Probabilistic Tsunami Hazard Analysis

Hong Kie Thio

URS Corp

Tsunami hazard - probabilistic

• Integration over a broad range of seismic 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)

• How do we extend probabilistic offshore waveheights to inundation (i.e. site behaviour)?

Expression of probability

• Assuming Poissonian (time-independent) process:

– P=1-e-γt , where P = probability of exceedance, γ = average annual rate of exceedance and t = exposure time.

– Average Return Period (ARP) = 1/Average Annual Rate

– Typical engineering levels:

• 10% in 50 years -> 475 years ARP

• 5% in 50 years -> 975 year ARP

• 2% in 50 years -> 2475 years ARP

Probabilistic Tsunami Hazard Analysis

Aim:

• Determine the probability of exceeding a certain hazard level (e.g. wave amplitude)

• Determine the hazard level that is exceeded for a particular probability (or set of probabilities)

Tsunami Hazard Curve

Application of PTHA

• Performance Based Engineering

– Chapter on Tsunami Loads in next iteration of ASCE 7

• Risk/Loss modeling

• Land use planning

What is the final product?

• Waveheight

• Inundation

• Flow depth - D

• Flow velocity – V (maybe at minimum flow depth)

• Momentum, momentum flux

• Drawdown, duration

• Vorticity

• Combinations of the above?

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

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

Aleatory: Magnitude Distribution

Slip Relations

Crustal Subduction

Alaska-Aleutian Subduction Zone

USGS model for PSHA:

• Coupling ~50%

• Strong segmentation

• Gutenberg-Richter relation for most segments

Further work for slip models

• Comprehensive scaling relations for subduction zone interface

– Maximum magnitude

– Average and maximum slip

– Concentrate on larger (M > 6.5) events

– Reduction in sigma?

– By-pass magnitude scaling?

• Stochastic slip models

Source recurrence model

• Generic model – Mmax based on Lmax

– Recurrence rate based on plate motions

• Specific model – Mmax, recurrence based on instrumental, hstoric and

paleo-tsunami observations

– Inferences from tectonic models (e.g. Marianas vs Chile type subduction)

• Increased weight on specific model depending on completeness and duration of catalog

Aleatory Uncertainty from Scenario

Modeling

Benchmarking - Okushiri

Effect of Variability on Hazard Curves

Effect of Tides on PTHA

Variability of global DEM’s

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

• Onshore – Difficult due to strong non-linearity

– May need to apply on the offshore waveheights and propagate in

Offshore waveheight hazard

72 yr

475 yr

975 yr

2500 yr

Source disaggregation

Cascadia Model

• Mw=8.1-9.2

• Dmax=2*Dave

• Asperities 1/3 of total rupture (x3)

• Narrow and wide models (x2)

• With and without splay (x2)

Probabilistic Inundation Maps

Probabilistic Inundation Maps

Half_Moon_Bay−0.96c

237.475˚237.5˚

237.525˚237.55˚

237.575˚

37.425˚

37.45˚

37.475˚

37.5˚

37.525˚

−20

7550010003000

ARP

Morro_Bay−0.96c

239.1˚ 239.125˚ 239.15˚ 239.175˚

35.325˚

35.35˚

35.375˚

35.4˚

35.425˚

35.45˚

−2

0

75

500

1000

3000

AR

P

Probabilistic Inundation Maps

Orick−0.96c

235.9˚235.925˚

235.95˚

41.275˚

41.3˚

075

50010003000

ARP

Klamath−0.96c

235.9˚235.925˚

235.95˚235.975˚

236˚

41.5˚

41.525˚

41.55˚

41.575˚

41.6˚

075

50010003000

ARP

Probabilistic Inundation Maps

-121.8˚ -121.775˚ -121.75˚

36.7˚

36.725˚

36.75˚

36.775˚

36.8˚

36.825˚

36.85˚

36.875˚

-2

0

75

500

1000

3000

AR

P

Santa_Cruz-0.96c

-122.1˚-122.075˚-122.05˚-122.025-̊122-̊121.975˚-121.95˚-121.925˚-121.9˚

36.95˚

36.975˚

-2

0

75

500

1000

3000

AR

P

Monterey-0.96c

-122˚ -121.975 -̊121.95-̊121.925˚-121.9˚-121.875 -̊121.85˚

36.6˚

36.625˚

-2

0

75

500

1000

3000

AR

P

Probabilistic Inundation Maps Avila_Beach-0.96c

-120.775˚-120.75˚-120.725˚-120.7˚-120.675˚-120.65˚-120.625˚-120.6˚

35.1˚

35.125˚

35.15˚

35.175˚

-2

0

75

500

1000

3000

AR

P

Pacifica-0.96c

-122.525˚ -122.5˚

37.6˚

37.625˚

37.65˚

-2

0

75

500

1000

3000

AR

P

West_Frisco-0.96c

-122.525˚ -122.5˚

37.7˚

37.725˚

37.75˚

37.775˚

-2

0

75

500

1000

3000

AR

P

Golden_Gate-0.96c

-122.475˚ -122.45˚

37.8˚

-2

0

75

500

1000

3000

AR

P

Probabilistic Inundation Maps Ventura-0.96c

-119.3-̊119.275˚-119.25˚-119.225-̊119.2-̊119.175˚-119.15˚

34.125˚

34.15˚

34.175˚

34.2˚

34.225˚

34.25˚

34.275˚

-2

0

75

500

1000

3000

AR

P

POLA-0.96c

-118.3˚-118.275˚-118.25˚-118.225˚-118.2˚-118.175˚-118.15˚-118.125˚-118.1˚-118.075˚-118.05˚-118.025˚-118˚

33.7˚

33.725˚

33.75˚

33.775˚

-2

0

75

500

1000

3000

AR

P

Huntington_Beach-0.96c

-118.025˚ -118˚ -117.975˚ -117.95˚

33.65˚

33.675˚

-2

0

75

500

1000

3000

AR

P

Santa_Monica-0.96c

-118.5˚ -118.475˚ -118.45˚ -118.425˚

33.95˚

33.975˚

34˚

34.025˚

-2

0

75

500

1000

3000

AR

P

Probabilistic Inundation Maps

Oceanside-0.96c

-117.4˚ -117.375˚ -117.35˚ -117.325˚

33.15˚

33.175˚

33.2˚

33.225˚

-2

0

75

500

1000

3000

AR

P

San_Diego-0.96c

-117.275˚-117.25˚-117.225˚-117.2˚-117.175˚-117.15˚-117.125˚-117.1˚

32.575˚

32.6˚

32.625˚

32.65˚

32.675˚

32.7˚

32.725˚

32.75˚

32.775˚

32.8˚

-2

0

75

500

1000

3000

AR

P

Conclusion

• Important to quantify uncertainties in every stage of the hazard model, including modeling uncertainties

• Aleatory variability in rupture models should be included

• Close coordination between the USGS Seismic Hazard Mapping program and NTHMP

PTHA Inundation in Hawaii

Honolulu−0.96c

202.1˚202.125˚

202.15˚202.175˚

202.2˚

21.3˚

21.325˚

21.35˚

−20

7550010003000

ARP

Hilo−0.96c

204.9˚ 204.925˚ 204.95˚ 204.975˚ 205˚

19.7˚

19.725˚

19.75˚

19.775˚

19.8˚

−2

0

75

500

1000

3000

AR

P

Probabilistic offshore waveheight hazard