscalarbasisfunctionhˆ∈S,see(2.5),isutilized.Anon-conforming
element(P1NC)isappliedforthefunctionofvelocity,denotedbythevectorbasisfunctionvˆ∈V,
see(2.6).Theunknown(DOFordegreeoffreedom)variableisplacedintheedgecentersofthe
triangularelement.Anillustrationisprovidedinfigure2.1.Multiplying(2.1)and(2.2)bytest
functionsandintegratingoverthedomainandboundaryyields(4.1)and(4.2).

ZN∂η∑∂thˆ+(h+η)v∙∇hˆ
Ωe1=e

ZNv∂∑∂tvˆ+(∇∙(vvˆ))∙v+(f×v)∙vˆ+g∇η∙vˆ
Ωe1=e

Cdv|v|
+ρ(h+η)∙vˆ−Ah∇v∙∇vˆdΩ
ZN+∑∂Ω(vv∙ne)∙vˆdΓ=0forvˆ∈V
e1=e(4.2)

(4.1)S∈hˆfor0=Γden∙vhˆ)η+h(e∂ΩZ1=e∑N+Ωd

22

whereΩisthemodeldomainwithboundaryΓ,nistheoutwardnormalvector.Thecomputational
formcanbederivedbyreplacingηin(4.1)andvin(4.2)withalinearcombinationoftheshape
functions:

Nη≈ηh=∑hˆjηj(4.3)
1=jMv≈vh=∑vˆkvk(4.4)
1=kwhereηjandvkrepresentnodevaluesforelevationandvelocity.Theshapefunctionsforelevation
andvelocity,whichareassociatedwiththej-thvertexandk-thedgearerepresentedbyhˆjandvˆk
respectively.Thefinalspacediscretizationareshownin(4.5)forelevation,whilethevectorvelocity
isdividedinto(4.6)foru-velocitycomponentand(4.7)forv-velocitycomponent.

∑∂ηhˆh+(h+ηh)(u∂hj+v∂hj)dΩ+∑(h+ηh)hˆj(un(x,e)+vn(y,e))dΓ=0
NZˆˆNΓZ
e=1Ωe∂t∂x∂ye=1∂Ωe
(4.5)

ZNh∑∂uvˆk+∂(uvˆk)u+∂(vvˆk)u+fvvˆk+g∂ηvˆk
e=1Ωe∂t∂x∂y∂x

ZNh∑∂vvˆk+∂(uvˆk)v+∂(vvˆ)v−fuvˆk+g∂ηvˆk
e=1Ωe∂t∂x∂y∂y

Cdvh|vh|h
+ρ(h+ηh)∙vˆk−Ah∇v∙∇vˆkdΩ
ZN+∑v(un(x,e)+vn(y,e))vˆkdΓ
∂Ωe1=eZN+∑u(un(x,e)+vn(y,e))vˆkdΓ=0,for1≤j≤N
∂Ωe1=e(4.6)

Cdv|vh|h
+ρ(h+ηh)∙vˆk−Ah∇v∙∇vˆkdΩ
ZN+∑∂Ωv(un(x,e)+vn(y,e))vˆkdΓ=0,for1≤k≤NΓ
e1=e(4.7)

descritizationimeT4.2

23

Thegeneralleapfrogtimeintegrationschemeisgivenin(4.8).Ithasthreetimelevelsi.e.t,t−1,
andt+1andhasasecond-orderofaccuracy.

t+1t−1
Fm−Fm=RHS(Fmt)(4.8)
tΔ2Δtisthetimesteplength,andRHSisafunctionofalltermsdependingont,andt−1.Theequation
ofcontinuity(2.1)andmomentum(2.2)canberewrittenintheleapfrogschemeasin(4.9)and
.elyvrespecti(4.10)

t+1t−1
η−η+∇∙(vt(h+ηt))=0(4.9)
tΔ2t+1t−1tt+1
v−v+(vt∙∇)vt+f×vt+g∇ηt+Cd|v|vt−∇∙(Ah∇vt−1)=0(4.10)
2Δtρ(h+η)

Thissimpleformoftheleap-frogschemecanevolveanumerical(wave)mode.Adiscussionabout
thismodeisgiveninsection4.2.1.Inordertoremoveit,weapplytheRobert-Asselinfilterµ¯t(see
section4.2.2).Then(4.9)and(4.10)canrewrittenasin(4.11)and(4.12)respectively.

ηt+1=ηt−1−2Δt∇∙(vt(h+ηt)+µ¯t(4.11)
vt+1=vt−1−2Δt(vt∙∇)vt+f×vt+g∇ηt+Cd|v|v−∇∙(Ah∇vt−1)+µ¯t(4.12)
tt+1
ρ(h+ηt)
Thefinaltimediscretizationareshownin(4.13)forelevation,whilethevectorvelocitydividedinto
(4.14)foru-velocitycomponentand(4.15)forv-velocitycomponent.

∑ηt+1hˆdΩ=∑ηt−1hˆ+2Δt(h+ηt)ut+vtdΩ
NZNZ∂hˆ∂hˆ
e=1Ωee=1Ωe∂x∂y
(4.13)ZN−∑vt(h+ηt)hˆnedΓ+µ¯t
∂Ωe1=e

24

∑ut+1vˆdΩ=∑ut−1vˆ−2Δt−ut∂(uvˆ)−ut∂(vvˆ)+fvtvˆ+gηt∂vˆ
NZNZtt
e=1Ωee=1Ωe∂x∂y∂x
C|vt|vt+1
+d∙vˆ−Ah∇vt∙∇vˆdΩ
ρ(h+ηt)
ZN−∑ut(utn(x,e)+vtn(y,e))vˆdΓ+µ¯t
∂Ωe1=e

∑vt+1vˆdΩ=∑vt−1vˆ−2Δtvt∂(uvˆ)+vt∂(vvˆ)+futvˆ+gηt∂vˆ
NZNZtt
e=1Ωee=1Ωe∂x∂y∂x
1+tt+Cd|v|v∙vˆ−Ah∇vt∙∇vˆdΩ
ρ(h+ηt)
ZN−∑vt(utn(x,e)+vtn(y,e))vˆdΓ+µ¯t
∂Ωe1=e

(4.14)

(4.15)

Inothercase,insteadofanexplicitleap-frog,severalauthors(e.g.ZhangandBaptista[2008]
forSELFE(tsunami)model,Walters[2005]fortsunamipropagationmodel,Balzano[1998]for
Wetting-Dryingmodel,GeistandZoback[1999]formodelingSanfrancisco1906tsunamievent)
prefertoemployasemi-implicittimeintegrationwithγ∈[0,1].Anexampleofanimplementation
ofthisschemeisgivenin(4.16),appliedonlyforthecontinuityequationfordemonstrationpurpose.

∑ηt+1hˆdΩ=∑ηthˆ+2Δt(h+η)γ(ut+1∂h+vt+1∂h+(1−γ)(ut∂h+vt∂h))
NZNZˆˆˆˆ
e=1Ωee=1Ωe∂x∂x∂x∂y
ZN+ηtdΩ−∑∂Ωvt(h+ηt)hˆnedΓ
e1=e(4.16)

4.2.1Physicalandnumerical(wave)mode
Inordertoshowthattheleapfrogschemeproducesanumerical(wave)mode,wefollowthepro-
cedurefromMihardjaandHadi[1994]afterRammingandKowalik[1980],byusinganfunctional
analogofasinusoidalasinitialwave(4.17)substitutedto(4.8),see(4.18).

25

Fmt=ζtΔteikmΔx(4.17)
whereζiswaveamplitude,andanalyticalwavefunctionfxt=Ae−iωteikx=Aeik(x−ct),withk=
2π/(wavelength),=(wavelength)/(waveheight),andk.=2π/(waveheight)=ω.

ζ(t+1)ΔteeikmΔx−ζ(t−1)ΔteeikmΔxζt.Δteeik(m+1)Δx−ζt.Δteeik(m+1)Δx
2Δt=−C2Δx(4.18)
Furtherstepismultiply(4.18)withζ−(t−1)Δt:

ζ(t+1)Δt−(t−1)ΔteeikmΔx−ζ(t−1)Δt−(t−1)ΔteeikmΔx
=tΔ2(4.19)ζt.Δt−(t−1)Δteeik(m+1)Δx−ζt.Δt−(t−1)Δteeik(m+1)Δx
C−xΔ2Usingλ=−C22ΔΔxt,andeliminateeikmΔx,andeeikΔx=2isinkΔx,(4.19)rewriteas(4.20)or(4.21):

ζ2Δt−1=−λζtΔt2isinkΔx(4.20)
ζ2Δt+λBt.Δt2isinkΔx−1=0(4.21)
(4.21)isactuallyaquadraticform(ax2+bx+c=0)ofζΔt,wherea=1,b=2isinkΔxand
c=−1.The(roots)solutionforthequadraticformis(4.22).Thesolutionisinacomplexnumbers
(a+bi=(a2+b2)eiθ,θ=arcsin(λsinkΔx)),whichhasrealvalues(1−λ2sin2kΔx)1/2andtwo
complexvaluescontainanimaginery(ζ1Δt=e−iθ)and(ζ2Δt=ei(φ+θ)).

BΔt=−iλsinkΔx±(1−λ2sin2kΔx)(4.22)
Fmt=(Pe−iθt+Qe(π+θ)t)eikmΔx(4.23)
Physical(wave)modeNumerical(wave)mode
Ftm=(R−Q)eik(mΔx−θt/k)+(−1)tQeik(mΔx+θt/k)(4.24)
Thentheupdateoftheanalyticalsolutionof(4.18)isgivenby(4.23).Whileinfurthersteps,with
helpsofconstantPandQ,andwaveinitialcondition(4.17)att=0,theresultcanbeR=P+Qor
P=R−Q.Thefinalsolutionofthepropagationwaveusingleapfrogschemeisgivenin(4.24).It
isreachedaftersubstituteP=R−Qinto(4.23).Here,thetimefilterschemeneedstobeemployed
tofilterthenumerical(wave)modes.

26

filtertimeRobert-Asselin4.2.2

TheRobert-AsselinfilterisatimefrequencyfilterdesignedbyRobert[1966]whichwasoriginally
modifiedfromShuman[1957]andthenfurtheranalysisincorporationwithnumericalmethods(i.e.:
leapfrog,semi-implicitandimplicit)byAsselin[1972].Thisfilteris,widelyusedbyscientists(as
atechnique),employedforcontrolinghighfrequency(wave)modeanddampingphysical(wave)
modeling.numericalinmode

µ¯t=µt+α(µ¯t−1−2µt+µt+1)(4.25)
µ¯t=µt+α(µt−1−2µt+µt+1)(4.26)
where(4.25)istheRobert-Asselinfilterfunction,(4.26)isaShumanfilterfunction,andα=γ/2
isfilterparameter.AccordingtoRammingandKowalik[1980]theRobert-Asselinfilterfunction
ismorepowerfullthantheShumansfilter.Otherauthor(s)furtheranalysetheapplicationofthese
filtersinnumericalmethods(e.g.Schlesingeretal.[1983]andWilliams[1992]).

4.3Timestepcontrol

Time-discretizationisachievedbyapplyinganexplicitleapfrogschemeasin[Imamuraetal.,
2006].TimesteplengthiscontrolleddynamicallyinordertoadheretotheCourant-Friedrichs-
Levy(CFL)number(4.27)[Courantetal.,1928]conditionforstabilityoftheexplicittimescheme
[Behrens,2008;Harigetal.,2008].

vΔt=λ≤1(4.27)
xΔvΔt≤Δx(4.28)
Ifconditionin(4.28)cannotbefulfilled,thesimulationbecomesunstable,whichisvisibleinun-
physicalwaveamplification.Theelementsize(Δx)changescorrespondingtothepropagatingwave
whichisrepresentedbyawavevelocity(v).TheCFLcriterionshouldbelessthan1.Aflowchart
oftheadaptivetimestepisshownatfigure4.1.Thestabilityoftheleap-frogschemeandCFL
conditionforthetsunamisimulationwasdiscussedbyGotoetal.[1997].

StepimeTT→t+ΔT

Setupbasisvˆandhˆ

Computevelocityv

messageDiagnosticcheckCFL

Computehssh

ηCriterion,τ

Refine,whereητ>TOR

tΔAdjust

27

Meshchanged?NYFigure4.1:Flowchartofthetimestepformeshadaptation.hˆisabasisfunctionofelevation,andvˆ
isabasisfunctionofvelocity.Alocalcriterionisdenotedbyητ.CFLstandsforCourant-Friedrichs-
Levy.TORisatoleranceofrefinementforthemesh.

28

schemeInundation4.4

TherunupschemeinTsunaFLASHadoptsamovingboundarytechniquefromTsunAWIfollowing
theideasof[Lynettetal.,2002],seesection2.4.Thereare3casesappearingintheimplementation
ofthetechnique[HibberdandPeregrine,1979;Shuto,1991;Lynettetal.,2002]:

1.Thenodesinanelementarewet,((h+η)(node,t)>0),thenthewaterlevelgradientiscalcu-
lated.

2.Thenodesinanelementaredry,((h+η)(node,t)≤0),withnowaterlevelgradient.

3.Anelementwhichhaswetanddrynodes.Thewaterlevelgradientislinearlyextrapolated
fromthewetnode(s)tothedrynode(s)bycalculatingthegradientastheweightedsumofthe
neighboringwetnodesgradients.Theextrapolationformulaisgivenin(2.7)and(2.8),while
theschemeisshowninfigure2.2(b).

frictionBottom4.5

Thebottomfrictiontermintheequation(4.29)iscommonlyusedforhydrodynamicmodelsin
shallowwaterarea,e.g.Provostetal.[1995].Inordertoimprovetheperformanceoftheinundation
scheme,e.g.tomimicphysicalbehaviorwhenthewaveapproachesashorearea,equation(4.30)is
2005].al.,et[Meiused

Cdv|v|
)η+h(

Cdv|v|
tanh(0.05(h+η))(h+η)

4.6Smagorinskyhorizontalviscosityterm

(4.29)

(4.30)

TheimplementationoftheSmagorinskyviscosityterm(equation4.31)inTsunaFLASHfollowsthat
oftheunstructuredfiniteelementtsunamimodelTsunAWI[Androsovetal.,2008;Harigetal.,
2008].Thisviscositytermiswidelyusedinhydrodynamicstructuredfinitedifferencenumerical

29

modeling,e.g.Staceyetal.[1995];Mellor[1996,2004];Krestenitisetal.[2007].Itmimicsturbu-
lentprocessesbyapplyingavelocity-dependenteddyviscosity.

Kh=cdxdy(∂u)2+1(∂v+∂u)2+(∂v)2(4.31)
∂x2∂x∂y∂y
Kh,intheequation(4.31),istheSmagorinskyviscosityhorizontal(wave)diffusionparameter
[Smagorinsky,1963],cisadimension-lessconstant.Smagorinsky[1963]originallyusedacoeffi-
cientofc≈0.28,howeverarangeof0.10-0.20isproposedbyMellor[1996,2004],andrangeof
0.01-0.20hasbeenusedbyKrestenitisetal.[2007],0.20isusedbyStaceyetal.[1995],while
Androsovetal.[2008]recommendarangeof0.04-0.40.
Atthispoint,forTsunaFLASH,theSmagorinskyconstantissetto0.30forthesimulationof
theSumatra-Andamanmega-tsunamievent2004(seefigure6.23)and0.001forthesimulationof
theAndamanminortsunami2009(seefigure6.26(b)).
OthertsunamimodelsthatusetheSmagorinskyschemeare:theSmoothedParticleHydro-
dynamics(SPH)codebyRogersandDalrymple[2008],theLargeEddySimulation(LES)model
byWuandLiu[2008],andtheLatticeBoltzmannmodelbyFrandsen[2008b].

30

toolsisualizationV5.1

Chapter5OOLST

TsunaFLASHisequipedwithsomeinterfacestovisualizationtools:animationandsnapshotsof
computationalstatecanbecreatedfromMatlabcompatibleoutputaswellasGMV(GeneralMesh
ieVoutput.wer)

plot.mtsunaflash5.1.1

ThiscodeismeantforplottingtheTsunaFLASHsimulationresults.Thetsunaflashplot.mhave
features:

1.ReadTsunaFLASHsoutput(singleorseries)file(s),

2.Plot3Dsurfsurfaceandmesh,

3.Plot3Dsurfmeshandnodevalues,

4.Plot2Dsurfacefromnodevalues,

5.Plot2Dblackandwhitemeshonly,

6.AutomaticallysaveeachplotasPNGfileseries.

movie.mtsunaflash5.1.2

ThiscodeismeantforanimatingtheTsunaFLASHsimulationresultsfrommatlaboutputformat(file
name:TsunaFlashmatlab.xxxx,[xxxx]=4digitseriesnumber).

rgb2bmp.sh5.1.3

31

Thergb2bmp.shisasimple(UNIX)shellscriptmeantforconvertingimageusingImageMagick
(free)softwarefromImageMagickStudioLLC[1999](http://www.imagemagick.org/).The
imageseriesofTsunaFLASHswhichisplottedinGMV(.rgb)requirestobeconvertedtobe
(Windows)bitmapfiles(.bmp)beforeitsanimated.Theanimation(.AVI)canbedonebyusingthe
(free)softwareofPjBmp2Avi.exe[Roberts,2002].

5.2Analysisandverificationtools

fft.mtsunami5.2.1

Thetsunamifft.m,isaMatlabscriptcombinationofthefunctionofFourierfiltersfromSignell
andList[2005]andthefunctionofFouriersvariationanalysisfromMathworks[2007].Thescript
ismeantforremovingthenon-tsunamieffectstothetimeserieswaterleveldatarecordedbytide
gaugeandbuoy.Non-tsunamieffectcanbeaharmonictidaloscillation,windshear,orotherdis-
turbances,whichmighthaveoccurredduringthetsunamiwavepropagationinthedeepoceanand
shallowwaterregion.
TheFourierfilterisconstructedbasedonWaltersandHeston[1982]thathasprincipalofthe
frequencydomainanalysis.Thelowfrequencyoftidalvariationsandthehighfrequencyofwind
wavestogetherwithothereffectssuchasbedstressinthenearshoreareremovedusingtheband-
passfilter[Dorn,1960a,b,1987;WaltersandHeston,1982;Drushkaetal.,2008].Theremoved
waverange,of60-120secforthehighfrequencyand60-120minutesforlowfrequency,is
followingPranowo[2002].Thefilteredresultsarediscussedinsection7.2andalsousedinsection
6.8.

magnitude.mtsunami5.2.2

tsunamimagnitude.m,isamatlabscript,usedforfurtheranalysesofthesimulationresultsthat
isbasedontheearthquakemomentmagnituderelatedtoatsunamimagnitudescalebasedonIida
[1963]andHatori[1994].TheoutputiswrittentoPNGandPDFfiles.

32

Table5.1:Theempiricalrelationamongtsunamimagnitude,maximumwaveheightandthedamage
[1974]Lisitzinaftercharacteristics,potential

mHmax[m]Damagepotentialcharacteristics
-10.5-0.7Nodamage
01-1.5Verylittledamage
12-3Shoredamage
24-6Someinlanddamageandlossoflife
38-12Severedestructionover400kmofcoast
416-24Severedestructionover500kmofcoast

m=log2Hmax(5.1)
mIida=(2.26Mw)−14.18(5.2)
mHatori=(2.66Mw)−17.5(5.3)
Thetsunamimagnitude(m)canbecalculatedfromthemaximumwaveheight(Hmax)on/near
tothebeachareabyusinganempiricalformula(5.1),whileitsrelationwiththeearthquakemoment
magnitude(Mw)isrepresentedby(mIida)in(5.2),bothareintroducedbyIida[1963].In1994,
Hatori[1994]proposedtheempiricalrelationfor(thelocal)Indonesianregion(mHatori),see(5.3),
wherethismagnitudeisoneuptotwogradeshigherincomparisontootherregionsevenwith
thesameearthquakemomentmagnitude[Tsujietal.,1995].Thequalitativecharacteristicsofthe
tsunamiaccordingtoitsmagnitudeareshownintable5.1.

tseries.mtsunaflash5.2.3

Thiscodeismeantforreading,extractingandplottingTsunaFLASHfileseries.Here,some(virtual)
gaugesorbuoysstationcoordinatescanbedefined.

beach.mrunupcomparetsunaflash5.2.4

33

ThiscodeismeantforplottingtheTsunaFLASHbenchmarkingsimulationresultsusingtheanalyti-
calsolutionofthefirstproblemsetofthe3rdInternationalWorkshoponLong-waveRunupModels
[Liuetal.,2008;Synolakisetal.,2008]),seeSection6.4.Thesimulationcanbecomparedatthe
timeof160sec,175secand220sec.Thecomparisonresultsarediscussedinsection6.4.

sattrack.mcomparetsunaflash5.2.5

ThiscodeismeantforplottingthecomparisonofTsunaFLASHresultswiththeofSumatra-Andaman
mega-tsunami2004eventssatellitetrackdataofJason-1andTopex/Poseidon,bothareinthecycle
of0129,providedbyPMEL/NOAA[Smithetal.,2005].Thecomparisonresultsarediscussedin
7.3.and6.86.7,section

5.3SeaBottomDeformationGenerator

rupdimslip.mtsunami5.3.1

Thiscodeismeanttocomputetheproperrupturedimension(faultlength(L)andwidth(W)),
anaveragedislocation(δ)andalsoananalysisoftheshearrigidity(µ)basedonanearthquake
magnitudescalinglawfromKanamori[1977];HanksandKanamori[1979]andempiricalformulas
fromOkal[2007];WellsandCoppersmith[1994];Papazachosetal.[2004],includingwhatisused
inRuptGen(seesection6.2.3).Theseismicmoment(Mo)and/ormomentmagnitude(Mw)is
neededasaninput,seesection6.2.4forhowtoderivethenecessaryparametersfromtheinformation
mechanisms.focaltheofTheoutputinformation(seeanexampleintable6.5)isusedforgeneratinginitialconditions
w).belo5.3.2section(see

Deform.f90BottomSea5.3.2

ThecodeisbasedontheclassicalstaticbottomdeformationfromMansinhaandSmylie[1971],
wherethedisplacementfieldsofinclinedfaultsareprojectedintothewatersurface.Theinitialcode
waswrittenbyImamura(DCRC,TohokuUniversityJapan)underTIMEProject.Somerevisions
weremadebyworldwidecommunitiesafterward[Imamuraetal.,2006].Theparameterssinput

34

aretheepicentercoordinate(longitudeandlatitude;+=◦Eand◦N,-=◦Wand◦S),dimensionof
rupture(length(L)andwidth(W)),focaldepthofhypocenter(D),strikeangle(y),dipangle(α),
slipangleorrake(λ),andanaveragedislocation(δ).Anexampleoftheparametersareavailablein
table6.4.Theempiricalformulasforgeneratingthefaultparametersarebrieflydiscussedinsection
6.2.4.Theoutputofthistoolwillbeaninitialseasurfacewaveinastructuredformatandneedto
beprojectedintotheunstructurednodes,seesection5.3.3below.

tsunami5.3.3projection.m

Thiscodeismeanttoprojecttheinitialseasurfacewave,inASCIItextstructuredformat,togener-
atedbytheprevioustool(seesection5.3.2)intotheunstructurednodesbeforeitsusedasaninput
model.theto

5.4Initialgridgeneratorforscenarioofrunupinachannel

ThistoolismeanttocreatethechannelgridforTsunaFLASHnecessaryofthesimulationforthe
benchmarkfollowsingthefirstproblemsetofthe3rdInternationalWorkshoponLong-waveRunup
Models[Liuetal.,2008;Synolakisetal.,2008].

6Chapter

35

MODELSETUP,NUMERICALEXPERIMENTRESULTSANDDISCUSSION

InordertostudythebehaviorsofTsunaFLASH,someexperimentshavebeendone.Theseare
experimentswithdiverseinitialconditions,experimentswithdiverseerrorestimatorsorrefinement
criteria,assessmentsoftheadaptationalgorithm(seesection6.5)andthecomputationalspeed(see
6.6).sectionThemodelisverifiedandvalidatedusingananalyticsolutionandobservationaldatafollow-
ingtherecommendationbySynolakisandBernard[2006];Synolakisetal.[2008].TsunaFLASHis
benchmarkedusingananalyticalsolutionofthefirstproblemfromthe3rdInternationalWorkshop
onLong-waveRunupModels[Liuetal.,2008],seesection6.4.Validationwithobservationaldata
iscarriedoutusingtheSumatra-Andamanmega-tsunamiof26December2004andtheAndaman
minortsunamiof10August2009testcases,seesection6.7andsection6.8respectively.
However,thereareotherimportantdatainputcomponentstoconsiderinscientifictsunami
numericalmodeling,whenthemodelisassumedbeingwelltested.Thecomponentsare:

a)thebathymetry/topographydata,

condition,initialtheb)

c)andthedataforverification.

Inthischapter,thebathymetry/topographydatausedisalowresolution(seesection6.1.1).
Thereisanotherexperimentinordertoinvestigatetheinfluenceoftwokindsofbathymetry/toporaphy
resolutioninsection7.1.2.Initialconditionscanbederivedfromthefaultparamaters(seesection
6.2.4and6.8),byemployingarupturegenerator(seesection6.2.3),orbycomputingasourcemodel
6.7).section(see

36

setupModel6.1

6.1.1Bathymetryandtopography

BathymetryandtopographydataarederivedfromGlobalETOPO5,whichhas5arc-minuteres-
olution[NOAA/NGDC,1988].Itiscombinedfromvarioussources,startingwiththeDigital
BathymetryDataBase5arc-minute(DBDB5)in1970,andthenaddingthecoastlinedigitizedby
CentralIntellegenceAgencyofU.Sin1977(knownasWorldDataBaseII),andalsoupdatedwith
modifieddataoftheSyntheticBathymetricProfilingSystem(SYNBAPSII)fromNavalOceano-
graphicOfficeofU.S[YoutseyandWoodyard,1993].In1988,theterrestrialtopographyofthe
DBDB5wasimprovedbyNGDCandknownasETOPO5,whilethebathymetrystayedthesame.It
waspublishedonlinein1993,andonCD-ROMin1995[NOAA/NGDC,1995].

TheGlobalETOPO5iswidelyusedforvariousstudiesandnumericalmodelinge.g.studyof
theeffectsofbathymetrytotsunamipropagation[Satake,1988],sourcemodelingofatsunamigen-
eratedbyanearthquake[Satake,1995;Song,2006],studyofthegeodynamicsofthecrust[Chand
andSubrahmanyam,2003;Tileyetal.,2003],estimationofaruptureprocessoftheSumatra-
Andaman2004earthquake[Ammonetal.,2005],numericalmodeling(simulation)oftsunamiprop-
agation[Gusiakov,2001;Pelinovskyetal.,2001;HarinarayanandHirata,2005;Manojetal.,2006;
Groeveetal.,2006],andtidalmodeling[Zhangetal.,2009].

TheaccuracyanderrorsoftheGlobalETOPO5werediscussedbySmith[1993];Jordahl
etal.[2004];LoschandHeimbach[2007];Sindhuetal.[2007];Kietpawpanetal.[2008].

meshsecoarInitial6.1.2

Forconductingthenumericalexperiments,thefinestrefinementlevelof17and20oftheinitial
coarsemeshareused,seetable6.1.Animageofaninitialcoarsemeshisshowninfigure6.2.Itis
createdusingthemoduleIGG(InitialGridGeneratorforamatos),seesection3.1.Anotherinitial
coarsemesh,forthebenchmarksimulationinsection6.4,iscreatedusingatoolfromsection5.4.

37

Figure6.1:Bathymetry(shownincolour,max.depthof9,923meters)andTopography(shownin

white,max.heightof7,833meters)fromtheGlobalETOPO-5[NOAA/NGDC,1988].

Table6.1:Highestlocalgridresolutioncorrespondstoadaptiverefinementlevel

lengthedgeMinimumResolutionRefinement

elvle

17

20

approx.(km2)

177

22

)mk(approx.

15.4

5.5

38

6.2:Figure

(a)

(c)

IGGproduceforcreatinganinitialcoarsemesh.

(b)

(d)

sequencecompleteThe

here.(a)level01,(b)level04,(c)level17,(d)level20withpunchedoutland.

is

not

wnsho

6.1.3Hardwareandsoftware

39

ThenumericaldevelopmentandexperimentsareperformedonaSunFireX4600M264bitmachine,
singleAMDOpteronDual-coreProcessor(8220)2.8GHz,andSUSELinux(EnterpriseServer10,
ServicePack1)astheoperatingsystem.TheperformanceofTsunaFLASHonthecomputeris
6.6.sectiontheindescribedTheFortran90compilerfromIntel(ifort)isused.ThecompilercontainstheMathKernel
Library(MKL)10.0forLinuxthatprovidesBasicLinearAlgebraSubprograms(BLAS)andLinear
AlgebraPACKage(LAPACK).TheGeneralMeshViewer(GMV)fromLosAlamosNationalLab-
oratory(LANL)USAandMatlabfromMathworksInc.isusedforvisualizationoftheexperiment
results.(simulation)

6.2Experimentonthediverseinitialconditions

TsunaFLASHistestedwithdiverseinitialconditions,suchas:acosinebell(section6.2.1),anelliptic
sourcetomimictheinitialwaveformgeneratedbyanearthquake(section6.2.2),asophisticated
realisticsourceinitialconditionusingtherupturegenerator(RuptGen,seesection6.2.3),andan
experimentalof(precomputed)waveexcitationusingfaultparameters(seesection6.2.4).Ina
separatesection,thebenchmarkofrunuponaslopingbeach(section6.4),usesafunctiontomimic
theinitialwavegeneratedbyanoffshoresubmarinelandslide.

bellCosine6.2.1

Forthefirstnumericalexperiment,acosinebellfunction(seeformula6.1)isusedasaninitial
condition.ItisdeployedinSundaStraitapproximatelyatKrakatoa(bahasa:Krakatau)coordinate
(105.5◦E,6.20◦Sor105.7◦E,6.9◦S).Itshowsthebehavioroftheadaptivegridinpresenceof
reflectingboundaryconditionsandcomplexbathymetry(seefigure6.3).
Theinitialconditionwithcosinebellfunctione.g.byWilliamsonetal.[1992]commonly
usedfortestingadvectionschemesandevaluatingnumericalmethodsofshallowwaterequations
onthesphere.Severalauthorswhoareusethiscosinebelle.g.:Nairetal.[2003]foraDiscontinous
Galerkintransportscheme,Huang[2004]forseveraladvectionschemeon2dimensionalYin-Yang
grids,Jablonowskietal.[2004]andSt-Cyretal.[2008]foranadvectionschemeonadaptivegrids

40

ti(a)0000no.mestep

0500no.esteptim(b)

Figure6.3:ExperimentusingcosinebellinitialconditionsinSundaStrait

forweatherandclimatemodels,whileFlyerandWright[2007]fortransportschemeonthesphere.

η(λ,θ)=(η0/2)(1+cos(πr/R))ifr<R(6.1)
0ifr≥R
whereηisaninitialseasurfaceheight,η0isamaximum(seasurface)height,risradiusof
thegreatcircleordistancebetween(λ,θ)andthebell(epi)center(λc,θc)=(xlon,ylat),R=isthe
earthsradius(6.37122x106m).

sourElliptic6.2.2ce

Theshapeofthetsunamiwaveexcitationisfrequentlymimickedbyshapeofanellipticaluplift
[Lisitzin,1974].Usinganellipticfunctiontomimictheinitialuplift,neglectingthefaultmecha-
nismparameters,wereconstructmoreorlessthecommonexcitationshapeofsingleOkadasplate
[Okada,1985,1992].Thisellipticsourcecontainsanupliftanddepressionarea(seefigure2and
figure3).Aformulaforthisinitialconditionisgivenby:

I(x,y)=sin(x)∗sin(y),(x,y)∈[0,2π]×[0,π](6.2)
EllipticsourcesarealsousedintheIntegratedTsunamiDatabase(ITDB)[ITDB/WLD,2007;

41

Gusiakov,2007].However,itisonlywithsingleupliftordepressionshape.Theconstructionofsuch
asourceisdemonstratedinfigure6.4.Withthissourcepreliminarytestrunshavebeenperformed
intheareaofnorthernSumatra(seefigure6.5).

Figure6.4:Constructionofellipticsourcefromtwosinefunctions

Figure6.5:EllipticsourceappliedinTsunaFLASH

6.2.3Couplingwitharupturegenerator

OnceTsunaFLASHwascompiledandexecuted,itcanautomaticallycommunicatewithRuptGen,a
separatesoftwareproducinganexcitation,seealgorithm6.2.1.RuptGenisaRuptureGenerator,
developedatGFZ-Potsdam,officiallyusedtocreateaninput(initialconditions)toTsunAWI,to
produceGITEWStsunamisimulationsforascenariodatabase.Itcalculatesthesea-floordeforma-
tionduetoco-seismicslipalongtheSundatrenchandrepresentstheplateinterfacebetweenthe

42

subductionareaoftheIndian-AustralianandupperSundaplates[Babeyko,2007;Babeykoetal.,
2008].

ThissophisticatedrupturegeneratorisbasedonelasticdislocationtheoryofOkadasso-
lution[Okada,1985]andtheruptureplateisbasedontheRegionalizedUpperMantle(RUM)
seismicmodel[GudmundssonandSambridge,1998].Theruptureplateisdevidedintorectan-
gularfaultplanes(patches)ofknowngeometryandposition,withadimensionofapproximately
40x15kminaverage,150patchesarepositioned(parallel)alongthetrenchand15patchesare
perpendiculartothetrench.Allinallthereare2250patches,withvaryingfocaldepthsof0-
60km,seefigure6.6.Eachpatchalsocontainsprecomputeddip-slip,strike-slipandsea-floor
deformationcomponentsbasedonWangetal.[2003];constantrake(λ)of90◦,arangeofrigid-
ity(3.17x1010≤µ≤6.69x1010N.m−2),ofdipangles(7.31◦≤α≤43.2◦),andofstrikeangles
(0.164◦≤x≤360◦),dependingonthetrenchgeometry.

Theexcitationorinitialconditioncanbeproducedbydefiningamomentmagnitude(Mw)
andepicenter(asgeographicalcoordinateorpatchcoordinates),byinsertingtheslipvalue(δ);or
byanensembleofsubfaultsasslipdistributions(δ(ξ,y)).Incaseofdefinedamomentmagnitude,
therupturedimensionswillbefirstestimatedusingsubsurfacerupturescalinglawsofWellsand
Coppersmith[1994](seesection5.3.1)andrigidity(µ)of3.5x1010N.m−2resultinginmulti-patches,
whichwillbesymmetric-distributedaroundtheepicenter.Inreality,theepicenterisnotalways
inthecenterofthetotalrupturedimension(e.g.Sumatra-Andamanmega-tsunami26December
2004,Bengkuluminortsunami12September2007),whichmeansthatdefiningaslipdistribution
ismoreexactandreliablethanjustdefiningthemomentmagnitudeandtheepicenter[Jietal.,
2002a,b;Brune,2008].Foranillustrationofthefaultgeometryandparametersseefigure6.9.The
applicationofslipdistributionforthetestcaseoftheSumatra-Andaman2004eventisavailablein
6.7.section

Figure

and

15

6.6:

RuptGen

patches

are

patches

map

perpendicular

along

to

the

the

Sunda

trench,

in

trench,

oerallv

150

are

patches

2250

are

(parallel)

patches

along

o,yk[Babe

the

2007]

43

trench

44

Algorithm6.2.1:COUPLERUPTGEN(nodes,ssh)

1.DumpthenodesfromTsunaFLASH
2.FeedingthenodestoRuptGen
3.RuptGensparameterinterfacedbyrupture.define
4.RuptGenproducingoutputssh
5.FeedingsshbacktoTsunaFLASH

6.2.4Faultparameters

Togeneratetheinitialconditionfromanearthquakeeventmanually,theinformationaboutfocal
mechanismorfaultplanesolutionshouldbeavailablefirst,whereafaultplaneconsistsoftwonodal
planes.Thestoryofhowanearthquakeeventisrepresentedasafocalmechanisminformationis
shownfollowinganorderoffigures6.7,6.8,and6.9.

Uptonow,onlyNEIC-USGSprovidesfocalparametersforpublicaccessonaroutinebasis
bothforrecentshockevents(seehttp://earthquake.usgs.gov/eqcenter/recenteqsww/)and
historicalshockevents(seehttp://neic.usgs.gov/neis/sopar/).Forhistoricalshockevent,
thefaultplanesolutionwillbeprovidedasGlobalCentroidMomentTensorsolution(formerly
knownasHarvardCMTcatalog,since2006movedtoLamont-DohertyEarthObservatory(LDEO)
ofColumbiaUniversity)andUSGScentroidmomenttensorsolution.Thesedifferbythealgorithm
toassesstheparameters.Forourpurposewearefreetochooseone.Followingparametersaregiven:
amomentmagnitude(Mw,nounit),seismicmoment(Mo,inN.m),strikeangle(y,indegree),dip
angle(α,indegree),rakeorslipangle(λ,indegree),focaldepth(D,inmetersorkilometers),
epicenter(ingeographiclongitudeandlatitude),centroidcoordinate(ingeographicallongitudeand
latitude),forbothnodalplanes.Apparently,theepicentercoordinateisnotthesameasthecen-
troids,basedonexperiencethecentroidismorerepresentative.Furtherinformationneededare
therupturedimension(faultlength(L)andwidth(W),bothareinmetersorkilometers)andaslip
amount(δ(ξ),meters),whichshouldbecalculatedusingempiricalformulas.
Theearthquakemagnitudescaleconversion[Kanamori,1977;HanksandKanamori,1979]

45

canbeusedforconvertingaseismicmomentseismic(Mo,inN.m)intoamomentmagnitude(Mw,
dimensionless),seeformula(6.3),orviceversa(6.4).Theseismicmomentcanbeusedtodetermine
thedislocationvalue(δ(ξ),inmeters)withdefinedrupturedimension,usingformula6.7.Inthis
case,shearmodulusorrigidityvalue(µ)(rangeof6-7x1010N.m−2foraninterplateearthquake,
and2-3x1010N.m−2foranintraplateearthquake),definedlength(L,inmeters)andwidth(W,
inmeters)oftherupturedimension,andthemeanvalueofdislocation(δ(ξ)rewriteas(δ),in
meters)shouldbetunedtopreservetheseismicmomentvalue[Aki,1972;KajiuraandShuto,1990;
2004].1994,Kanamori,Tocalculate,theproperrupturedimension(LandW,bothareinkilometers)andthemean
valueofdislocation(δ,inmeters),onecoulduse(6.5),(6.6)and(6.7)respectively.Thoseformulas
arederivedfromtheformula(6.4),andformula(6.3)usingrigidity(µ)of3.0x1011dyne.cm−2
[KanamoriandAnderson,1975],aspectratio(W/L)of0.5[Geller,1976],andamaximumstrain
ratio(δ/L)of5.0x10−5[KanamoriandBrodsky,2004].

2Mw=3(log10Mo−9.1)(6.3)
Mo=µL1Wδ(6.4)
)(3oML=(8.6x104)(6.5)
Mo(31)
W=(1.72x105)(6.6)
Mo(31)
δ=(1.72x106)(6.7)
Inthemeantime,therearevariousempiricalformulas,e.g.WellsandCoppersmith[1994]
andPapazachosetal.[2004].WellsandCoppersmith[1994]providearegressionsrelationship
amongmagnitude,rupture(andsubsurfacerupture)length,rupture(andsubsurfacerupture)width,
rupture(andsubsurfacerupture)area,andsurfacedisplacement(categoriesinstrike-slip,reverse,
normal,andgeneral),derivedfromapprox.244events.Theregressionsamongthemagnitudeand
subsurfacerupturedimensionofWellsandCoppersmith[1994]hasbeenusedbyRuptGen,see
section6.2.3.Papazachosetal.[2004]separatedtheempiricalformulabystrike-slipfaulting,dip-
slipfaultingincontinentalregionsandsubductionregions.Theempiricalformulaswillnotfurther

46

bediscussedinhere,buttheimplementationofthoseempiricalformulasarementionedinsection
5.3.1.Oncethefaultparametersareavailable(seetheexampleintable6.4),thenextstepisto
calculatethestaticdisplacementattheoceanbottombasedondislocationtheory,i.e.Mansinha
andSmylie[1971];MatsuuraandSato[1989];Okada[1985,1992].ThetheoriesofMansinhaand
Smylie[1971]andOkada[1985],aremoreorlesssame,withtheonlydifferencethatOkada[1985]
allowsfortensilecracks[Okal,2007].TheexperimentresultbasedonOkada[1985,1992]forthe
minorAndamantsunami2009eventisprovidedinsection6.8.Thestaticseabottomdeformation
theoryofMansinhaandSmylie[1971]isimplementedasatoolinsection5.3.2.

6.3Experimentonthediverseerrorestimators

Experimentstoassestheperformanceofdiverseerrorestimatorsusedforrefinementcriterionwere
performed.Thereare3differenterrorcriteria:

•Thegradientofseasurfaceheight(ssh)valuewithineachelement(ητ=∇h).

•Theaveragingvalue(ητ=h−h¯),wherehisthetruesshandh¯istheaverageofneighboring
vsshalues.

•Themaximumabsolutevalueofsshvaluewithineachelement(ητ=h).

TheBengkulu12September2007minortsunamiisusedtotestthecriteria.Theexcitationis
generatedbyRuptGen(seesection6.2.3)basedonaslipdistributionfromLoritoetal.[2008],which
preservestheearthquakemagnitudeMw8.4using39subfaults,resultingfromseismicmoment
(Mo)4.52x1021Nm,withamaximumupliftof3.21mandmaximumdepressionof-1.35m.This
seismicmomentisjustabithigherthanLoritoetal.[2008](Mo4.21x1021Nm).
Thegradient-basedcriterion(ητ=∇h)issimpleandeasytocompute,butnotrobust.For
steepseasurfaceelevation(ssh)thegridisrefinedbecauseofabiggradient,whilewhentheprop-
agatedwaveinthedeepwaterbecomeslongthesshgradientlowthenleadstogridcoarsening.
Typicalevolutionofthenumberofnodes,elementsandedgesaredepictedinfigure6.11.While

(b)

(a)

(c)

47

Figure6.7:ThedeterminationofNodalPlanes(NP)inthefocalmechanism;(a)Whenseismic

stationsdetectanearthquake(seeintheleftpanel:thesignalofgroundmotionsillustratedaswhite

andblackdots,andthesymbolofcrossproductistheepicenter),someofthestationswillreceive

asignalofthefirstgroundmotion(compressional,blackdots)andsomeotherstationswillreceive

secondgroundmotion(rarefactional,whitedots).Thedistributionofthefirstmotioncanbeused

todefinethetwonodalplanes,thefirstwouldbetheFaultPlane(NP1)andthesecondshouldbe

AuxiliaryPlane(NP2);(b)Inthis3-dimensionalillustrationofdip-slipearthquakethetwonodal

planesareclearlyrepresented;(c)Imaginaryfocalspherearoundthefaultepicenterisusedfor

projectionofthegroundmotionsdirectionswhichrepresentedbythetwonodalplanestobeafocal

mechanismdiagramknownasbeachball.[CoxandHart,1986;USGS,2009a].Forbeachballcases

6.8.figuresee

48

6.8:Figure

Thesimplecasesofpurenormaldip-slip,reversedip-slip(thrust),andstrike-slipmotion

onafault.Theupperimagesshowblockdiagramsillustratingthefaultmotion;andthelowerimages

thecorrespondingfaultplanesolutionwhichiscommonlyrepresentedasbeachball,theblackarea

ispushingthetensionawayfromthefocalarea(compression,[+]),whilethewhiteareaispulling

thetensiontowardthefocalarea(rarefaction,[-]).[USGS,2009a].

Figure6.9:aultFplaneΣ(

)geometryoftypicalinterplatesubductioninaneearthquakzone49

be-lowtheseafloor;Qisanepicenter,Pishypocenter;FaultlengthisparalleltotheStrike-axis

(y-direction);Faultwidthisparalleltothedip-axis(x-direction).(a)3Dprofileshowsthecontour

ofslipdistribution(δ(ξ,y)

)intheaultfplane.(b)Cross-sectionalwvieoftherupturezonetypeofdip-slip(a≤δ≤b)wherevariableslipisdefinedasδ(ξ)≡[δ+−δ−],whileαisthedipangle.[Geist
1999]wska,Dmoand

50

figure6.10(b)givessnapshotofthesimulationwithsomeemphasisonthegridrefinement.Obvi-
ously,therefinementcriterionisnotcapableofcapturingthewavefront,onceitbecomessmallor
shallow.Therefore,thewavepropagationintothedeepoceanisnotaccuratelycaptured[Pranowo
2008].al.,etTheaveragingbasedcriterion,(ητ=h−h¯),issimple,easy,androbust.Inhere,after
computetheaverageofsshfromnodesofelementssurroundingthetruenode,whileinthisprocess
thetruenodeisexcluded,thenitisusedforsubtracttothesshoftruenode.Whiletheneighborhood
nodecanbeanegative,positiveorzeroofsshvalue.Typicalevolutionofthenumberofnodes,
elementsandedgesisshowninfigure6.12.
Theabsolutemaximumbasedcriterion,(ητ=h),istrivialsinceevensimpler,easierto
computethanpreviouserrorindicators,andquiterobust.Theperformanceoftheresultsisshown
infigure6.13.ThiscriterionisusedforthetestcaseonAceh2004tsunami,whichisvalidatedwith
observationdata(seesection6.7andfigure6.24).

6.4Bechmark:Runuponaslopingbeach

Weusethefirstproblemfromthe3rdInternationalWorkshoponLong-waveRunupModels[Liu
etal.,2008;Synolakisetal.,2008].TheinitialvalueproblemoriginallyisbasedonCarrieretal.
[2003]whointroduces4functionsforinitialwavevalues.WeadopttheN-waveleadingdepression
functiontomimicaninitialwave(η)thatisgeneratedbyanoffshoresubmarinelandslide(seefigure
[2003]:al.etCarrier6.15(a))

η=a1exp{−k1(x−x1)2}−a2exp{−k2(x−x2)2}
with{a1=1a2=0.006,
3a2=0.018,
1k1=9k2=0.4444,
k2=4.0,
x1=4.1209,
x2=1.6384}

(6.8)

(a)

(c)

(b)

(d)

51

Figure6.10:ExperimentswiththediverseerrorindicatorsusingBengkulu2007minortsunami.(a)

Inhomogeneousinitialupliftattimestepno.0000;(b)Gridattimestepno.9975,using(ητ=
∇h);(c)Gridattimestepno.9975,criterion:(ητ=h−h¯);(d)Gridattimestepno.9975,
criterion:(ητ=h)

52

Figureiterationinner(a)

(c)globalmax.andmin.seasurfaceheight

6.11:Experimenterroranasindicator

resultsusinggradientaluevofseawnunkno(b)(DOF)

elocityvmaximumglobal(d)

acesurfheightatelement(ητ=∇h)

iterationinner(a)

(c)globalmax.andmin.seasurfaceheight

Figure6.12:Experimentresultsusingvaeragingwnunkno(b)(DOF)

elocityvmaximumglobal(d)

(ητ=h−h¯)asanerrorindicator

53

54

(a)iterationinner

(c)globalmax.andmin.seasurfaceheight

(DOF)wnunkno(b)

vmaximumglobal(d)elocity

Figure6.13:Experimentresultsusingthemaximumabsolutevalueofseasurfaceheightatelement

(ητ=h)

asanerrorindicator

56

(a)

(b)

Figure6.15:Waveformof(a)equation6.8[Carrieretal.,2003],(b)initialconditionforTsuna-
2008]al.,et[LiuFLASH

isusedinhere.Seefigure6.19,6.20,and6.21.

Theexperimentresultsshowsignificantperformancesofthemeshrefinementandcoarsening
process,includingthestabilityforalladaptionalgorithmsusingFGL=10CGL=9withTOR=0.07
TOC=0.05.Goodagreementwiththeanalyticalsolutionisshowninfigures6.19(c),6.20(c),and
6.21(c).Theagreementisconsistentwiththescenariowithanon-adaptivemesh(FGL=CGL=9),
6.18.figuresee

Weemployanempiricalcorrelationcoefficientstoanalysethedifferentalgorithms.Thesce-
nariosimulationofTOR=0.07TOC=0.05isused,andtheresultisshowninfigure6.17.Thesimu-
lationsandanalyticalsolutions,ingeneral,arehighlycorrelated.Linearcorrelationincreaseswith
higherrefinementofthegridlevels.Byusingthiscorrelationalso,theeffectofdiverseadaptation
wn.shoclearlyisalgorithm

Theadaptationalgorithm(6.5.1)and(6.5.3)showstheexpectedresults,thatanapplicationof
theadaptivemethodhasbeensuccessful.ItisindicatedthatthecorrelationresultsoftheFGL=10
CGL=9simulationarealmostthesameasthenon-adaptivesimulationatT=160sandT=175s,but
afterlongersimulationtime(T=220s)showsevenbetterresultsthannon-adaptive.

Figure6.16:

sec160=T(a)

(b)sec175=T

sec220=T(c)

57

ThebenchmarkresultsofTsunaFLASHusingthefirstproblem-setofIWLRM[Liu

etal.,2008]:runupontheplanebeachtotheanalyticalsolutionthatperformsagoodagreement.

Blacksolidlinerepresentsbeach1/

10slope,reddotisthemodelsimulationresult,whilebluesolidlineistheanalyticalsolution.ThissimulationusesfollowingparametersFGL=10CGL=9

TOR=0.07TOC=0.05,errorindicatorητ=h,andadaptationalgorithm(6.5.1)

τ=

58

Figure6.17:CorrelationbetweenTsunaFLASHsimulationandanalyticalsolutionfordifferentadap-

tationalgorithmsandgridlevels.

160=t(a)sec

sec175=t(b)

=t(c)sec220

Figure6.18:ThebenchmarkresultsofTsunaFLASHusingthefirstproblem-setofIWLRM[Liu

etal.,2008]:runupontheplanebeachtotheanalyticalsolutionthatperformsagoodagreement.
Blacksolidlinerepresentsbeach1/10slope,reddotisthemodelsimulationresult,whilebluesolid
lineistheanalyticalsolution.ThissimulationusesfollowingparametersFGL=9CGL=9TOR=0.07
TOC=0.05,errorindicatorητ=h,andadaptationalgorithm(6.5.1)

Algorithm6.5.1:OLD(t,reset,update,adapt)

t←t+Δt
lrefine=true
whilelrefinedanditer<max
reset(t,t−Δt)
doupdate
adapt(lrefined)
return(t)

Algorithm6.5.2:PROPOSAL01(t,reset,update,adapt)

t←t+Δt
lrefine=true
whilelrefinedanditer<max
reset(t,t−Δt)
doupdate
adapt(lrefined)
iflrefined=true
thenreset(t,t−Δt)
update
return(t)

59

60

(a)FGL=9CGL=5TOR=0.07TOC=0.05

(b)FGL=9CGL=5TOR=0.05TOC=0.04

(c)FGL=10CGL=9TOR=0.07TOC=0.05

(d)FGL=10CGL=9TOR=0.05TOC=0.04

Figure6.19:TsunaFLASHverificationforrunupontheplanebeachtestcase.Comparisontothe

analyticalsolution,usinganerrorindicatorofητ=h,andalgorithm6.5.1,theresultof(c)
FGL=10CGL=9TOR=0.07TOC=0.05showsgoodagreement.EachpanelshowsT=160sec,

T=175sec,T=220secrespectivelyfromlefttoright;blacksolidlinerepresentsbeach1/10slope,

reddotrepresentsthemodel,whilebluesolidlineistheanalyticalsolution.

(a)FGL=9CGL=5TOR=0.07TOC=0.05

(b)FGL=9CGL=5TOR=0.05TOC=0.04

(c)FGL=10CGL=9TOR=0.07TOC=0.05

(d)FGL=10CGL=9TOR=0.05TOC=0.04

61

Figure6.20:TsunaFLASHverificationforrunupontheplanebeachtestcase.Comparisontothe

analyticalsolution,usinganerrorindicatorofητ=h,andalgorithm6.5.2,theresultof(c)
FGL=10CGL=9TOR=0.07TOC=0.05showsgoodagreement.EachpanelshowsT=160sec,

T=175sec,T=220secvrespectielyfromlefttoright;blacksolidlinerepresentsbeachreddotrepresentsthemodelresults,whilebluesolidlineistheanalyticalsolution.

1slope,10/

62

Algorithm6.5.3:PROPOSAL02(t,reset,update,adapt)

t←t+Δt
lrefine=true
whilelrefinedanditer<max
reset(t,t−Δt)
ifiter=1
dothenadapt(lrefined)
iflrefined=true
thenupdate
adapt(lrefined)
iflrefined=true
thenreset(t,t−Δt)
update
return(t)

speedComputational6.6

Inordertoassessthecomputationalspeedthebenchmarksimulation(section6.4)isused.Tsuna-
FLASHisexecutedonasingleAMDOpteron2.8GHzprocessorwiththeexplicitnon-adaptive
scheme(FGL=CGL=9).Theexperimenttakes22minutesCPUtimefor600secsimulation(0.1
secoftimesteps)with66,719ofunknowns(DOFs).Forthesamesimulationbutusinganadaptive
scheme(FGL=10CGL=9)takes26minCPUtime(givemax.84,575unknownsandmin68,879
unknowns),andFGL=9CGL=5experimenttakes5minutesCPUtime(givemax.26,183unknowns
andmin.6,830unknowns).Thesimulationsareperformedwithoutprintinganyoutputfiles(ASCII
formatforGMVandMatlab).Whenthesimulationisconfiguredtoproduceoutputfiles(inbothfor-
mat),thisisaddingmoreCPUtime;+2minutesforCGL=FGL=9,+5minutesforCGL=5FGL=9,
and+4minutesforCGL=9FGL=10.Thesummaryisshownintable6.2.
Otherauthorsperformingcomputationalspeedexperimentswiththesamebenchmarkprob-

(a)FGL=9CGL=5TOR=0.07TOC=0.05

(b)FGL=9CGL=5TOR=0.05TOC=0.04

(c)FGL=10CGL=9TOR=0.07TOC=0.05

(d)FGL=10CGL=9TOR=0.05TOC=0.04

63

Figure6.21:TsunaFLASHverificationforrunupontheplanebeachtestcase.Comparisontothe

analyticalsolution,usinganerrorindicatorofητ=h,andalgorithm6.5.3,theresultof(c)
FGL=10CGL=9TOR=0.07TOC=0.05showsgoodagreement.EachpanelshowsT=160sec,

T=175sec,T=220secvrespectielyfromlefttoright;blacksolidlinerepresentsbeachreddotrepresentsthemodelresults,whilebluesolidlineistheanalyticalsolution.

1/slope,10

64

Table6.2:Computationalspeedresultsofthebenchmarkproblemset-1(600sectime)simulation

Max.Min.Max.Min.CPUtime
No.ExperimentNodesNodesUnknownUnknowns[minutes]

1.CGL=5FGL=93,02783226,1836,83012
2.CGL=9FGL=97,6337,63366,71966,71924
3.CGL=9FGL=109,6177,87384,57568,87928

lemset-1e.g.Frandsen[2008a];Pedersen[2008];ZhangandBaptista[2008].Frandsen[2008a]
executedthesimulationusingLatticeBoltzmannModel(StandardLBMon100,000nodesand
2nd-orderFiniteDifferenceson5,000nodes)onastandardPC3.0GHzprocessor.Theyreport
1.862hoursCPUtime,whilePedersen[2008]executesthesimulationusingaBoussinesqscheme
on3,171nodes,whichtookonlyapprox.30secCPUtime.However,itwasnotmentionedwhat
kindofcomputer/processorwasused.ZhangandBaptista[2008]usingtheSELFE(Semi-implicit
Eulerian-LagrangianFinite-Element)modelreport16hoursCPUtimeonasingleAMDOpteron
2.2GHzprocessorfor600secnon-adaptivesimulationwith176,011nodes.Seetable6.3.

6.7TestcaseonSumatra-Andamanmegatsunami2004

Severalauthorsproposedsourcemodels,whichisreconstructtheruptureprocessofAcehtsunami
2004,e.g.:Wattsetal.[2005],Layetal.[2005],Ammonetal.[2005],Hirataetal.[2006],Tanioka
etal.[2006],Banerjeeetal.[2007],Vallee´[2007],Rhieetal.[2007],Sørensenetal.[2007],H´ebert
etal.[2007],Chliehetal.[2007],FujiiandSatake[2007],PiatanesiandLorito[2007]andHoechner
[2008].al.etWhileGeorgeandLeVeque[2006]employdynamicmotionoftheseafloorbottombasedon
Ammonetal.[2005]forgeneratingtheinitialconditionrelatedtotheAndaman-Sumatratsunamiof
2004fortheiradaptivesimulation,weuseRuptGen(seesection6.2.3).Ourslipdistributionfollows
oneofHoechnersschemes[Hoechneretal.,2008]whichisanimprovedresulttotheGPSinversion
databasedupliftfromBanerjeeetal.[2007].Thecorrespondingcoseismicslipdistributionserves

65

Table6.3:Computationalspeedresultsofthebenchmarkproblemset-1simulationdonebyother
authors

No.ExperimentNodesCPUtime[minutes]

SELFE1.176,011[2008]BaptistaandZhangLBMStandard2.100,000[2008a]Frandsen-FD2nd-order3.5,000[2008a]FrandsenBoussinesqNLSW4.3,171[2008]Pedersen

960

112

33

30

ascomplexinputtoRuptGenandresultsinatotalseismicmoment(Mo)7.19x1022Nmconstructed
from574ruptures,correspondingtoamomentmagnitude(Mw)9.17,whichcomparewellwiththe
Mw9.2usedinTitovetal.[2005],Mw9.15fromChliehetal.[2007]andMw9.14asinGeistetal.
[2007].themaximumupliftis5.87mandmaximumdepressionis-2.16m.Thetotalexcitationis
showninfigure6.22(a).ThisexcitationshapemoreorlesscorrespondstotheshapeinGeistetal.
[2007].Fromtheexperimentusingagradientbasedcriterion,(ητ=∇h),withsomeemphasis
onthegridrefinement.Obviously,therefinementcriterionisnotcapableofcapturingthewave
front,onceitbecomessmallorshallow.Therefore,thewavepropagationintothedeepoceanisnot
accuratelycaptured[Pranowoetal.,2008].
Twosimulationsusingtheabsolutemaximumsshbasedcriterion,(ητ=h),givesignificant
propagation.BoththesimulationsdifferbytheapplicationofSmagorinskyviscosityandconstant
visosity,respectively,seefigure6.22and6.23.ThecombinationofFGL=9CGL=2,TOR=0.007
TOC=0.005,andSmagorinskyconstantof0.3probablyyieldsthebestrefinementandcoarsening
mesh.

66

Inordertovalidateagaintsobservationdata,weusesatellitetracks(figure6.24)whichare
providedbyPMEL/NOAA[Smithetal.,2005].Theresultsshow,ingeneral,thatseasurface
elevationfromTsunaFLASHfitsobservationsinthenorthernpart,whileinthesouthernpartcor-
respondenceisnotsogood.However,inthesouthernpart,thedoublepeakevensmallisvisible,
whencomparingtotheJason-1track(figure6.24(b)).Whileseasurfaceelevationcorrespondswell
withmeasurementsfromtheTopex/Poseidontrack(figure6.24(c)),thearrivaltimesofsimulated
leadingwavearelateforbothtracks.

6.8TestcaseonAndamanminortsunami2009

On10August200919:56UTCaminortsunamiwastriggeredbyanearthquake,withitsepicenter
at(92.885◦Eand14.096◦N)closetothenorthernendoftherupturezoneoftheSumatra-Andaman
mega-tsunamiof26December2004.Severalvaluesformomentmagnitudeandhypocenterdepth
werereportedby:GFZPotsdam(Mw7.4at67kmdepth),USGS(Mw7.6at33.1kmdepth),JMA
(Mw7.7),andPTWC(Mw7.7).PTWCissuedatsunamiwarningviaemailsRSSfeedat20:06
UTC,5minutesaftertheearthquakeinformationmessagefromGeofonGFZ-Potsdam(20:01UTC).
At22:12UTCPTWCsentatsunamiwarningcancellation.Eventhoughtherewerenosignificant
waterlevelchangesdetectedbythenearestbottompressureunitandtidegaugesattheAndaman
IslandsonIndianteritoryaccordingtoINCOISat21:15UTC,aminortsunamiwasdetectedby
23401.TARDThefocalmechanismoftheearthquakeMw7.5(Mo2.62x1020N.m)isobtainedfromUSGS
(seesection6.2.4).Theaveragedislocationiscalculatedbyassumingashearmodulusorrigidity
(µ)of3.5x1010N.m−2or35GPa,andrupturedimension(50x50km)isdefinedusingOkal[2007]
withanexperimentallyaspectratio(W/L)of1insteadofsomeproperaspectratiosattable6.5.The
completefaultparameters,usedforcreatingtheinitialconditions,areprovidedinatable6.4.
Thecalculatedaveragedislocationofthisintraplateevent(2.99m)issimilartothevalue
estimatedbyPapazachosetal.[2004]forstrike-slipfaulttype(3.236m)withrigidityof30.200
GPa.ThemeanvalueofdislocationandtherigiditygivenbyOkal[2007]isinthesamerangeas
inPapazachosetal.[2004]fordip-slipfaultatthesubductionregion,whilethedislocationgivenin
WellsandCoppersmith[1994]istoohigh,ortherigidityistoosmall,forthiskindofevent(seetable

(a)t=0min

(c)min24=t

hours1.6=t(e)

min12=t(b)

hour1=t(d)

hours2=t(f)

67

Figure6.22:Experimentresults,usingabsolutemaximumbasedcriterion,(ητ=h)asanerror
estimator,FGL=9CGL=2,TOR=0.007TOC=0.001,onAceh2004forthetestcase.Thesealevel

colorscaleusedisforbettervisualization,whereactualmaximumupliftis5.87metersandmaxi-

mumdepressionis-2.16meters.Inheretherefinementisclearlyshownwhilecoarseningdoesnot

.occur

68

min0=t(a)

hours1.2=t(c)

(b)t=28min

(d)hours2=t

Figure6.23:Experimentresults,usingabsolutemaximumbasedcriterion(ητ=h)aserrores-
timator,FGL=9CGL=2,TOR=0.007TOC=0.005,Smagorinskyconstantof0.3,onAceh2004for

testcase.Thesealevelcolorscaleusedisforbettervisualization,whereactualmax.upliftis5.87

metersandmaximaldepressionis-2.16meters.Inhere,thecoarseningisclearlyshownaswellthe

refinement.

Figure

6.24:

(b)2004;Its

TsunaFLASH

erificationv

for

(a)

(b)

(c)

2004Aceh

ent.ve

verificationwithJason-1;(c)Itsverificationwith

(a)

Satellite

tracks

on

26

69

December

Topex/Poseidon;At(b)and(c)blue

linerepresentsobservationaldata,redlinerepresentsmodeldata.

70

Table6.4:FaultparametersoftheexcitationforAndamanminortsunami2009simulationfroman
earthquakemagnitude(Mw)of7.5

ParameterUnitValueReference
USGS92.885E◦LongitudeUSGS14.096N◦LatitudeUSGS20km(D)DepthStrike(y)◦63USGS
Dip(α)◦64USGS
Rake(λ)◦-61USGS
Defined50km(L)LengthWidth(W)km50Defined
Dislocation(δ)m2.99Calculated

6.5).Itproducesmaximumupliftof0.1632mandmaximumdepressionof-0.7250m.However,
thosemaximumvaluesbecome0.1480mand-0.2448mforupliftanddepression,respectively,
whenprojectedintotheinitialmeshnodes(21,393nodes).Thenumberofnodesgrowsto213,955
nodesafter139.50minutesofsimulationtime.Seefigure6.25.
TheDARTbuoy23401hadachancetorecordthetsunamiwave.Twomethodsareusedfor
removingtidalperiodvariationsfromthetimeseriesdata.Thefirstmethodistosubtractthetidal
variationinusingtidepredictiontimeseriesvalues[EgbertandErofeeva,2002;Egbertetal.,1994].
Thesecondmethod,thetidalvariationsareconsideredlowfrequencycomponentsandwindwaves
togetherwithotherbedstressesinthenearshoreashighfrequencycomponents.Bothperturbation
areremovedusingband-passfilters[Dorn,1960a,b,1987;WaltersandHeston,1982;Drushkaetal.,
2008](seethefiltertoolinsection5.2.1andfurthertestingapplicationinsection7.2).Theresults
ofbothmethodsdiffersignificantly,seefigure(6.26(a)).Thesubtractedone(greensolidline)is
stillcontaininghighfrequencycomponents.Weusethefilteredtimeseries(blacksolidline)asit
resemblesthetimeseriespublishedattheNOAAhomepage[NOAA/NCTR/PMEL,2009].

71

Table6.5:Thecomputationresultsoftheasinglerupturedimension,anaveragedislocation
andshearrigidity,totheMw7.5(USGS)orMo2.239x1020N.m[Kanamori,1977;Hanksand
Kanamori,1979],basedonvariousempiricalformulas(seesection5.3.1)

ReferenceNo.

1.2.

3.

4.

5.

6.

[2007]Okal[1994]CoppersmithandellsW

[1994]CoppersmithandellsW

modifiedbyBabeyko[2007]

etapazachosP[2004]al.

aultfe-slipstrik[2004]al.etapazachosP

dip-slipfaultatcontinentalregion

etapazachosP[2004]al.

dip-slipfaultatsubductionregion

W/LL[km]W[km]δ[m]µ[GPa]

0.50.3

0.3

0.1

0.3

0.6

1.95833.80367.60650.0234.95633.798124.15410.765

-29.17485.114-

30.2003.23617.179133.352

30.2003.80225.11977.625

50.1191.04749.54586.099

72

Thesimulationresultsdisplayonlyverysmallbumpinfrontofthefirstwave-through(see

figure6.26(b)).WeuseaSmagorinskyconstantof0.001.Thearrivaltimeislaterthaninthe

TsunAWIsimulationaswellasintheDART23401timeseries(seefigure6.26(a)).However,after

≈21:15UTCthewaveshapeiswellcaptured.Thedeviationfromthedataprobablyresultsfrom
theuncertaintyintheinitialcondition,e.g.therupturedimensionandthedislocationsofthesame

earthquakemagnitude(Mw)of7.5willhavediffervaluesbasedonvariousempiricalformulas(see

table6.5).TheSmagorinskyhorizontaldiffusionparametermayalsocontributetotheuncertainty

andmayneedfurtherinvestigation(seesection4.6).

(a)t=0.00min

(c)min55.80=t

min111.60=t(e)

min27.90=t(b)

min83.70=t(d)

min139.50=t(f)

73

Figure6.25:WavepropagationfollowedbygridevolutionduringsimulationforAndamanminor

tsunami10August2009event.Theinitialconditionhasmaximumelevationof0.1480mand

minimumelevationof-0.2448m.

74

Figure

6.26:

(a)

August102009

Comparison

of

TsunaFLASHeventtotheobservationdata

smallbumpisshownin

area).red-dash-circled

simulationthe

simulation

results

for

the

Andaman

minor

tsunami

ofDART23401andTsunAWImodelresults.(b)A

whenresult

using

constantySmagorinsk

0.001,of

(see

the

7Chapter

TSRESULMISCELLANEOUS

75

Thischaptercollectsmiscellaneousexperimentofresultsobtainedduringthethesisproject
duetostudyingthesourcemodel(seesection6.2.3andsection6.2.4),andtoolsdevelopment(See
section5.2.1).HereweuseTsunAWI[Behrens,2007,2008;Harigetal.,2008]throughoutsection
7.1describesexperimentsonthePadang(next)futuretsunamiusingRuptGen[Babeyko,2007;
Babeykoetal.,2008],section7.2isfortheexperimentonfilteringgaugedata,andsection7.3
containstheinvestigationonthediversesourcemodelsfortheSumatra-Andamanmega-tsunami.

7.1ExperimentonthePadang(next)futuretsunami

AftertheSumatra-Andamanmega-tsunami2004whichwasfollowedbytheNiastsunamiin2005,
thecommunitiesaregirdingforthenextkillerwavestrikingalongthecoastalareaofPadang-
Bengkuluregion,causedbytheSundamegathrustfault[StoneandKerr,2005].Somenumeri-
calsimulationtostudythenextmega-tsunamiintheregionhasbeenpublishede.g.Borreroetal.
[2006];McCloskeyetal.[2008,2010].CurrentlywesternSumatraisdrawingtheattentionofscien-
tists(i.e.GITEWSprojectchoosingthePadangregionasoneofthepilotareas[Khomarudinetal.,
2010],andLast-mileEvacuationprojectpreparingtheevacuationmapforPadangcity[Taubenb¨ok
etal.,2009]),sinceinterplatestresshasbeenalreadyreleasedbytheBengkuluearthquakeand
tsunamion12September2007eventLoritoetal.[2008];Borreroetal.[2009];Pranowoand
Kongko[2009];followedbyseveralrecentearthquakesepicentersinMentawaibasinon16Au-
gust2009Mw6.6(USGS),on30September2009Mw7.5(USGS),and23December2009Mw
6.0(USGS).AccordingtotheSeismologists,KerrySieh(EarthObservatoryofSingapore)andJohn
McCloskey(UniversityofUlsterinColeraine,NorthernIreland),eventhoughsomestresshadbeen
releasedrecentlyin2009,amuchbiggerearthquakeisprobablewithinthenextfewdecadessince
allthestrainisstillthere,wherethemega-thrustunderSiberutislandhasnotrupturedsince1797
[Bowden,2009;Bhattacharya,2009;McCloskeyetal.,2010].

76

7.1.1Reconstructionofthesourcemodel

InAugust23-262009,theInternationalSeminarontheOfficialTsunamiHazardMapandtheInter-
nationalSeminaronEarthquakeandTsunamiPadang,wereheldattheAndalasUnversity,Padang,
Indonesia.Natawidjaja[2008]proposedaslipdistributionforthemostprobablefortsunamisource
Padang,afterChliehetal.[2008],whichislessthantheruptureareainthe1883event(Mw8.9-
9.1)[Natawidjajaetal.,2006]butprobablyclosetothe1797event(Mw8.5-8.7)McCloskeyetal.
[2010].ThesourcemodelisderivedfromthegeodeticdataofSuGAr(SumatraGPSAray)whichis
measureddailyandalsopaleo-geodeticdata,whichwasrecordedfromthecoralmicro-atolwestof
Sumatra.Weconductedanexperimenttoreconstructwhatwasproposedinthe(slide)presentation
(figure7.1(a)),by201rupturesutilizingtheRuptGen[Babeyko,2007;Babeykoetal.,2008].This
manualreconstructionwasnecessary,sincetheoriginalsourcedatawasnotdisclosedatthattime.
ThisexperimentstillneglectedtheinfluenceoftheMentawaiearthquake(Mw6.6)16August2009,
(Mw7.5)30September2009,and(Mw6.0)23December2009sincethemega-thrustsaccumulated
stressunderMentawaiislandsdidnotrelaxaccordingtoMcCloskeyetal.[2010].

Thereconstructionresultsofthetotalmomentmagnitude(Mw)8.92353,moreorless,is
nearlythesametowhatNatawidjaja[2008]sproposed(max.Mw8.9),showninfigure7.1(b)and
7.1(c),whiletheexcitationisshowninfigure7.2(a).

Toreconstructthetotalmomentmagnitudetotheproposedminimum(Mw8.8),wesubtract
oftheMw8.92353scenariotheslipdistributionoftheBengkulu12September2007earthquake
fromLoritoetal.[2008]andobtainMw8.87359.Thedetailsof201rupturesforMw8.87359are
availableintableB.1andB.2,seealsotheexcitationresultinfigure7.2(b).

Interseismiccouplingcoefficientsrangefrom0(fullydecoupledpatchescreepingatthecon-
vergenceplate)to1(fullycoupledorfullylockedpatches)[KatoandSeno,2003;Chliehetal.,
2008].Thecouplingmapreferenceandthereconstructionresults,infigure7.1(a)-leftandfig-
ure7.1(b),showthatbeneaththeislandofSiberut,Sipora,andPagaistronginterplatecoupling
ispresentthereforethefaultisstronglylockedandthehighestpotentialofaccumulatedstressis
available.Thispotentialisrepresentedbytheprobableofaccumulationslipforthe(next)futurebig
earthquakeandtriggerthetsunami,seefigure7.1(a)-rightand7.1(c).

(a)CouplingandslipdistributionproposedbyNatawidjaja[2008]afterChliehetal.[2008]

(b)Reconstructionresultofthecoupling

(c)Reconstructionresultoftheslip(andtheexcitation)

77

Figure7.1:ThereliablecouplingandslipdistributionforthesourceofPadangearthquakeforthe

(next)futureproposedbyNatawidjaja[2008]afterChliehetal.[2008]whichlocatedinfrontof

PadangregionwithmomentmagnituderangeofMw8.8-8.9,see(a);Thereconstructionresult,

usingRuptGen[Babeyko,2007;Babeykoetal.,2008],oftheinterseismiccoupling(b)andslip

distributionandthecontourofexcitation(c)withouttheBengkuluearthquake12Septemberis

takingintoaccount,totalmomentmagnitudeisMw8.92353.

78

(a)TheinitialconditionofMw8.92353

(b)TheinitialconditionofMw8.87359

Figure7.2:(a)Mw8.92353;(b)Mw8.87359afteromitthemomenmagnitudeofBengkulu12
September2007earthquake,seethedetailsofthesourceparameterintableB.1andB.2

7.1.2ComparisononthetopographyofSRTMandHRSC

Thenextstepoftheexperimentistorunthesimulationbasedonthereconstructionsourcemodel
ofsection7.1.1,usingTsunAWI[Behrens,2007,2008;Harigetal.,2008],toassesstheimpactto
Padangcity.Twokindsoftopographydata-setsareused,i.e.thehighresolution(50metersres.of
HRSC)[DLR/RSSGmbH,2007]andlowresolution(1minuteres.ofSRTM)[DLR,2003].HRSC
dataiscapturedbyaHighResolutingStereo-graphicCamera,installedonanaircraft[Schlurmann,
2010],whileSRTMdataismeasuredbyShuttleRadarTopographymissionusingX-bandandC-
band.Thedifferencesofbothdatasetsareshownbyfigure7.3,wherethelevelofdetailinHRSC
inqualitativelyvisibleby3canalsandmoredetailscomparedtoSRTM(seefigure7.3(a)).Indeed
quantitativelytheexampleofaprofileatLatitudeof-0.950showsthatinthecoastalareathetwo
datasetshavedifferencesofapprox.10meters(seefigure7.3(b)and7.3(c)).

Thesimulationresultbasedontheslipdistributioninfigure7.1(c)representingMw8.92353
showsthatsignificantinundationinPadangcityandsurroundingsarecausedbyhighlevelofdetail
andthelowerprofileisinthescenariousingHRSCdata-set,seefigure7.4(a).Theinundationresults

79

basedonthescenarioofMw8.87359(seethesourceparamatersattableB.1andB.2;andtheinitial
conditioninfigure7.2(b))donotdiffermuchfromthepreviousone.ThescenariousingtheSRTM
data-setdoesnotexposelargeinundation(figure7.4),probablybecausethelandelevationdatais
stillcontainingfaultyelevationduetoreflectionfromthetopoftressandbuildings.

7.2ExperimentonfilteringgaugesdataofJavaminortsunami2009event

Aminortsunamiwavesignalwascapturedbygaugeson02September2009thatwastriggered
byaMw7.0earthquakewith(mostly)reversedip-slipcharacteristicwithsomestrike-slip(NP1:
Strike(y)of54◦,Dip(α)of39◦,Rake(λ)of112◦;NP2:Strike(y)of206◦,Dip(α)of55◦,
Rake(λ)of73◦;seeSection6.2.4forthedescriptionoffaultparameters)southofJavaat07:55
UTC[USGS,2009b],orat14:55WIB[BMKG,2009].Thiseventcausedalotofdiscussioninthe
GITEWScommunity,becauseitshowedanarrivaltimeofzerointhetimeofsimulationforthe
TEWSscenariodatabase.TheambiguityaboutthearrivaltimedefinitionregardingtotheTEWS
isdiscussedinBehrens[2009],whichdefinitionissuitabletobeusedforthescenariomatching
scheme.Generally,thearrivaltimeofatsunamitriggeredbyadip-slipearthquakeisquitesignificant
toberecognizedbutnotforitstriggeredbythestrike-slip.Here,thequestionisaddressedtofind
theuniquearrivaltimeofthe(unique)near-fieldminortsunamitriggeredbyastrike-slipearth-
quake.Thissubjectisinitiallyforthenextfurtherresearch,sincewehavedifficultytointerpretdata
fromcoastal/harborgauges.Here,weneedtoolsforanalysisandalsoneedmoredataexamplesto
understand.Weshowoneexampleofthecase.
Forthisexperiment,thetimeseriesofwaterleveldatafromtwonear-fieldstations(i.e.Pame-
ungpeukandPelabuhanRatu,BakosurtanalStations)andtwofar-fieldstations(i.e.Prigi2and
Christmasisland)totheepicenterat107.396◦Eand7.825◦S(seefigure7.6),areanalysedusinga
tooltsunamifft.matthesection5.2.1.
ThemaximumwaterlevelresidualinPameungpeuk(StationID:PAME)isat15:12WIB
or08:12UTC(7minutesaftermainshockoftheearthquake),maximumperiod(33.1min)is2
minutesafterthemainshock(14:57WIB/07:57UTC),andthepowerfrequencyis5hours8min-
utesafterthemainshock(19:03WIB/12:03UTC)atfloodtide,seefigure7.7.InPelabuhanRatu

80

Figure

7.3:

(b)

-0.950LatitudeatHRSC

Theexampleoftheprofile

wvie3D(a)

theofsnapshot

(c)

-0.950LatitudeatTMSR

topographydataof(a)HRSC

[DLR/RSS

GmbH,2007];(b)SRTM[DLR,2003].ItshowsthattheHRSCprofileismuchdifferenttothe

TM,SRwhereattheLatitudeof0.950◦

Shasferencesdifabout10metersatthecoastalarea.

Figure

7.4:

ofscenario

Inundation

results

using8.92353,wM

2003].[DLR,

of

the

(a)

(b)

simulation,

ofdataytopograph

based

on

HRSC(a)

the

slip

utiondistrib

in

figure

[DLR/RSS(b)2007];GmbH,

81

7.1(c),

TMSR

82

(StationID:PELA),themaximumwaterlevelresidualisat15:33WIBor08:33UTC(38minutes
aftermainshockoftheearthquake),maximumperiod(33.1min)is2minutesafterthemainshock
(14:57WIB/07:57UTC),andthepowerfrequencyis9hours56minutesafterthemainshock(23:51
WIB/16:51UTC)atebbtide,seefigure7.8.ThemaximumofwaterlevelresidualinChristmasis-
land(StationID:Christmas)isat15:34WIBor08:34UTC(39minutesaftermainshockofthe
earthquake),seefigure7.10.InPrigi(StationID:PRIGI2),themaximumofwaterlevelresidualis
at19:39WIBor12:39UTC(4hours44minutesaftermainshockoftheearthquake),seefigure7.9.

Thediscussionisnowfocusedonthetwonear-fieldstations(i.e.PameungpeukandPelabuhan
Ratu),sincethetwofar-fieldstations(i.e.Prigi2andChristmasisland)isactuallystillhardlytodis-
cussedandneedfurtherinvestigation.Ifthearrivaltimeisderivedfromthefirstmaximumof
residualwaterlevelreachingthestations[UNESCO−IOC,2006a],thenPamengpeukisreachedat
15:02WIB/08:02UTC(12.170cmheight)andPelabuhanRatuat15:11WIB/08:11UTC(07.710
cmheight).Thebathymetryintheregionoftheepicenter,isapproximatelybetween1500mand
1700mdeep.Thus,thewavephasespeed(c=√g.h,g=gravitationalacceleration=9.8m.s−2,
h=waterdepth)isabout±7275-7744m/min.Assumingthewavephasespeedtobe7500m/min
andconsideringthedistancetotheepicenter,thearrivaltimebasedonthefirstmaximumofresidual
waterlevel,atPameungpeuk(±50.46kmfromtheepicenter)moreorlesslooksreliable(±7min-
utes),butappearstooearlyforPelabuhanRatu.IfthedistanceofPelabuhanRatuinwaterisabout±
190-200km,thewavewouldbearrivingafteraround±25-27minutes.Thefilteredresultsshow
thewaveisarriving16minutesafterthemainshock.Ontheotherhand,itlookslikethatthewave
raysarepenetratingaccordingtolanddistance(±120-125kmfromtheepicenter)atPelabuhan
Ratu.Occurrenceofthemaximumwaveperiod(33.1min)2minutesafterthemainshock,atboth
stations(14:57WIB/07:57UTC),canbeanindicationthatthewaterleveltakesonadisturbance
fromgroundshakingorpossiblyfromthehorizontalbottomdeformation,sincetheepicenterisnear
tothestations[Lisitzin,1974;Gonz´alezetal.,2007;Dutykh,2008].Theindicationispresumably
coincidewiththeshakemapinfigure7.5,wherebothstationareintherangeofbetweenmoderate
andstrongperceivedshaking.

83

Figure7.5:Shake-mapofMw7.0earthquakeeventinsouthernJava[USGS,2009b].PAMEis

gaugestationatPameungpeukandPELAisgaugestationatPelabuhanratu.

7.3ExperimentonthediversesourcemodelofSumatra-Andamanmega-tsunami2004event

ThisexperimentisconductedinordertoinvestigatewhichsourcemodeloftheSumatra-Andaman

2004eventfitswelltothesatellitetracksofJason-1andTopex.Thereare8scenarios,derivedfrom

apreviousstudy(seetable7.1).Fromthosescenarios,only5scenariosareusedforcomparison

againsttheSatellitetracks,i.e.Layetal.[2005]ScenarioA,Taniokaetal.[2006],Hirataetal.

[2006],Banerjeeetal.[2007],andHoechneretal.[2008]ScenarioC.

Layetal.[2005]usethebroadbandseismicdatafromtheinternationalFederationofDigital

SeismicNetworks(FDSN)andalsotheHarvardCentroidMomentTensorsolution(information)

fromNEIC-USGSforgeneratingtheirrupturemodels(1200-1300kmlength),withtherupture
speedof2.5km.s−1.Taniokaetal.[2006]generatetheirrupturemodel(1200kmlength)usingthe

inversionofatsunamiwaveformat5tidegauges(Sibolga,Belawan,PortBlair,Vishakapatnam,

andColombo),seismologicaldatafromAmmonetal.[2005]andthecoseismicverticaldeforma-

tionobservedalongthenorthwestcoastofAceh,Simeulueisland(inIndonesia),Andamanand

84

Figure

7.6:

A

map

of

a

tide

augeg

stations

(indicated

by

wyello

pin)

and

hquakearte

epicenter

(indicatedbyyellowcircle).ThestationslocatedinsouthernJava,Indonesia,fromwesttoeast

respectivelyare:PelabuhanRatu,Pameungpeuk,Cilcap,Sadeng,Prigi2.Fortheexperiment,the

stationofCilacapandSadengareexcludedsincenosignificanttsunamiwavesignaldetectedthere.

Thereisonegaugestation,alsoused,atChristmasislandofAustralia.

Figure

7.7:

imeT

(a)

(c)

ofseries

aterw

elvle

ual,(c)Powerfrequency,(d)Periods.

the

ameungpeukP

station

(a)

(b)

(d)

leaterWelv

corded,re

(b)

85

Resid-

86

Figure

7.8:

imeT

(a)

(c)

ofseries

aterw

Residual,(c)Powerfrequency,(d)

elvle

the

Periods.

uhanPelab

Ratu

station

(a)

(b)

(d)

aterW

elvle

recorded,

(b)

(a)

(b)

Figure7.9:TimeseriesofwaterlevelthePrigi2station(a)Waterlevelrecorded,(b)Residual.

(a)

(b)

87

Figure7.10:TimeseriesofwaterleveltheChristmasislandstation(a)Waterlevelrecorded,(b)

Residual.

88

Nicobarislands(inIndia).Thedislocationthatusedforourscenariosimulationisobtainedfrom
themaximumslipvaluesintherecommendedrangeof1.7km.s−1rupturespeed.Thesourcemodel
byHirataetal.[2006]wasinvertedfromthesatellite(Jason-1andTopex)seasurfaceheightdif-
ferencedata.Paleo-geodeticdataofSimoesetal.[2004]andseismologicaldatafromtheHarvard
CentroidMomentTensorarealsousedfortheirproposedtherupture(1400kmlength).Thedislo-
cationthatusedforourscenariosimulationisalsoobtainedfromthemaximumslipvaluesinthe
recommendedrange.ThereweresomecontinuousGPSdata(cGPS)andsurveyed(sGPS)stations
usedbyBanerjeeetal.[2007]togetareliablecompletepictureoftherapidslipmotiondistribu-
tionduringtheSumatra-Andaman2004megaearthquake(approx.1355kmrupturelength).In
themeantime,Hoechneretal.[2008]usedthosedatatogetherwiththedatafrompreviousstudies,
employslipinversionmethodsincludingslipfaultingandseveralearthlayeringmodels,togenerate
themostrecentandreliablerupturemodel(1200-1300kmlength)oftheSumatra-Andamanmega
earthquake2004.Furtherestimationoftheproperrupturedimensionhasbeendonebyusingatool
5.3.1.sectioninThecomparisonresultstoJason-1tracksshowthatthebestresemblanceisachivedbysource
inLayetal.[2005],Taniokaetal.[2006],andHoechneretal.[2008],whiletheTopexdataare
estimatedbestbyHoechneretal.[2008],Hirataetal.[2006]andLayetal.[2005],seefigure7.12
and7.13.Intheend,thesourcemodelofHoechneretal.[2008]isusedforanofficialtestcase,see
section6.7.Thereasonforthischoceisthatitisthemostrecentsourcemodelamongothers,andit
isconstructedbasedonseismicandreliablegeodeticdata.Agoodagreementofthesatellitetracks
andasimulationresultisachievedbytheTUNAMI-N2modelImamuraetal.[2006].

(a)[Layetal.,2005]ScenarioA

(c)2006]al.,et[Hirata

(b)[Taniokaetal.,2006]

(d)[Banerjeeetal.,2007]

(e)[Hoechneretal.,2008]ScenarioC

89

Figure7.11:The5initialconditionsaregeneratedfortheexperimentoftheSumatra-Andaman

2004eventfrom8scenariosintable7.1.

90

(a)

Sat-trackvsLayetal.[2005]ScenarioA

(b)Sat-trackvsTaniokaetal.[2006]

(c)Sat-trackvsHirataetal.[2006]

Figure7.12:Thesimulation(red-solid-line)oftheSumatra-Andamanmegatsunami2004compared

withthesatellitetracks(Sat-tracks,blue-solid-line)ofJason-1andTopex(left-andright-panel,in

respectively,eachfigure),usingtheinitialconditionbasedon(a)Layetal.[2005]ScenarioA,(b)

Taniokaetal.[2006],(c)Hirataetal.[2006].

(a)Sat-trackvsBanerjeeetal.[2007]

(b)Sat-trackvs[Hoechneretal.,2008]ScenarioC

91

Figure7.13:Thesimulation(red-solid-line)oftheSumatra-Andamanmegatsunami2004compared

withthesatellitetracks(Sat-tracks,blue-solid-line)ofJason-1andTopex(left-andright-panel,

inrespectively,eachfigure),usingtheinitialconditionbasedon(a)Banerjeeetal.[2007],(b)

Hoechneretal.[2008]ScenarioC.

92

Table7.1:Totalmomentseismic(Mo),momentmagnitude(Mw)andshearrigidity(µ)ofthediverse
sourcemodelfortheexperimentofSumatra-Andaman2004event

modelSourceonbasedNo.

1.2.3.4.5.6.7.8.

oMwM[N.m]

µ2]−[N.m

Layetal.[2005]ScenarioA8.75x10229.223.00x1010
Layetal.[2005]ScenarioB6.38x10229.143.00x1010
Taniokaetal.[2006]7.20x10229.205.00x1010
Hirataetal.[2006]9.86x10229.263.50x1010
Banerjeeetal.[2007]6.40x10229.143.50x1010
Hoechneretal.[2008]ScenarioA6.71x10229.153.00x1010
Hoechneretal.[2008]ScenarioB9.18x10229.243.17x1010-6.68x1010
Hoechneretal.[2008]ScenarioC7.19x10229.173.17x1010-6.68x1010

Conclusions8.1

8Chapter

ORKWFUTUREANDCONCLUSIONS

93

TsunaFLASH,anewtsunamimodelthatfirsttimesolvedinanadaptivetriangularfiniteelement
mesh.Ithasbeenvalidatedwiththeanalyticalsolutionandfielddatafollowsthestandardevaluation
fortsunamimodelaccordingtoSynolakisetal.[2008].Regardingtovalidationtotherealevents,
severalnoteshasbeenexperienced,i.e.:difficultiesofthedataacquisitionandprocessing,andin
understandingthe(physical)mechanism.Thisistrulyinterdisciplinaryresearch.
Theresultsofnumericalexperiments,benchmarkandtestcasesshowthatTsunaFLASHis
promisingforthenextfuturescientifictsunamimodeling.Itisverifieduptoacertainlevel.The
are:conclusions

1.Variouskindsoftheinitialconditionsmathematicalfunctionalformsandrealisticstaticsea
bottomdeformationarewellperformedbyTsunaFLASH.

2.Themaximumabsolutevalueofseasurfaceheightvalueatelementnodes(ητ=h)isa
simple,welltestedandrobusterrorestimatorrefinementcriterion.

3.TsunaFLASHissuccessfullybenchmarkedusingthefirstproblemfromthe3rdInternational
WorkshoponLong-waveRunupModels.

4.Experimentswiththevariousoftheadaptationalgorithmshavebeenperformedsuccesfully.
Itturnsoutthatitiscrucialtodefinetolerancesandresolutionofthemeshappropriately.

5.Thecomputationalspeedstudyissuccesfulandthecontributionoftheadaptiveschemeis
promising.Thetotalcomputationaltimeisrelatedtothefinestadaptationlevel.

6.TsunaFLASH,ingeneral,performeswellandisverifiedbyfieldobservationaldataintest
casesderivedfromactualevents,e.g.theSumatra-Andamanmegatsunamiof26December

94

2004(seasurfaceelevationderivedfromJason-1andTopexsatellitetracks)andtheAndaman
minortsunamiof10August2009(timeseriesofwaterleveldatarecordedbyDART23401).

7.Thelowresolution(≈5min)bathymetryisstillfeasibletobeusedfornumericalsimulations
whencomparingonlytoobservational(buoy/gauges)dataatdeepocean.Topographydata
isverysensitivewhensimulatinginundation,wherehighresolutiondataiscontributinga
realisticandrepresentativeinundationarea.

8.ApreliminaryexperimenttestingahorizontalSmagorinskyviscositytermtype,showsthat,
therecommendedconstantis≈0.001-0.3.

eFutur8.2orkw

EventhoughTsunaFLASHhasalreadybeenbenchmarkedwithonecaseofananalyticalsolution
andtwotestcasesoffielddataobservations,furthertestsareneededtoimprovetheperformance.
FutureworkcanbedirectedtothebenchmarkingthatfollowsthestandardofNOAAfortheevalu-
ationontsunaminumericalmodeling[Synolakisetal.,2007].Thesuggestedlaboratorybenchmark
experimentsare:runupofasolitarywaveonasimplebeach[Synolakis,1987],runuponthecircu-
larisland[Briggsetal.,1995],andrunupoftheokushiritsunamionthecomplexbeachofMonay
Valley[Liuetal.,2008].Afurthertestcasesuggestedisthesourcemodelofthe1993Hokkaido
Nansei-Okitsunami[Takahashi,1996]withcomplexbathymetry-topographydata[Takahashietal.,
1995].Afurtherinvestigationontheimplementationofthebottomfrictionscheme(manningrough-
ness)intoTsunaFLASHfollowingImamuraetal.[2006];Harigetal.[2008];Imamura[2009]and
anapplicationoftheSmagorinskyhorizontalviscosityterm[Smagorinsky,1963]forTsunaFLASH
isalsointerestingtoimprovetheoverallresults.

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120

oductionIntrA.1

AAppendix

HOWTORUNTsunaFLASH

TsunaFLASHisanimplementationofasimplewavedispersionmodelbasedontheshallowwater
equationsdiscretizedbyafiniteelementmethod.ThefiniteelementsemployedisP1conforming
elementsforthewaterheightandP1non-conformingelementsforthevelocitycompontents.This
discretizationhasbeenintroducedbyHanertetal.[2005].Theimplementationisbasedonan
implementationbyD.Sein,S.DanilovandothersfromTsunamiModelingGroupatAlfredWegener
InstituteforPolarandMarineResearch.
Thetitle/nameofthisprojectissomewhatmisleading,sinceTsunaFLASHdoesnotemploya
semi-Lagrangiandiscretizationmethod,butwestilluseitsincethatisacoolname.
ToworkwithTsunaFLASHwillneedamatosasalibrary,bothcanbedownloadedfrom
addresses:homepage

http://www.amatos.info/1.

http://www.aforge.awi.de/amatos/2.

Itwillneedregistrationapprovedbyadministrator(s).
Togettheworkingcopy,needSubversion(SVN)clientsoftwaretoworkwith.TheSVNsoftware
download,installation(invariousplatform)andmoretutorialcanbefoundat:
http://subversion.tigris.org/Inhere,wearepreferringtostartdownloadthefilesfromtherepository,usingthe
UNIX/Linuxterminal,canbedonebysvn-syntaxcommand:
:amatosfor

linux>[username]--usernamecheckoutsvn<enter>http://svn.aforge.awi.de/svn/amatos/amatos2d/trunk

:TsunaFLASHfor

[username]--usernamecheckoutsvnlinux><enter>http://svn.aforge.awi.de/svn/amatos/Tsunaflash2d/trunk

121

Oncethefilessuccessfullydownloaded,theuserprofilesarestoredinthe(folder)directory.
Forfurtherdevelopmentorapplicationtotheworkingcopyortoseeifanyupdatefileintherepos-
itory,oftheamatosandTsunaFLASH,canbecheckedbysvn-syntaxcommands:

statussvnlinux><enter>

Thepossiblystatusofeachfilecanbeflagedbysvn-clientas:
U-updatedandavailableonlyintherepository
M-workingcopyfileisdifferent(recent)comparetowhatavailableintherepositoryA-addedin
therepositorybutisnotcommittedyet
?-thefileisonlyexistedontheworkingcopydirectory

Togetupdatesoftheworkingcopyfromtherepository,thesvn-syntaxcommand:

<enter>upsvnlinux>

Toupdatethefilesintherepositorywiththerecentonefromtheworkingcopydirectory,thesvn-
commands:syntax

linux>svncommitfilename-m"comments/shortdescription/notification"<enter>

Toaddnewfilestotherepositoryfromtheworkingcopydirectory,thesvn-syntaxcommandsshould
w:follo

linux>svnadd[/directory/nameoffileincludingtheextension]<enter>
linux>svncommit[filename]-mcomment/shortdescription/notification<enter>

ThedirectorystructureofTsunaFLASHcanbeseeninfigureA.1.

122

tsunaflash2d

compile

data

doc

eval

include

lib

ruptgen

src

poweraix

ia64linux

intelmacosx

sparcsolaris

viznet4flash

flash

system

cray-f90

mpi

nag-f90

posix-f90

std-f90

timing

FigureA.1:TheDirectorystructureofTsunaFLASH

amatosBuildingA.2library

Gotothefollowdirectory:

<enter>amatos2d/compile/linux_ia64/cdlinux>

123

ModifyorsetthedirectoryspathintheMakefileandthenbuildingthelibrarybysyntaxcommand:

libgmakelinux><enter>

Ifeverythingwentright,thereshouldbeafilelibamatos.aandlibamatos.sointhe
lib/linuxia64directoryandsomekindofGRIDapi.modintheinclude/linuxia64direc-
tory.amatosisalsoprovidingMakefileformachineofaixPower,irixmips,linuxia32,and
solarissparc.Forfurtherdetailsofamatos,pleasereadtheusersguideofamatos[Behrens,
2003].

TsunaFLASHExecutingandBuildingA.3

Gotothefollowdirectory:

tsunaflash2d/compile/linux_ia64/cdlinux>

ModifyorsetthedirectoryspathandalsospecifythefileincludedintheMakefile,espe-
ciallysettheLIBDIRtoamatos2d/lib/linuxia64,INCDIRtoamatos2d/compile/linuxia64,
MODDIRtotoamatos2d/include/linuxia64.
BuildingtheexecutablefileofTsunaFLASHandincludingsomeneededfilescanbedonebysyntax
command:

<enter>datacopyTSUNAFLASHgmakelinux>

Forcleaningthefolder,justtypesyntaxcommand:

<enter>tidygmakeunix>

ToexecutingtheTsunaFLASHcanbedonebysyntaxcommand:

unix>TSUNAFLASH-b-fParameters.dat<enter>

124

orforcompletelistoftheexecutablecanbeseenbysyntaxcommand:

<enter>-hTSUNAFLASHlinux>

Onceitsexecute,therunningoutputinformationwillappearonthescreenduringthesimulation.
ThesubdirectoryofTsunaFLASHinthecompilecontainsOS-specificfiles(Makefile)forbuild-
ingtheexecutablesandlibrariesformachine:aixpower,linuxia64,solarissparcand
.intelmacosx

includeFilesA.4

DatasinputforTsunaFLASHare:

1.Parametercontrolfile(Parameters.dat)

2.Bathymetryandtopographydata(forexample:ETOPO5.ASC)

3.Initialgriddata(forexample:indikigg20.dat)

thesyntaxcommandtoincludethesedatainputsarealreadysetintheMakefile.The
Parameters.datisnowavailable:

1.Parameters.channel(useforexperimentinthechannel).

2.Parameters.channel.elliptic.dat(useforexperimentinthechannel).

3.Parameters.aceh04.dat(useforAceh2004tsunamitestcase).

4.Parameters.bnklorito.dat(useforBengkulu2007tsunamitestcase)

Inprinciple,theParameters.datcanbedefinebyuserforfurtherexperiment.Theinitialgridis
awnoailable:v

1.Triang.chanel.dat(initialgridforchannel).

2.indikigg17.dat(initialgridforIndianOcean-refinementlevel17).

3.indikigg20.dat(initialgridforIndianOcean-refinementlevel20).

4.etopo5worldocean20.dat(initialgridforworldocean-refinementlevel20).

125

TheETOPO5.ASCNOAA/NGDC[1988],containsbathymetry(representbynegativevalues)and
topography(representbypositivevalues),LatandLonaregivenforNorthWestcornerofselection
areacoveredbya4321x2161matrixof5-minutegridvaluesstartingattheNorthwestcornerofthe
area(NWlat=90◦,NWlon=0◦)andthengivenEastwardalongincreasingLongitudefor4321
values,thenstepping5minutesSouthforthenextrow.LastrowasthelastentriesisSEcorner
pointoftheselectedarea(SElat=−90◦,SElon=360◦).
RuptGenwithCouplingA.5

TousetheinitiationfromRuptGenBabeyko[2007],pleasefollowthestepswhichisnowonly
availableforLinuxmachine:

1.Copythefiles:executableruptgen,ruptgen.define,ruptgen.cfg,andpi15150.piinto
ia64/tsunaflasd2d/compile/linux

2.Createlinktogfdirectory(asthetarget)inthedirectoryof
tsunaflasd2d/compile/linuxia64/,bylinux-syntaxcommand:

unix>ln-s[target][linkname]

forxample:e

gf/tsunaflash2d/ruptgen/gf-slnunix>

3.OnceTsunaFLASHsuccessfullycompiled,wecouldplayaroundusingruptgen.define
todefineearthquakemomentmagnitude(-mw)[normalrange:6.7-9.2];andepicenter
coordinatesbeforeexecutingTsunaFLASH.Theepicentercoordinatescanbedefinedin
decimalgeographics(-xy)[LatitudeNorthandLongitudeEast=Positive;LatitudeSouth
andLongitudeWest=Negative]orinpatchescoordinate(-ij)[i-max=15,j-max=150](see

126

PatchesNumeration.png).Thefileofruptgen.defineisconnectedtothelineof395of
initial.f90FVMxample:eorF

9115-ij9.00-mw-2.00100.00-xy9.00-mw

Thesummarydetailsofruptureprocessedwillbecreatedasafilesummary.out.

4.AnotheroptionofinitiationusingRuptGenisgeneratingbyslipdistribution.Thiscanbe
donebycommentedline395anduncommentline396intheFVMinitial.f90.Theslip
distributionfilewhichnowavailableare:

(a)slippadangnexfuturerun2009.slip(ThesourcepredictionforPadanginthe
nextfuturetsunamibasedonNatawidjaja[2008]afterChliehetal.[2008]beforethe
Bengkuluearthquake12September2007takingintoaccount)
(b)slippadangnfminusbnk120705.slip(ThesourcepredictionforPadanginthe
nextfuturetsunamibasedonNatawidjaja[2008]afterChliehetal.[2008]thatthe
Bengkuluearthquake12September2007basedonLoritoetal.[2008](reconstruction
result)havebeensubtracted,seethedetailsintableB.1)
(c)Sumatra04hoechner07.slip(Sumatra-Andaman2004mega-tsunami[Brune,2008])
(d)Sumatra04hoechner08.slip(Sumatra-Andaman2004mega-tsunami[Hoechner
2008])al.,et

outputFilesA.6

Theoutputofthesimulationcanbein:

1.GMVformat(filename:Tsunaflashgmv.xxxx,[xxxx]=4digitseriesnumber).

2.MATLABformat(filename:TsunaFlashmatlab.xxxx,[xxxx]=4digitseriesnumber).

Duringtherunningsimulation,theoutputfilecanbevisualizedwithoutinterruptingtheprocess).

visualizationOutputA.7

127

TheoutputofsimulationinGMVformatcanbevisualizedusingfree-software
namelyGeneralMeshViewerfromLosAlamosNationalLaboratory(LANL)-USA
.http://www-xdiv.lanl.gov/XCM/gmv/GMVHome.html)(Theoutputofsimulationinmatlabformatcanbevisualizedusingmatlabscriptwhichavail-
ableinthedirectoryoftsunaflash2d/eval.

estrictionsrUseageA.8

CopyrightA.8.1

TICENOCOPYRIGHTThesoftwareareprovidedfornon-commercialuseonly.Seethelicenseconditionsandthewarranty
.TsunaFLASHforconditions

Copyrightofamatosc2003-2007J¨ornBehrens
CopyrightofTsunaFLASHc2007-2009J¨ornBehrens
ProfessorofNumericalMethodsinGeosciences
KlimaCampus,UniversityofHamburg
5gGrindelber20144Hamburg,Germany
Phone:+49-40-428387734
Fax:+49-40-428387712
Email:.dewjoern.behrens@zma

CopyrightofRuptGenver.1.1c2007-2008AndreyBabeyko
Geo-Forschung-Zentrum(GFZ)GermanResearchCentreforGeosciences
ModellingGeodynamic2.5,SectionTelegrafenberg,C41.22
Potsdam14473Phone:+49-331-288-1919

128

Fax:+49-331-288-1938
Eail:Andrey.Babeyko@gfz-potsdam.de

LicenseA.8.2

TheuseofTsunaFLASHisgrantedfreeofchargeforanunlimitedtime,providedthefollowingrules
applied:andacceptedare

1.Youmayuseormodifythiscodeforyourownnoncommercialandnonviolentpurposes.

2.Thecodemaynotbere-distributedwithouttheconsentoftheauthors.

3.Thecopyrightnoticeandstatementofauthorshipmustappearinallcopies.

4.Youacceptthewarrantyconditions(seewarranty).

5.Incaseyouintendtousethecodecommercially,weobligeyoutosignanaccordingtolicence
authors.thewithagreement

antyarrWA.8.3

Thiscodehasbeentesteduptoacertainlevel.Defectsandweaknesses,whichmaybeincludedin
thecode,donotestablishanywarrantiesbytheauthors.
Theauthorsdonotmakeanywarranty,expressorimplied,orassumeanyliabilityorresponsibility
fortheuse,acquisitionorapplicationofthissoftware.

amatoshttp://www.amatos.info/

http://www.aforge.awi.de/amatos/

TsunaFLASHhttp://www.aforge.awi.de/amatos/wiki/TsunaFLASH/

BAppendixSOURCEPARAMETERSOFPADANG(NEXT)FUTUREEARTHQUAKE

129

ThepredictionofthesourceparameterforthePadang(next)futureearthquake,thiscom-
putationresult,usingRuptGen[Babeyko,2007;Babeykoetal.,2008],isareconstructionofthe
predictionsourceofNatawidjaja[2008]afterChliehetal.[2008]andhavebeenalreadysubtractthe
Bengkuluearthquake12September2007(reconstructionresult)basedonLoritoetal.[2008].
Earthquakeconsistsof201ruptures,totalmomentmagnitudeMw=8.87359,totalmoment
seismicMo=2.57265e+22Nm,maximumuplift=3.2783m,andmaximumdepression=-1.35536
m.ThefaultdimensionanddislocationareprovidedintableB.1;whilefocaldepth,dip,strikeand
rigidityareprovidedintableB.2.

TableB.1:SourceparametersofPadang(next)futureearthquake:faultdimensionanddislocation

RuptureNo.MwMoEpi-LonEpi-LatIJIDXL[km]W[km]δ[m]
1-0101.034-4.75411865128039.995812.2110
2-0101.115-4.6853866128139.887412.64050
3-0101.198-4.61465867128239.751612.91420
4-0101.284-4.54276868128339.561113.13440
5-0101.373-4.46789869128439.30714.04070
6-0101.469-4.389028610128538.95514.53440
77.241169.15661e+19101.574-4.301788611128638.510916.98344
87.265689.96612e+19101.695-4.201228612128738.016318.72534
97.309551.15965e+20101.831-4.083518613128837.518522.07764
107.227398.7315e+19101.956-3.964788614128936.705216.99154
117.149456.67067e+19102.046-3.869468615129036.238113.14854
127.164817.03432e+19100.641-4.62023873129339.480912.72644
137.158576.88431e+19100.722-4.55011874129439.435712.46934
14-0100.803-4.48157875129539.308212.40040
15-0100.886-4.41235876129639.144412.89220
16-0100.972-4.34173877129738.951413.01880
17-0101.060-4.27001878129838.738813.44690
18-0101.153-4.19558879129938.532114.11940
pagextneonContinued

130TableB.1–continuedfrompreviouspage
RuptureNo.MwMoEpi-LonEpi-LatIJIDXL[km]W[km]δ[m]
19-0101.250-4.118008710130038.346114.66140
207.349841.3328e+20101.357-4.033638711130138.172116.62646
217.371011.4339e+20101.475-3.938918712130237.884918.02336
227.389021.52592e+20101.602-3.834208713130337.592219.32936
237.331421.25063e+20101.718-3.731418714130437.315915.95936
247.262769.86601e+19101.806-3.643888715130536.819612.75986
257.165917.06105e+19100.412-4.34978883130839.202312.86564
267.275801.03206e+20100.496-4.28021884130938.753012.68186
277.274821.02856e+20100.580-4.21144885131038.467112.73276
287.282171.05502e+20100.666-4.14188886131138.237713.13866
297.365861.40861e+20100.755-4.07127887131238.045113.22328
307.376311.46039e+20100.846-3.99934888131337.881313.76858
31-0100.941-3.92506889131437.738614.15880
32-0101.040-3.847918810131537.609414.85480
33-0101.147-3.765118811131637.542216.16950
34-0101.261-3.675288812131737.529917.14680
35-0101.379-3.579948813131837.519517.38340
367.309361.15886e+20101.485-3.488648814131937.324114.78516
377.260049.77385e+19101.572-3.408558815132036.842512.63276
387.167027.08821e+19100.191-4.07378893132339.290712.8864
397.365171.40523e+20100.278-4.00601894132439.105012.83398
407.365821.40843e+20100.365-3.93813895132538.818512.95808
417.369191.42489e+20100.453-3.86939896132638.555213.19908
427.436111.79544e+20100.544-3.79954897132738.349213.376610
437.445761.85625e+20100.637-3.72787898132838.221913.875710
447.448991.87707e+20100.732-3.65427899132938.171514.049910
45-0100.831-3.577808910133038.184314.87320
46-0100.936-3.496288911133138.243715.70380
47-0101.046-3.409898912133238.309816.35280
48-0101.157-3.320328913133338.257616.30090
497.303051.13391e+20101.259-3.235458914133438.141814.15656
507.273321.02326e+20101.347-3.159468915133537.782212.89676
517.171707.20352e+1999.975-3.79083903133839.743012.94664
527.287171.07338e+20100.063-3.72379904133939.609412.90436
537.371861.43811e+20100.151-3.65679905134039.580212.97648
547.438381.80952e+20100.240-3.58934906134139.577713.063110
557.445521.85476e+20100.331-3.52063907134239.562613.394710
567.452761.90167e+20100.424-3.44977908134339.559513.734610
577.456751.9281e+20100.518-3.37711909134439.557513.926210
pagextneonContinued

No.eRuptur585960616263646566676869707172737475767778798081828384858687888990919293949596

Mw----7.395957.292877.174597.293397.376917.44357.451557.455137.46377----7.411017.392717.179327.2977.380237.450457.45637.458447.471397.47521-7.499297.500497.492097.392067.185757.300787.385437.394497.461807.465407.47723

TableB.1–continuedfrompreviouspage
MoEpi-LonEpi-LatIJIDX
0100.616-3.3013690101345
0100.719-3.2212490111346
0100.825-3.137390121347
0100.933-3.0507290131348
1.56286e+20101.034-2.9680890141349
1.09471e+20101.126-2.8930390151350
7.27599e+1999.7578-3.503089131353
1.09669e+2099.8459-3.436229141354
1.46339e+2099.934-3.369239151355
1.84181e+20100.022-3.301989161356
1.89375e+20100.112-3.233549171357
1.91729e+20100.204-3.163489181358
1.97542e+20100.297-3.091569191359
0100.394-3.0166791101360
0100.495-2.9383791111361
0100.600-2.8561991121362
0100.707-2.7715591131363
1.64635e+20100.810-2.6895691141364
1.54551e+20100.907-2.6133991151365
7.39569e+1999.5359-3.212949231368
1.11047e+2099.6233-3.144949241369
1.48027e+2099.7103-3.077399251370
1.8866e+2099.7980-3.009499261371
1.92506e+2099.8875-2.940519271372
1.93934e+2099.9783-2.870779281373
2.02805e+20100.072-2.79919291374
2.05504e+20100.168-2.7249592101375
0100.268-2.6484192111376
2.23321e+20100.374-2.5678792121377
2.24251e+20100.482-2.4848392131378
2.17842e+20100.591-2.4025192141379
1.54202e+20100.692-2.3262592151380
7.56181e+1999.3068-2.925219331383
1.12503e+2099.3937-2.854029341384
1.5071e+2099.4801-2.784299351385
1.55504e+2099.5681-2.714169361386
1.96202e+2099.6581-2.643359371387
1.98657e+2099.7493-2.572439381388
2.06937e+2099.8435-2.500219391389

131

L[km]W[km]δ[m]
014.745639.5451015.262139.5476015.863739.5488015.857839.5385814.171739.3857613.336339.0883412.897240.2967612.923740.4089812.915140.46731012.986640.52101013.336940.56971013.497640.58491013.905440.5891014.468640.5973014.964240.5494015.659940.4678015.638440.2801814.701339.9950813.893239.7292412.94640.8052612.899640.9931812.840941.17051013.047441.31291013.282341.411013.367141.45221013.9941.41831014.199341.3509014.89741.17531015.600240.90081015.794240.56651015.473340.2246813.775439.9785413.218040.8630612.974141.2919812.944541.5814813.291541.78401013.368141.93381013.498342.04931014.048442.0865pagextneonContinued

132TableB.1–continuedfrompreviouspage
RuptureNo.MwMoEpi-LonEpi-LatIJIDXL[km]W[km]δ[m]
977.481282.09855e+2099.9410-2.426249310139041.995714.277310
987.497112.21645e+20100.043-2.350039311139141.846215.133310
997.305691.14428e+20100.151-2.270409312139241.596915.71935
1007.510882.32441e+20100.263-2.188839313139341.180616.127010
1017.499552.23525e+20100.376-2.107809314139440.755915.670010
1027.382971.49436e+20100.477-2.034379315139540.507213.17548
1037.192917.75116e+1999.0690-2.64251943139841.149413.45474
1047.308441.15521e+2099.1559-2.56731944139941.406113.28556
1057.395451.56019e+2099.2432-2.49332945140041.716413.35728
1067.468972.01118e+2099.3329-2.41919946140141.972113.690610
1077.467362.00005e+2099.4241-2.34548947140242.161913.553510
1087.476932.06728e+2099.5172-2.27187948140342.259413.976810
1097.484562.12247e+2099.6138-2.19707949140442.350414.319110
1107.494822.19899e+2099.7147-2.121159410140542.340914.838710
1117.507142.29463e+2099.8210-2.043239411140642.242415.520110
1127.516132.36699e+2099.9331-1.963219412140742.037116.087710
1137.371071.43416e+20100.049-1.882629413140841.756616.35516
1147.426931.73938e+20100.162-1.805639414140941.400615.00488
1157.393951.55209e+20100.265-1.736159415141040.730113.60968
1167.191067.70176e+1998.8254-2.36873953141340.212013.68064
1177.314181.17834e+2098.9138-2.28941954141440.406813.88666
1187.400701.58875e+2099.0043-2.21016955141540.521614.00278
1197.469362.01389e+2099.0971-2.13146956141640.612914.167910
1207.465841.98954e+2099.1907-2.05412957141740.711113.962810
1217.480072.0898e+2099.2872-1.97680958141840.788014.638710
1227.485442.12894e+2099.3882-1.89806959141940.801714.907910
1237.498262.2253e+2099.4942-1.818569510142040.766815.596010
1247.504162.27115e+2099.6054-1.738009511142140.712215.938810
1257.519322.39322e+2099.7232-1.656309512142240.501216.882910
1267.513052.3419e+2099.8447-1.574789513142340.321516.594510
1277.417191.68184e+2099.9607-1.500019514142439.877615.06258
1287.190057.67504e+1998.5849-2.10281963142839.392313.91694
1297.317561.19219e+2098.6773-2.02141964142938.940814.57886
1307.399081.57985e+2098.7728-1.93876965143038.664514.59318
1317.462041.96366e+2098.8694-1.85733966143138.482814.579110
1327.461181.95784e+2098.9671-1.77713967143238.308714.602010
1337.473272.04127e+2099.0683-1.69628968143338.180915.275210
1347.480462.09261e+2099.1747-1.61372969143438.108715.689010
1357.492132.1787e+2099.2863-1.530029610143538.170416.308110
pagextneonContinued

No.eRuptur136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174

Mw7.500047.453247.444997.423287.387107.187897.313117.389497.451627.453257.460617.469347.478697.494477.446397.449807.346007.285567.195437.308437.385177.385097.451137.453567.462907.474477.430827.453557.467467.440497.277857.193327.302157.300507.379347.380137.378127.386127.40131

TableB.1–continuedfrompreviouspage
MoEpi-LonEpi-LatIJIDX
2.23903e+2099.4032-1.4453796111436
1.90486e+2099.5274-1.3597396121437
1.85135e+2099.6557-1.2754296131438
1.71759e+2099.7800-1.1989096141439
1.51584e+2099.8945-1.1323396151440
7.61796e+1998.3574-1.840329731443
1.17399e+2098.4558-1.759349741444
1.52838e+2098.5563-1.677459751445
1.89422e+2098.6572-1.596349761446
1.9049e+2098.7597-1.515119771447
1.95394e+2098.8657-1.432799781448
2.01375e+2098.9765-1.348419791449
2.07984e+2099.0920-1.2617397101450
2.19634e+2099.2141-1.1724797111451
1.8603e+2099.3443-1.0805197121452
1.88236e+2099.4809-0.9899497131453
1.31524e+2099.6157-0.90748897141454
1.06742e+2099.7345-0.84033597151455
7.81881e+1998.1478-1.574339831458
1.15519e+2098.2515-1.496479841459
1.50575e+2098.3555-1.418709851460
1.50535e+2098.4602-1.340679861461
1.89103e+2098.5670-1.261089871462
1.90693e+2098.6762-1.180029881463
1.96949e+2098.7889-1.096489891464
2.0498e+2098.9064-1.0090698101465
1.7629e+2099.0316-0.9167398111466
1.90689e+2099.1672-0.81808398121467
2.00077e+2099.3130-0.71751898131468
1.82279e+2099.4583-0.62671898141469
1.03939e+2099.5815-0.55645598151470
7.76198e+1997.9532-1.2981809931473
1.13037e+2098.0600-1.227829941474
1.12394e+2098.1673-1.156309951475
1.47575e+2098.2754-1.083019961476
1.47978e+2098.3848-1.008119971477
1.46951e+2098.4955-0.9310929981478
1.51071e+2098.6084-0.8510879991479
1.59209e+2098.7266-0.76517099101480

133

L[km]W[km]δ[m]
1016.730538.2370817.724538.3822817.277638.2690816.101138.0983814.381137.6447414.426737.7175615.001537.2658814.882336.67781014.956236.18611015.176535.86181015.683535.59581016.250435.40571016.814735.34041017.701835.4500818.597835.7243818.666236.0154617.322136.1564614.011036.2781414.873537.5491615.005336.6596814.922236.0380815.156435.47181015.466434.93351015.772134.54441016.398434.31491017.096034.2570818.367434.2784819.718534.5377820.423334.9875818.453035.2786614.013135.3203414.797437.4679614.706036.6020615.005835.6668815.086934.9346815.419834.2737815.551933.7467816.196633.3120817.230333.0001pagextneonContinued

134

TableB.1–continuedfrompreviouspage
RuptureNo.MwMoEpi-LonEpi-LatIJIDXL[km]W[km]δ[m]
1757.421641.70789e+2098.8530-0.6722159911148132.935618.51988
1767.455591.92035e+2098.9922-0.5690659912148233.009120.77728
1777.398981.5793e+2099.1475-0.4571989913148333.429522.49666
1787.444481.8481e+2099.3030-0.3562129914148433.951619.44058
1797.277061.03654e+2099.4324-0.2825759915148533.895214.56226
1807.180307.42077e+1997.8853-0.9470831004148936.879114.37284
1817.181617.45435e+1997.9944-0.8836481005149036.089414.75374
1827.173817.25638e+1998.1038-0.8177101006149135.265014.69774
1837.290841.08708e+2098.2132-0.7499451007149234.586214.96726
1847.287881.07604e+2098.3229-0.6794751008149333.996015.07236
1857.293531.09723e+2098.4344-0.6059801009149433.421615.63336
1867.312291.17069e+2098.5526-0.52587510010149532.686017.05546
1877.324581.22145e+2098.6791-0.43700010011149632.003818.17426
1887.366871.41353e+2098.8213-0.33505810012149731.292221.51046
1897.286191.06978e+2098.9876-0.21520710013149830.888224.73844
1907.359571.37834e+2099.1578-0.10286710014149930.810621.30286
1917.272681.02098e+2099.2990-0.022542510015150030.975815.69546
1927.177177.34096e+1997.9387-0.5364581016150637.165814.10854
1937.176127.3144e+1998.0455-0.4764301017150736.665414.24934
1947.180697.43073e+1998.1539-0.4132171018150836.051114.72264
1957.186707.58677e+1998.2654-0.3459201019150935.481015.27334
1967.204398.06474e+1998.3831-0.27318510110151034.926916.49314
1977.219438.49469e+1998.5092-0.19211210111151134.208917.73704
1987.271171.01566e+2098.6538-0.096187510112151233.523921.64044
1997.325701.22616e+2098.83170.024697510113151332.652926.82234
2007.279811.04646e+2099.02040.14407010114151431.936823.40464
2017.183567.50486e+1999.17650.23066010115151531.458317.04044

Note:Thecoordinateoftheepicentereach(unstructured)rectangularruptureisinEpi-LonandEpi-Latthat
correspondtoIandJasthecoordinateoftheRuptGenspatchesmap,whileIDXisthepatchindex.The
rupture/patchdimensionisrepresentedbyLforlengthandWforWidth,δistheaveragedislocationorslip
values.ForthedescriptionofRuptGenisavailableintheSection6.2.3andfigure6.6.

135

TableB.2:SourceparametersofPadang(next)futureearthquake:focaldepth,dip,strikeandrigid-
ity

Epi-LonNo.eRuptur101.0341101.1152101.1983101.2844101.3735101.4696101.5747101.6958101.8319101.95610102.04611100.64112100.72213100.80314100.88615100.97216101.06017101.15318101.25019101.35720101.47521101.60222101.71823101.80624100.41225100.49626100.58027100.66628100.75529100.84630100.94131101.04032101.14733101.26134101.37935101.48536

Epi-Lat-4.75411-4.6853-4.61465-4.54276-4.46789-4.38902-4.30178-4.20122-4.08351-3.96478-3.86946-4.62023-4.55011-4.48157-4.41235-4.34173-4.27001-4.19558-4.11800-4.03363-3.93891-3.83420-3.73141-3.64388-4.34978-4.28021-4.21144-4.14188-4.07127-3.99934-3.92506-3.84791-3.76511-3.67528-3.57994-3.48864

IJD[km]α[◦]y[◦]µ[N.m−2]
8651819.1216319.259114.00E+10
8662218.4479319.49754.44E+10
8672618.0434319.944435.12E+10
8683017.7307320.067395.79E+10
8693416.5521320.426456.47E+10
86103815.9745320.36926.64E+10
86114213.6226320.223556.65E+10
86124612.3343319.780656.66E+10
86135010.4384319.019526.67E+10
86145413.6159314.007196.68E+10
86155817.7111312.675086.69E+10
8731018.319318.783493.59E+10
8741418.7106319.639973.80E+10
8751818.8184319.922944.00E+10
8762218.0752320.265464.44E+10
8772617.8935320.587285.12E+10
8783017.3055320.785635.79E+10
8793416.4572321.389246.47E+10
87103815.8324321.692396.64E+10
87114213.9209322.237966.65E+10
87124612.8227321.56836.66E+10
87135011.9431320.129826.67E+10
87145414.5152316.54816.68E+10
87155818.2694314.548456.69E+10
8831018.1139320.535633.59E+10
8841418.3857320.103163.80E+10
8851818.3095320.476694.00E+10
8862217.7248321.169284.44E+10
8872617.6079321.617095.12E+10
8883016.889322.062445.79E+10
8893416.41322.467756.47E+10
88103815.621322.282886.64E+10
88114214.4225322.340066.65E+10
88124613.4903321.582056.66E+10
88135013.3033320.285996.67E+10
88145415.6966317.786346.68E+10
pagextneonContinued

136

Epi-LonNo.eRuptur101.57237100.19138100.27839100.36540100.45341100.54442100.63743100.73244100.83145100.93646101.04647101.15748101.25949101.3475099.97551100.06352100.15153100.24054100.33155100.42456100.51857100.61658100.71959100.82560100.93361101.03462101.1266399.75786499.84596599.93466100.02267100.11268100.20469100.29770100.39471100.49572100.60073100.70774100.81075

TableB.2–continuedfrompreviouspage
Epi-LatIJD[km]α[◦]y[◦]µ[N.m−2]
-3.4085588155818.4597316.038876.69E+10
-4.073788931018.0842322.113493.59E+10
-4.006018941418.1602322.608783.80E+10
-3.938138951817.9803322.711864.00E+10
-3.869398962217.6411322.729874.44E+10
-3.799548972617.3993322.473985.12E+10
-3.727878983016.7546322.514315.79E+10
-3.654278993416.5409322.448926.47E+10
-3.5778089103815.6013322.290766.64E+10
-3.4962889114214.7568322.291536.65E+10
-3.4098989124614.1586321.593326.66E+10
-3.3203289135014.2047320.415746.67E+10
-3.2354589145416.4127319.530116.68E+10
-3.1594689155818.0687319.263866.69E+10
-3.790839031017.9966323.096943.59E+10
-3.723799041418.0576322.790533.80E+10
-3.656799051817.9539322.903274.00E+10
-3.589349062217.8308322.941644.44E+10
-3.520639072617.375322.777185.12E+10
-3.449779083016.9319322.793115.79E+10
-3.377119093416.6921322.428196.47E+10
-3.3013690103815.7396322.20676.64E+10
-3.2212490114215.194321.822556.65E+10
-3.137390124614.6047321.176266.66E+10
-3.0507290135014.6102320.857236.67E+10
-2.9680890145416.3946320.386536.68E+10
-2.8930390155817.4536320.690616.69E+10
-3.503089131018.068322.892493.59E+10
-3.436229141418.0296323.047143.80E+10
-3.369239151818.042322.994334.00E+10
-3.301989162217.9393322.773764.44E+10
-3.233549172617.4529322.707295.12E+10
-3.163489183017.2385322.52035.79E+10
-3.091569193416.7178322.176616.47E+10
-3.0166791103816.0491322.330886.64E+10
-2.9383791114215.504321.891786.65E+10
-2.8561991124614.799321.649056.66E+10
-2.7715591135014.8199321.363526.67E+10
-2.6895691145415.7883321.179416.68E+10
pagextneonContinued

Epi-LonNo.eRuptur100.9077699.53597799.62337899.71037999.79808099.88758199.978382100.07283100.16884100.26885100.37486100.48287100.59188100.6928999.30689099.39379199.48019299.56819399.65819499.74939599.84359699.941097100.04398100.15199100.263100100.376101100.47710299.069010399.155910499.243210599.332910699.424110799.517210899.613810999.714711099.821011199.9331112100.049113100.162114

TableB.2–continuedfrompreviouspage
Epi-LatIJD[km]α[◦]y[◦]µ[N.m−2]
-2.6133991155816.7329322.45886.69E+10
-3.212949231017.9976322.215463.59E+10
-3.144949241418.0645322.206543.80E+10
-3.077399251818.1499322.187744.00E+10
-3.009499262217.8528322.187724.44E+10
-2.940519272617.5269322.429965.12E+10
-2.870779283017.4121322.454945.79E+10
-2.79919293416.6137322.413726.47E+10
-2.7249592103816.362322.507166.64E+10
-2.6484192114215.5756322.160796.65E+10
-2.5678792124614.857322.205566.66E+10
-2.4848392135014.6704322.314156.67E+10
-2.4025192145414.9817322.951296.68E+10
-2.3262592155816.8803323.972926.69E+10
-2.925219331017.6148320.325463.59E+10
-2.854029341417.9571321.130143.80E+10
-2.784299351817.9997321.366374.00E+10
-2.714169362217.5143321.666594.44E+10
-2.643359372617.4107322.129195.12E+10
-2.572439383017.2376322.35065.79E+10
-2.500219393416.5427322.766226.47E+10
-2.4262493103816.27322.840366.64E+10
-2.3500393114215.3264323.403396.65E+10
-2.2704093124614.7419324.033846.66E+10
-2.1888393135014.3611324.269156.67E+10
-2.1078093145414.7893324.605016.68E+10
-2.0343793155817.6737324.171626.69E+10
-2.642519431017.2951319.208413.59E+10
-2.567319441417.5225319.097753.80E+10
-2.493329451817.4255319.760544.00E+10
-2.419199462216.988320.644324.44E+10
-2.345489472617.1651321.320945.12E+10
-2.271879483016.6299321.627185.79E+10
-2.197079493416.2212322.565756.47E+10
-2.1211594103815.6384323.254836.64E+10
-2.0432394114214.9354324.278616.65E+10
-1.9632194124614.3968324.744666.66E+10
-1.8826294135014.1565325.552056.67E+10
-1.8056394145415.4609325.86956.68E+10
pagextneonContinued

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138

No.eRuptur115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153

Epi-Lon100.26598.825498.913899.004399.097199.190799.287299.388299.494299.605499.723299.844799.960798.584998.677398.772898.869498.967199.068399.174799.286399.403299.527499.655799.780099.894598.357498.455898.556398.657298.759798.865798.976599.092099.214199.344399.480999.615799.7345

TableB.2–continuedfrompreviouspage
Epi-LatIJD[km]α[◦]
17.0922581594-1.7361517.000710395-2.3687316.741114495-2.2894116.598318595-2.2101616.399322695-2.1314616.647126795-2.0541215.857630895-1.9768015.563934995-1.8980614.8611381095-1.8185614.5344421195-1.7380013.7052461295-1.6563013.9481501395-1.5747815.4002541495-1.5000116.703610396-2.1028115.924514496-2.0214115.908518596-1.9387615.924222696-1.8573315.898626796-1.7771315.180630896-1.6962814.770934996-1.6137214.1982381096-1.5300213.8325421196-1.4453713.0426461296-1.3597313.3862501396-1.2754214.3846541496-1.1989016.1494581596-1.1323316.096910397-1.8403215.464514497-1.7593415.591418597-1.6774515.512422697-1.5963415.281726797-1.5151114.776230897-1.4327914.249734997-1.3484113.7618381097-1.2617313.0597421197-1.1724712.4202461297-1.0805112.374501397-0.9899413.3512541497-0.90748816.5881581597-0.840335

y[◦]µ[N.m−2]
6.69E+10324.382023.59E+10317.129823.80E+10317.905794.00E+10318.99984.44E+10319.991945.12E+10320.69455.79E+10321.578086.47E+10322.541936.64E+10323.545816.65E+10324.690386.66E+10325.427316.67E+10326.911046.68E+10327.287813.59E+10318.308853.80E+10318.237184.00E+10319.219484.44E+10319.999195.12E+10320.530575.79E+10321.576766.47E+10322.525486.64E+10323.880776.65E+10324.87156.66E+10326.540896.67E+10327.576986.68E+10329.295696.69E+10330.762223.59E+10319.13243.80E+10320.804564.00E+10321.139284.44E+10321.262165.12E+10321.940985.79E+10322.738756.47E+10323.088096.64E+10323.510246.65E+10324.129846.66E+10325.544656.67E+10327.290516.68E+10329.993786.69E+10332.45337pagextneonContinued

No.eRuptur154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186187188189190191192

Epi-Lon98.147898.251598.355598.460298.567098.676298.788998.906499.031699.167299.313099.458399.581597.953298.060098.167398.275498.384898.495598.608498.726698.853098.992299.147599.303099.432497.885397.994498.103898.213298.322998.434498.552698.679198.821398.987699.157899.299097.9387

TableB.2–continuedfrompreviouspage
Epi-LatIJD[km]α[◦]
15.600910398-1.5743315.460414498-1.4964715.548618598-1.4187015.302522698-1.3406714.988526798-1.2610814.691330898-1.1800214.118334998-1.0964813.5311381098-1.0090612.5785421198-0.9167311.704461298-0.81808311.2947501398-0.71751812.5192541498-0.62671816.5856581598-0.55645515.683210399-1.29818015.783214499-1.2278215.459918599-1.1563015.374822699-1.0830115.034926799-1.0081114.904230899-0.93109214.29834999-0.85108713.4236381099-0.76517012.4733421199-0.67221511.0998461299-0.56906510.2419501399-0.45719811.8737541499-0.35621215.9431581599-0.28257516.159144100-0.94708315.7308185100-0.88364815.7924226100-0.81771015.5008267100-0.74994515.39308100-0.67947514.8248349100-0.60598013.56393810100-0.52587512.71454211100-0.43700010.71694612100-0.3350589.30515013100-0.21520710.82265414100-0.10286714.76485815100-0.022542516.4702226101-0.536458

y[◦]µ[N.m−2]
3.59E+10323.824083.80E+10323.582634.00E+10323.254444.44E+10323.262085.12E+10323.245185.79E+10323.415286.47E+10323.360266.64E+10323.434946.65E+10323.763376.66E+10324.577156.67E+10326.557216.68E+10329.641186.69E+10330.883353.59E+10326.011113.80E+10326.009654.00E+10325.362284.44E+10325.632415.12E+10325.412025.79E+10325.076766.47E+10324.354926.64E+10323.560576.65E+10323.69886.66E+10323.395316.67E+10325.041676.68E+10328.970146.69E+10331.080453.80E+10330.879144.00E+10330.421774.44E+10329.294975.12E+10328.173965.79E+10326.930516.47E+10325.960256.64E+10324.748216.65E+10323.982866.66E+10323.03876.67E+10324.007486.68E+10328.037656.69E+10332.654264.44E+10330.84181pagextneonContinued

139

140

TableB.2–continuedfrompreviouspage
RuptureNo.Epi-LonEpi-LatIJD[km]α[◦]y[◦]µ[N.m−2]
19398.0455-0.47643010172616.3029330.007665.12E+10
19498.1539-0.41321710183015.7649328.835895.79E+10
19598.2654-0.34592010193415.1826328.590136.47E+10
19698.3831-0.273185101103814.0357328.515776.64E+10
19798.5092-0.192112101114213.0333327.290156.65E+10
19898.6538-0.0961875101124610.6518326.641666.66E+10
19998.83170.024697510113508.5748326.193716.67E+10
20099.02040.14407010114549.84054329.924066.68E+10
20199.17650.230660101155813.5761333.223326.69E+10

Note:Thecoordinateoftheepicentereach(unstructured)rectangularruptureisinEpi-LonandEpi-Latthat
correspondtoIandJasthecoordinateoftheRuptGenspatchesmap,Disthefocaldepth,αisDipangle,yis
Strikeangle,µisshearrigidity,whiletheRake(λ)valuesareconstantof90◦.ForthedescriptionofRuptGen
isavailableintheSection6.2.3andfigure6.6.Thefault(parameter)geometryisillustratedinfigure6.9.