Tsunami Generation and Propagation

272 Pages·2019·9.473 MB·English

by  Tatsuhiko Saito

Springer Geophysics
Tatsuhiko Saito
Tsunami
Generation
and
Propagation
Springer Geophysics
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Tatsuhiko Saito
Tsunami Generation
and Propagation
TatsuhikoSaito
NationalResearchInstituteforEarth
ScienceandDisasterResilience
Tsukuba,Ibaraki,Japan
ISSN2364-9119 ISSN2364-9127 (electronic)
SpringerGeophysics
ISBN978-4-431-56848-3 ISBN978-4-431-56850-6 (eBook)
https://doi.org/10.1007/978-4-431-56850-6
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Preface
Inthestudyoftsunamis,researchershavetraditionallyanalyzedtide-gaugerecords
andsurveyedinundationareas.Inadditiontothesecoastalobservations,sea-bottom
pressuregaugesarenowwidelydeployedindeepoceans.Offshoreobservationscan
detect tsunamis promptly near the source, and short-wavelength tsunamis can be
clearlyobservedusingtheserecords.Afterthe2011Tohoku-Okiearthquake,obser-
vationswerecarriedoutatarraystationsinsidetheearthquakefocalareainorderto
detect tsunamis more rapidly. At the stations inside the focal area, tsunami signals
arerecordedsimultaneouslywithseismicwaves.
Thetsunamidatahavechangeddramaticallyasthemethodsofobservationhave
changed.Atheoryshouldalsobedevelopedfortheeffectiveuseofthenewrecords.
We can use dispersive theory to analyze offshore records. Seismic-wave theory
would be helpful for analyzing the tsunami records inside the focal area. At the
forefront of tsunami research, new application studies and numerical methods are
advancing greatly, as reported in journals. However, description of fundamental
theories and the derivation of basic equations are often skipped in the reports, but
deriving the equations is not always straightforward. Textbooks may be a more
suitablevenueforexplainingthefundamentaltheories.
WhenIstarteddoingtsunamiresearch,itwasdifficultformetofindbooksthat
explainindetail how toderive fundamentalequationsandhow toapply numerical
methodsfromtsunamigenerationtopropagation,althoughtherearemanyexcellent
textbooks about fluid dynamics and tsunamis at present. This book focuses on the
quantitative modeling of earthquake tsunamis using real data and mathematical
representations. Considering that seismic waves cannot be neglected in tsunami
observations,wetreatbothfluiddynamicsandelasticdynamics.Itriedtoreasonably
organizetheseismologyandtsunamiresearchtoconstructatheoreticalframework
fortsunamigenerationduetoearthquakes.
Icouldnothavecompletedthisbookwithoutthehelpandencouragingwordsof
mysupervisorsandcolleagues. KenjiSatake carefullyreviewed thedraft andgave
importantcomments.IthankTakashiFurumura,YuichiroTanioka,TakutoMaeda,
HiroyukiKumagai,andEiichiFukuyama.Theircommentsandsuggestionsarevery
v
vi Preface
important in the study of earthquakes and tsunamis. Kentaro Emoto and Tatsuya
Kubota helped me very much with their comments about seismic waves and
tsunamis.DaisukeInazu,ToshitakaBaba,HiroakiTsushima,RyotaHino,Takayuki
Miyoshi,SatbyulKim,ShunsukeTakemura,andNelsonPulidoworkedwithmeon
tsunami,forwhichIamverygrateful.IexpressmydeepestgratitudetoHaruoSato.
Hisenthusiasmforhisresearchandteachinghelpedmakegeophysicsenjoyablefor
me.Ithankallthosewhohelddiscussionswithmeandprovidedvaluablecomments
ontheresearch.
Tsukuba,Japan TatsuhikoSaito
Contents
1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 OffshoreTsunamiObservations. . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 The2011Tohoku-OkiEarthquake. . . . . . . . . . . . . . . . . . . . . . . . 5
1.3 ObservationInsideEarthquakeFocalArea. . . . . . . . . . . . . . . . . . 11
1.4 FocusofThisBook. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2 OverviewofTsunami. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.1 EarthquakesandTsunami:APossibleScenarioinNankai
Trough,Japan. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.1.1 NankaiTrough,Japan. . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.1.2 EarthquakeRuptureModel. . . . . . . . . . . . . . . . . . . . . . . . 18
2.1.3 ATwo-StepMethodforSimulatingTsunamiGeneration
andPropagation. . .. . . . . . . . . . . . . . . . . . . . . . . . .. . . . 21
2.1.4 SeismicWavesandPermanentSea-BottomDisplacement. . . 21
2.1.5 TsunamiGenerationandPropagation. . . . . . . . . . . . . . . . 23
2.1.6 SlowRupture. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.2 TsunamiGeneration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.3 TsunamiPropagation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.3.1 PropagationSpeed. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
2.3.2 Amplification. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
2.3.3 Nonlinearity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
2.3.4 Inundation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . 40
2.4 PointsofTsunamiGenerationandPropagation. . . . . . . . . . . . . . . 41
Appendices. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
AppendixA:SimulationMethodofTsunamiGeneratedby
anEarthquake. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
AppendixB:PhaseVelocityinNonlinearLong-Wave
Equations:TheFirst-OrderApproximationMethod. . . . . . . . . . . . 44
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
vii
viii Contents
3 PropagationofTsunamiandSeismicWaves. . . . . . . . . . . . . . . . . . . 49
3.1 GoverningEquations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
3.1.1 StressandStrain. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
3.1.2 EquationofMotionandConstitutiveLaws. . . . . . . . . . . . 54
3.2 Tsunami:DynamicsofIncompressibleFluid. . . . . . . . . . . . . . . . 57
3.2.1 FundamentalEquationsofTsunami. . . . . . . . . . . . . . . . . 57
3.2.2 Tsunami. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
3.2.3 EnergyDensityandEnergyFluxDensityfor
IncompressibleFluid. . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
3.3 SeismicWaves:ElasticDynamics. . . . . . . . . . . . . . . . . . . . . . . . 82
3.3.1 P,S,andRayleighWaves. . . . . . . . . . . . . . . . . . . . . . . . 83
3.3.2 OceanAcousticWaves. . . . . . . . . . . . . . . . . . . . . . . . . . 94
3.3.3 EnergyDensityandEnergyFluxDensity
forElasticMedium. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
3.4 WavesinContinuumMedium. . . . . . . . . . . . . . . . . . . . . . . . . . . 101
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
4 Earthquakes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
4.1 APointSourceandSeismicWaveExcitation. . . . . . . . . . . . . . . . 105
4.1.1 APointShearDislocationSource:EquivalentBody
ForceandMomentTensor. . . . . . . . . . . . . . . . . . . . . . . . 105
4.1.2 DisplacementFieldfromaPointSource. . . . . . . . . . . . . . 110
4.2 FiniteFaultModelandScalingLaw. .. . . .. . . .. . . .. . . .. . . .. 116
4.2.1 StressDrop. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
4.2.2 ScalingLaw. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
4.2.3 UsingtheScalingLawforTsunamiSimulation. . . . . . . . . 124
4.3 SeismicWaveSimulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
4.3.1 FiniteDifferenceMethod. . . . . . . . . . . . . . . . . . . . . . . . . 126
4.3.2 SeismicWaves,OceanAcousticWaves,andPermanent
Displacement. . .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. 134
4.3.3 BridgingSeismicWaveSimulationtoTsunami
PropagationSimulation. . . . . . . . . . . . . . . . . . . . . . . . . . 137
AppendixA:SeismicWavePropagationin2-DSpace:
P-SVProblem. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
5 TsunamiGeneration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
5.1 OceanAcousticWavesandTsunami:DifferentDrivingForces. . . 149
5.2 LinearPotentialTheory. . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . 151
5.2.1 GoverningEquations. . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
5.2.2 SolvingLaplaceEquationwithBoundaryConditions. . . . . 156
5.3 Generation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
5.3.1 Visualization. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
5.3.2 AnalyticalSolutions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
5.3.3 PressureChange. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174
Contents ix
5.4 BridgingGenerationtoPropagation. . . . . . . . . . . . . . . . . . . . . . . 184
5.4.1 ContributionofSea-DepthVariation. . . . . . . . . . . . . . . . . 184
5.4.2 SynthesisofOcean-BottomPressureRecords. . . . . . . . . . 187
Appendices. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193
Appendix5A:Equation(5.28). . . . . . . . . . . . . . . . . . . . . . . . . . . 193
Appendix5B:TsunamiPropagationfromanInitialHeight
DistributionandZeroVelocityDistribution. . . . . . . . . . . . . . . . . 198
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202
6 PropagationSimulation. . . . . .. . . . .. . . . . .. . . . . .. . . . .. . . . . .. 205
6.1 NonlinearandDispersiveTsunami. . . . . .. . . . .. . . . . .. . . . . .. 205
6.1.1 NonlinearWaves. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207
6.1.2 DispersiveWaves. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212
6.2 TsunamiEquationsDerivedfromEquationsofMotion. . . . . . . . . 214
6.2.1 IntegrationwithRespecttoSeaDepth:3-Dto
2-DEquations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214
6.2.2 Long-WaveApproximations. .. . . . . . . . . . . . . . . . . . .. . 225
6.3 NumericalSimulations:FiniteDifferenceMethod. . . . . . . . . . . . . 234
6.3.1 LinearLong-WaveEquations:SimplestEquations. . . . . . . 234
6.3.2 NonlinearLong-WaveEquations:Inundation.. . . . . . . . .. 238
6.3.3 LinearDispersiveEquations:DeepOcean. . . . . . . . . . . . . 244
6.3.4 NonlinearDispersiveEquations. . . . . . . . . . . . . . . . . . . . 249
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252
7 Epilogue. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255
7.1 TsunamiPropagation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255
7.2 TsunamiGeneration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257
7.3 EarthScienceandDisasterPrevention. . . . . . . . . . . . . . . . . . . . . 257
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 258
Index. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261