playing against nature: improving earthquake hazard assessment & mitigation seth stein, earth...
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Playing against nature: improving earthquake hazard
assessment & mitigationSeth Stein,
Earth & Planetary Sciences,
Northwestern University
Jerome Stein, Applied
Mathematics, Brown
University
G52A-04 Tohoku, Japan 3/2011 M 9.1
Japan spent lots of effort on national hazard map, but
2011 M 9.1 Tohoku, 1995 Kobe M 7.3 & others in areas mapped as low hazard
In contrast: map assumed high hazard in Tokai “gap”
Geller 2011
Tohoku earthquake broke many segments
2011 Tohoku Earthquake 450 km long fault, M 9.1 (Aftershock map from USGS)
J. Mori
Expected Earthquake Sources 50 to 150 km segments M7.5 to 8.2(Headquarters for Earthquake Research Promotion)
Tsunami runup approximately twice
fault slip (Plafker, Okal &
Synolakis 2004)
M9 generates much larger tsunami
Mitigation planning assumed maximum magnitude 8 Seawalls 5-10 m high
CNN
NYTStein & Okal, 2011
QuickTime™ and a decompressor
are needed to see this picture.
NY Times 3/31/2011
Expensive seawalls - longer than Great Wall of China -proved ineffective
180/300 km swept away or destroyed
In some cases discouraged evacuation
2008 Wenchuan earthquake (Mw 7.9) was not expected: map showed low hazard based on lack of recent
earthquakes
Didn’t use GPS data showing 1-2 mm/yr (~Wasatch)
Earthquakes prior to the 2008 Wenchuan event
Aftershocks of the Wenchuan event delineating the rupture zone Stein et al., 2012
Haiti
2001 hazard map
http://www.oas.org/cdmp/document/seismap/haiti_dr.htm
2010 M7 earthquake shaking much greater than predicted for next 500 years
Map didn’t use GPS data
Similar problems occur worldwideThe earth often surprises us
Do these reflect systemic problems with hazard mapping or simply low probability events (someone
wins the lottery)?
How can we do better at assessing hazards and mitigating them?
QuickTime™ and a decompressor
are needed to see this picture.
NY Times 11/2/2011
Choosing mitigation policy involves hazard assessment, economics, politics
Too expensive to rebuild for 2011 sized tsunami
>100 $B for new defenses only slightly higher than old ones
“In 30 years there might be nothing left there but fancy breakwaters and empty houses.”
Hazard maps are hard to get right: successfully predicting future shaking depends on accuracy
of four assumptions over 500-2500 years
Where will large earthquakes occur?
When will they occur?
How large will they be?
How strong will their shaking be?
Uncertainty & possible map failure result because these are often hard to assess, especially in plate
interiors & other slowly deforming zones
Plate Boundary Earthquakes•Major fault loaded rapidly at constant rate
•Earthquakes spatially focused & temporally quasi-periodicPast is fair predictorIntraplate Earthquakes
•Tectonic loading collectively accommodated by a complex system of interacting faults•Loading rate on a given fault is slow & may not be constant•Earthquakes can cluster on a fault for a while then shiftPast can be poor predictor
Plate A
Plate B
Earthquakes at different time
Stein, Liu & Wang 2009
during the periodprior to the periodinstrumental events
Earthquakes in North ChinaEarthquakes in North China
Large events often pop up where there was little seismicity!
OrdosPlateau
Sha
nxi G
rabe
n
Bohai Bay
Beijing
1303 HongtongM 8.0
Liu, Stein & Wang 2011
Weihi rift
during the periodprior to the periodinstrumental events
Earthquakes in North ChinaEarthquakes in North China
Large events often pop up where there was little seismicity!
OrdosPlateau
Sha
nxi G
rabe
n
Bohai Bay
Beijing
1556 HuaxianM 8.3
Weihi rift
Liu, Stein & Wang 2011
during the periodprior to the periodinstrumental events
Earthquakes in North ChinaEarthquakes in North China
Large events often pop up where there was little seismicity!
OrdosPlateau
Sha
nxi G
rabe
n
Bohai Bay
Beijing
1668 TanchengM 8.5
Weihi rift
Liu, Stein & Wang 2011
during the periodprior to the periodinstrumental events
Earthquakes in North ChinaEarthquakes in North China
Large events often pop up where there was little seismicity!
OrdosPlateau
Sha
nxi G
rabe
n
Bohai Bay
Beijing
1679 SanheM 8.0
Weihi rift
Liu, Stein & Wang 2011
during the periodprior to the periodinstrumental events
Earthquakes in North ChinaEarthquakes in North China
Large events often pop up where there was little seismicity!
OrdosPlateau
Sha
nxi G
rabe
n
Bohai Bay
Beijing
1966 XingtaiM 7.2
1976 TangshanM 7.8
1975 HaichengM 7.3
Weihi rift
Liu, Stein & Wang 2011
No large (M>7) events ruptured the same fault segment twice in past 2000 years
In past 200 years, quakes migrated from Shanxi Graben to N. China Plain
Historical
Instrumental
Shan
xi G
rabe
n
Weihi rift
Newman et al., 2001
180%
275%
Hazard maps involve
assumptions about
- Mmax of largest future events
-Ground motion model
-Timing of future earthquakes
(time-independent or time-
dependent)
Since all have large
uncertainties, wide range of
plausible hazard models
154%
%106
Hazard maps involve
assumptions about
- Mmax of largest future events
-Ground motion model
-Timing of future earthquakes
(time-independent or time-
dependent)
Since all have large
uncertainties, wide range of
plausible hazard models
Stein et al, 2012
Stein et al., 2012
Uncertainty typically factor of 3-4
Often can’t be reduced much due to earthquake variability
Hazard is essentially unknowable within broad range
One can chose a particular value depending on preconception, but the uncertainty remains and only time will tell how good the choice was
Seismological assessment of hazard maps
Various metrics could be used, e.g. compare maximum observed shaking in subregion i, xi to
predicted maximum shaking pi
Compute Hazard Map Error HME(p,x) = i (xi - pi)2/N
and compare to error of reference map produced using a null hypothesis
HME(r,x) = i (xi - ri)2/N
using the skill score
SS(p,r,x) = 1 - HME(p,x)/HME(r,x)
Positive score if map does better than null
Some testing challenges
1) Short time record: can be worked around by aggregating regions.
2) Subjective nature of hazard mapping, resulting from need to chose faults, maximum magnitude, recurrence model, and ground motion model. This precludes the traditional method of developing a model from the first part of a time series and testing how well it does in the later part. That works if the model is "automatically" generated by some rules (e.g. least squares, etc). In the earthquake case, this can't be done easily because we know what happens in the later part of the series.
3) New maps made after a large earthquake that earlier maps missed are problem for counting statistics.
Frankel et al, 2010
Before 2010 Haiti M7 After 2010 Haiti M7
4X
4) Overparameterized model (overfit data):
Given a trend with scatter, fitting a
higher order polynomial can give
a better fit to the past data but a worse fit to future data
Analogously, a seismic hazard map fit to details of past
earthquakes could be a worse predictor of
futureones than a smoothed
map
How much detail is useful?
Linear fit
Quadratic fit
Consider map as means, not end
Assess map’s success in terms of contribution to
mitigation
Even uncertain or poor maps may do
some good
Societal assessment of hazard maps
Societally optimal level of mitigation minimizes
total cost = sum of mitigation cost + expected loss
Expected loss = ∑ (loss in ith expected event x assumed probability of that event)
Compared to optimum
Less mitigation decreases construction costs but increases expected loss and thus total cost
More mitigation gives less expected loss but higher total cost
Stein & Stein, 2012
For earthquake, mitigation level is construction codeLoss depends on earthquake & mitigation level
Optimum
Loss estimate scenarios based on hazard model
Estimate loss as function of magnitude, ground shaking model, recurrence rate, and mitigation level
This case
Current mitigation
10-100 fatalities
~ $100B damage
Examine range of parameters & use to find optimum
http://earthquake.usgs.gov/earthquakes/eqarchives/poster/2011/20110516.php
Present Value of Future LossesExpected average loss over T years is LT
Interest rate i
PVFL = LT t 1/(1+i)t = LT DT
DT = 1/(1+i) + 1/(1+i)2 + ... + 1/(1+i)T
= ((1+i)T -1 ) / (i(1+i)T) ≈ 1/i for T large
For interest rate i=0.05, DT = 15.4 for 30 years, and 19.8 for 100 years. For long enough times, the limit as T becomes infinite is DT = 1 / I, so if i = 0.05, D = 20. This is essentially the same as the value for 100 years.
Even without uncertainty, mitigation rarely will be optimal for societal reasons,but can still do some good
Net benefit when mitigation lowers total cost below that of no mitigation
Net loss when mitigation raises total cost above that of no mitigation
Within range,
inaccurate hazard maps produce nonoptimal mitigation,
raising cost, but still do some good (net benefit)
Inaccurate loss estimates have same effect
Summary
Limitations in our knowledge about earthquakes, notably space-time variability,
limit how accurately hazard maps can be made
Although uncertain maps likely produce nonoptimal mitigation, they still do some good
if they’re not too bad
Testing maps & quantifying uncertainties will help some
Need to recognize & accept uncertainties