The Physics of Tsunami Generation: The Physics of Tsunami Generation: Recent Advances and Persistent Recent Advances and Persistent
ProblemsProblems
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Eric L. GeistEric L. Geist
U.S. Geological SurveyU.S. Geological Survey
http://walrus.wr.usgs.gov/tsunamihttp://walrus.wr.usgs.gov/tsunami
OutlineOutline IntroductionIntroduction Problem 1Problem 1: : Fault SlipFault Slip
Scaling of average slip with MScaling of average slip with Mww
Distribution of slipDistribution of slip Problem 2Problem 2: : Tsunami EarthquakesTsunami Earthquakes
Why, Where?Why, Where? Problem 3Problem 3: : Landslide TsunamisLandslide Tsunamis
Coupling of slide dynamics with the water columnCoupling of slide dynamics with the water column Problem 4Problem 4: : Tsunami ProbabilityTsunami Probability
Computational methodsComputational methods Summary Summary
Introduction: Source Introduction: Source PhysicsPhysics
EarthquakesEarthquakes Constitutive Constitutive
RelationsRelations Linear elasticLinear elastic
Anelastic (plastic) Anelastic (plastic) near fault zone*near fault zone*
Equations of MotionEquations of Motion
ForcingForcing TectonicsTectonics Gravity*Gravity*
LandslidesLandslides Constitutive RelationsConstitutive Relations
ViscousViscous Bingham PlasticBingham Plastic Bi-linear Flow Bi-linear Flow
(Newtonian, Bingham)(Newtonian, Bingham) Herschel-Bulkley Herschel-Bulkley
(non-linear)(non-linear) OtherOther
Rigid bodyRigid body GranularGranular
Equations of Motion Equations of Motion (Cauchy)(Cauchy)
ForcingForcing GravityGravity Seismic Loading*Seismic Loading*
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σ ij = Cijpqε pq
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ρ˙ ̇ u i = fi +σ ij, j
Tsunami Generation: Tsunami Generation: EarthquakesEarthquakes
um(r) = Di (r0)ν j (r0)Umij (r,
Σ∫∫ r0)dΣ
Σ Rupture area
Di (r0) Slip distribution
ν j (r0) Surface normal
Gmi (r,r0) Static elastic Green's functions
λ,μ Lamé constants
Umij (r,r0) =λ(r0)δijGm
n,n(r,r0)+μ(r0)Gmi, j (r,r0)+Gm
j,i (r,r0)[ ]
Rybicki (1986)
Tsunami Generation: Tsunami Generation: EarthquakesEarthquakes
Effect of Horizontal Effect of Horizontal DisplacementsDisplacements
Tanioka & Satake, 1996€
uh = ux∂H∂x
+uy∂H∂y H: Water Depth (positive downward)
Earthquake Rupture:Earthquake Rupture:Levels of ApproximationLevels of Approximation
t0t1 t2 t3
t4
D
DD(t) |f(t)|
f0f0≈ ≈
Actual Fault Displacement History
Average Dislocation Model
Equivalent Body Force System
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M0 = μAD Scalar Seismic Moment
Lay & Wallace (1995)
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MW = 23
logM0 −10.73Moment Magnitude
Scaling of Average SlipScaling of Average SlipProblem #1
Scaling of Average SlipScaling of Average Slip
Slip DistributionSlip Distribution
Observed Slip Observed Slip DistributionsDistributions
Ihmlé (1996a,b)
1992 Mw=7.7 Nicaragua EQ
2D Effect of Distributed 2D Effect of Distributed SlipSlip
Seismic Source SpectraSeismic Source Spectra Hartzell & Heaton Hartzell & Heaton
(1985)(1985) Polet & Kanamori Polet & Kanamori
(2000)(2000)
Self-affine slip spectrumSelf-affine slip spectrum(Hanks, 1979; Andrews, 1980; Frankel, 1991; Herrero & Bernard, 1994; Tsai, 1997; Hisada, 2000; 2001; Mai & Beroza, 2000; 2002)
Strong ground motion applications(e.g., Berge et al., 1998; Somerville et al., 1999)
D(k) =CΔσμ
Lkγ k>kc
Stochastic Source Stochastic Source ModelModel
Jason-1 Altimetry: Pass 129, Jason-1 Altimetry: Pass 129, Cycle 109Cycle 109
Joint inversion of tide gauge Joint inversion of tide gauge and satellite altimetry and satellite altimetry
(TG+SA) data(TG+SA) data
MMw = 9.1w = 9.1
TG+SATG+SA
Vr = 1.0km/sVr = 1.0km/s
TG+SATG+SA
Vr = 1.5km/sVr = 1.5km/s
TG+SATG+SA
Vr = 2.0km/sVr = 2.0km/s
Fujii and Satake (BSSA, in press)Fujii and Satake (BSSA, in press)
Courtesy Y. FujiiCourtesy Y. Fujii
Tsunami EarthquakesTsunami Earthquakes Originally defined & identified by Kanamori (1972)Originally defined & identified by Kanamori (1972) Further elaborated by Kanamori & Kikuchi (1993)Further elaborated by Kanamori & Kikuchi (1993)
Class 1: Non-accreting margins, surface rupture at trenchClass 1: Non-accreting margins, surface rupture at trench Class 2: Accreting margins, triggered landslidesClass 2: Accreting margins, triggered landslides
Class 1: Characterized by slow rupture velocitiesClass 1: Characterized by slow rupture velocities Increased tsunami excitation fromIncreased tsunami excitation from
High slip relative to MHigh slip relative to Mww
Shallow depthShallow depth Deep water above sourceDeep water above source
Maybe correlated with rough topography of the downgoing Maybe correlated with rough topography of the downgoing plate (Tanioka, et al., 1997; Polet & Kanamori, 2000, Bilek plate (Tanioka, et al., 1997; Polet & Kanamori, 2000, Bilek & Lay, 2002)& Lay, 2002)
Coseismic anelastic deformation ? Coseismic anelastic deformation ? (Tanioka & Seno, 2001)(Tanioka & Seno, 2001)
Problem #2
Local Tsunami Runup vs. Local Tsunami Runup vs. MMww
July 2006 Java Tsunami July 2006 Java Tsunami EarthquakeEarthquake
Chen Ji, UCSBhttp://neic.usgs.gov/neis/eq_depot/2006/eq_060717_qgaf/neic_qgaf_ff.html
Abandoning Scaling Abandoning Scaling RelationshipsRelationships
Spontaneous rupture Spontaneous rupture modeling modeling (Oglesby et al., 1998; (Oglesby et al., 1998; 2000 a,b; 2001; 2002; 2003a, b; 2000 a,b; 2001; 2002; 2003a, b; 2005)2005)
InputsInputs Frictional properties of fault Frictional properties of fault Elastic properties of Elastic properties of
surrounding rockssurrounding rocks Pre-stress distributionPre-stress distribution Critical slip-weakening Critical slip-weakening
distancedistance Full elastodynamic Full elastodynamic
modelingmodeling Interaction of seismic waves Interaction of seismic waves
with rupture propagationwith rupture propagation
Bilek & Lay (2002)
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f = f0 + a ln VV0
⎛ ⎝ ⎜ ⎞
⎠ ⎟+b ln θ
θ0
⎛ ⎝ ⎜ ⎞
⎠ ⎟
Dieterich-Ruina friction law
LandslidesLandslides
Varnes (1978)
Problem #3
Tsunami Generation: Tsunami Generation: LandslidesLandslides
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Patrick Lynett, Texas A&M
Santa Barbara Channel Submarine Santa Barbara Channel Submarine LandslidesLandslides
Goleta Slide
Gaviota Slide
Image courtesy of Monterey Bay Aquarium Image courtesy of Monterey Bay Aquarium Research InstituteResearch Institute
Dating the Palos Verdes Dating the Palos Verdes LandslideLandslide
Debris flow interval
Age = 7500 yrs. Normark et al., (2004)C-14 ages:
Core 510
Seismically-Induced Seismically-Induced Submarine LandslidesSubmarine Landslides
Triggering Triggering (Biscontin et al., 2004; Biscontin & (Biscontin et al., 2004; Biscontin & Pestana, 2006)Pestana, 2006) Seismic loading -> Excess pore pressureSeismic loading -> Excess pore pressure Possibility of later failure from pore pressure Possibility of later failure from pore pressure
redistributionredistribution Initial (and Inertial) DisplacementsInitial (and Inertial) Displacements
2D compliant model 2D compliant model (Kayen & Ozaki, 2002)(Kayen & Ozaki, 2002)
Post-Failure DynamicsPost-Failure Dynamics BING flow dynamics model BING flow dynamics model (Imran et al., 2001)(Imran et al., 2001) Example: Palos Verdes Example: Palos Verdes (Locat et al., 2004)(Locat et al., 2004)
Seismically Induced Landslides: Seismically Induced Landslides: Dynamic ComplianceDynamic Compliance
Text from G.K. Gilbert on the1906 event (Lawson, et al., 1908) -"There was also a horizontal shifting of mud over a considerable area", "At various places along the shore...the tidal mud seemed crowded against the firmer ground at the shore, being pushed up into a ridge" "Maximum shifting...was not less than 30 feet."
Courtesy: Rob Kayen (USGS)
Seismically-Induced Seismically-Induced Landslides:Landslides:Post-Failure DynamicsPost-Failure Dynamics
Locat et al. (2004)
What’s the Chance of a What’s the Chance of a Tsunami?Tsunami?
Necessary IngredientsNecessary Ingredients Statement of the ProblemStatement of the Problem
What size?What size? Where?Where? Exposure Time?Exposure Time? Starting When?Starting When?
Distribution of Event SizesDistribution of Event Sizes Distribution of Inter-Event TimesDistribution of Inter-Event Times
Empirical ApproachEmpirical Approach Computational ApproachComputational Approach
Probabilistic Tsunami Hazard Analysis (PTHA)Probabilistic Tsunami Hazard Analysis (PTHA)
Problem #4
Computational Probabilistic Computational Probabilistic Tsunami Hazard Analysis Tsunami Hazard Analysis
(PTHA)(PTHA) Based on PSHABased on PSHA Differences:Differences:
Inclusion of far-field sourcesInclusion of far-field sources Numerical propagation modelsNumerical propagation models
Determine source model (e.g., EQ’s)Determine source model (e.g., EQ’s) Source ParametersSource Parameters Location (Zonation)Location (Zonation) Frequency-Magnitude DistributionFrequency-Magnitude Distribution
Earthquake CatalogEarthquake Catalog Seismic moment balanceSeismic moment balance
Propagation-Inundation modelPropagation-Inundation model Compute for each sourceCompute for each source
Calculate Aggregate ProbabilitiesCalculate Aggregate Probabilities
Case Study: Seaside, ORCase Study: Seaside, ORTsuPilot Working Group
Distribution of EQ SizesDistribution of EQ Sizes
0.00001
0.0001
0.001
0.01
0.1
1
7 7.5 8 8.5 9 9.5
M
Cumulative Number per Year
Alaska-AleutianMexicoS. AmericaAndaman Island-Sumatra
Mc=9.09,b=.81
Mc=8.53,b=.98
Mc=8.41,b=.87
Mc=9.41,b=1.23
Flinn-Engdahl Regions
Kagan (1997)
Distribution of Landslide Distribution of Landslide SizesSizes
ten Brink et al. (2006)
Puerto Rico
Calculating ProbabilitiesCalculating Probabilities
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Ppois =1− exp(−λT )
Cumulative probability that an event Cumulative probability that an event will occur during time will occur during time TT
Non-Poissonian Inter-Event Non-Poissonian Inter-Event TimesTimes
Hilo
Global
Poisson
Gamma
Parsons & Geist (in prep.)
SummarySummary
Problem 1: SlipProblem 1: Slip Old theoryOld theory
DislocationsDislocations Recent AdvancesRecent Advances
Technology: Deep-Sea Tsunami MeasurementsTechnology: Deep-Sea Tsunami Measurements Results from Sumatra 2004, 2005 Earthquakes: Lower Results from Sumatra 2004, 2005 Earthquakes: Lower
Average Slip Relative to MAverage Slip Relative to Mww
In ProgressIn Progress Large Fluctuations in Slip: LLarge Fluctuations in Slip: Lévy Law Slip Distributionsévy Law Slip Distributions
Persistent ProblemsPersistent Problems Scaling UncertaintyScaling Uncertainty
SummarySummary
Problem 2: Tsunami EarthquakesProblem 2: Tsunami Earthquakes Recent AdvancesRecent Advances
Broadband SeismologyBroadband Seismology In ProgressIn Progress
Spontaneous, Dynamic Rupture ModelsSpontaneous, Dynamic Rupture Models Persistent ProblemsPersistent Problems
Where and Why: Frictional and Pre-Stress Where and Why: Frictional and Pre-Stress Conditions of the Shallow Inter-Plate ThrustConditions of the Shallow Inter-Plate Thrust
SummarySummary Problem 3: Landslide TsunamisProblem 3: Landslide Tsunamis
Old theoryOld theory Rigid BlockRigid Block
Recent AdvancesRecent Advances Technology: Multibeam Bathymetry, DatingTechnology: Multibeam Bathymetry, Dating Constitutive Description of Landslide DynamicsConstitutive Description of Landslide Dynamics
In ProgressIn Progress Understanding Seismic TriggeringUnderstanding Seismic Triggering
Persistent ProblemsPersistent Problems Multiple rheologiesMultiple rheologies Coupling Post-Failure Dynamic Models with Coupling Post-Failure Dynamic Models with
HydrodynamicsHydrodynamics
SummarySummary Problem 4: Tsunami ProbabilityProblem 4: Tsunami Probability
Old theoryOld theory Seismic-GapSeismic-Gap
Recent AdvancesRecent Advances Power-Law Frequency-Size Distribution for TsunamisPower-Law Frequency-Size Distribution for Tsunamis Statistics of Subduction Zone EarthquakesStatistics of Subduction Zone Earthquakes Power-Law Frequency-Size Distribution for Submarine Power-Law Frequency-Size Distribution for Submarine
LandslidesLandslides In ProgressIn Progress
Non-Poissonian Timing: Temporal ClusteringNon-Poissonian Timing: Temporal Clustering Short-Term Forecasting: Accelerated Moment ReleaseShort-Term Forecasting: Accelerated Moment Release
Persistent ProblemsPersistent Problems Time-Dependent RuptureTime-Dependent Rupture Probabilities of Extreme EventsProbabilities of Extreme Events