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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