Probabilistic Tsunami Hazard 

Analysis

Hong Kie Thio

URS Corporation
Tsunami hazard - probabilistic

• Integration over a broad range of tsunami 

sources with varying sizes and recurrence rates

• Formal inclusion of uncertainties through logic 

trees and distribution functions

• Straightforward for offshore waveheights because 

of linear approximation (analogous to stiff site 

condition)

• Extension probabilistic offshore waveheights to 

inundation
Magnitude/frequency of tsunami sources

Size of Tsunami (m)

Recurrence Rate (1/yr) (annual probability of exceedence)-1

1

.1

.01

.001

.0001

1

10 100 1000

Distant Earthquakes

Local Earthquakes

Landslides

Volcanoes

Asteroid Impact

Power et al., 2005
Concepts of Probability

Frequency (aleatory)

• Describes the natural 

(physical) variability of 

earthquake processes

• Typically expressed in the 

form of distribution 

functions

Judgment (epistemic)

• Expresses the uncertainty in 

our understanding of 

earthquake processes

• Included as different 

branches of a logic tree that 

each express a different 

opinion, or belief

ARP
PTHA vs PSHA

Source – Magnitude, 

location

recurrence

GMPE – site, M, R

Non-linear soil analysis 

– SHAKE, FLAC, etc

Source – Magnitude, 

location (large R)

recurrence, slip

Long wave model–

bathymetry, numerical 

solution FD, FV, 

offshore

Inundation – nonlinear numerical 

analysis, 

analytical/empirical 

relations
What are the largest uncertainties in 

PTHA?

• Source models

– Recurrence

– Mmax

– Slip Distribution

• Digital Elevation Models

– Near-shore Bathymetry

– Onshore Elevations (SRTM: errors of >10 m) 

• Numerical Models

– Near-shore Propagation/Inundation
Sumatra and Tohoku

Stein et al., 2012 
Slip Relations

Average slip Average and Maximum Slip
Source recurrence model – epistemic 

uncertainty, max magnitude

Model Segment Mmax Lon. range Recur

USGS All 7-8 -195.0 - -144.0 G-R

Yakataga 7 – 8.1 -145.5 - -139.5 G-R

East 9.2 -154.5 - -144.0 Max

Kodiak 8.8 -154.5 - -149.0 Max

Semidi 8 – 8.5 -158.0 - -154.0 G-R

Shumagin - -163.0 - -158.0 -

Western 8-9.2 -190.0 - -163.0 G-R

Komandorski 8 – 8.2 -195.0 - -190.0 G-R

McCafrey Alaska 9.5 -144 - -164 Max

East Aleutian 9.3 -164 - -180 Max

Western Aleutian 9.3 -180 - -195 Max
Source models

Base model

• Follows global scaling 

relations

• Mmax determined by overall 

dimensions of source

• Recurrence determined by 

plate rates

• What is maximum width?

• What is maximum slip?

– Related to Wmax?

Source specific model

• Based on observed 

earthquakes/tsunamis

• Historical record

• Paleo-tsunami deposits

• But: limited sampling
Aleatory Uncertainty from Scenario 

Modeling/Benchmarking and Tides
Effect of Aleatory Uncertainty on 

Tsunami Hazard Curves
How and where do we apply our 

uncertainties

• Source

– In many ways similar to seismic

– Variability in slip and scaling are important

• Offshore

– Straightforward in case of probabilistic exceedance

amplitudes (sigma, tides)

• Onshore

– Difficult due to strong non-linearity

– May need to apply on the offshore waveheights and 

propagate inward

– Apply variability in bottom friction?
Subfault Green’s function summation

+

Probabilistic offshore waveheight

hazard
Source disaggregation
Cascadia Scenarios

• Magnitude: 4x (8.5-9.2)

• Sigma (slip): 5x (-2, -1, 0, +1, +2) 

• Tide: 3x

• Splay: 2x (with and w/o)

• Width: 2x (80 - 120)

• Trench: 2x

• Slip Variation: 3x (Dmax=2*Dave)


Inundation uncertainty

• Bottom friction

– Manning of dimensionless

– Distribution of friction coefficients

– Variable friction

• Variable algorithm

– Finite difference/volume etc

– Dispersive algorithms
PTHA for submarine landslides

Source characteristics

• Dynamics (speed)

– Uncertainty through variation 

of physical parameters 

(friction?)

• Shape/cohesion

– From observed slides

• Volume

– From observed slides

Recurrence

• Excitation

– Strong coupling with 

earthquake occurrence?

– Decoupled from earthquake 

occurrence for very rare 

slides?

• Sediment input

• Slope

• Global sea level
Submarine slide sensitivity

Slide velocity and 

thickness Slide 

direction