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