Transcript agu12 - Department of Earth and Planetary Sciences

Playing against nature: improving
earthquake hazard assessment &
mitigation
Seth 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
Geller
2011
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”
Tohoku earthquake broke many segments
Expected Earthquake Sources
50 to 150 km segments
M7.5 to 8.2
(Headquarters for Earthquake Research Promotion)
2011 Tohoku Earthquake
450 km long fault, M 9.1
(Aftershock map from USGS)
J. Mori
Mitigation planning assumed maximum
magnitude 8 Seawalls 5-10 m high
Stein & Okal, 2011
NYT
Tsunami runup
approximately twice fault
slip (Plafker, Okal &
Synolakis 2004)
M9 generates much
larger tsunami
CNN
QuickTime™ and a
decompressor
are needed to see this picture.
Expensive
seawalls longer than
Great Wall of
China proved
ineffective
180/300 km
swept away
or destroyed
NY Times 3/31/2011
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
2010 M7 earthquake shaking
much greater than predicted
for next 500 years
http://www.oas.org/cdmp/document/seismap/haiti_dr.htm
Map didn’t use GPS data
Similar problems occur worldwide
The 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?
Choosing mitigation
policy involves
hazard assessment,
economics, politics
Too expensive to
rebuild for 2011
sized tsunami
QuickTime™ and a
decompressor
are needed to see this picture.
>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.”
NY Times 11/2/2011
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-periodic
Past is fair predictor
Plate B
Plate A
Earthquakes at
different time
Intraplate 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 shift
Past can be poor predictor
Stein, Liu & Wang 2009
Liu, Stein & Wang 2011
during the period
prior to the period
instrumental events
Earthquakes in North China
Beijing
Bohai Bay
Ordos
Plateau
1303 Hongtong
M 8.0
Weihi rift
Large events often pop up where there was little seismicity!
Liu, Stein & Wang 2011
during the period
prior to the period
instrumental events
Earthquakes in North China
Beijing
Bohai Bay
Ordos
Plateau
Weihi rift
1556 Huaxian
M 8.3
Large events often pop up where there was little seismicity!
Liu, Stein & Wang 2011
during the period
prior to the period
instrumental events
Earthquakes in North China
Beijing
Bohai Bay
Ordos
Plateau
Weihi rift
1668 Tancheng
M 8.5
Large events often pop up where there was little seismicity!
Liu, Stein & Wang 2011
during the period
prior to the period
instrumental events
Earthquakes in North China
1679 Sanhe
M 8.0
Beijing
Bohai Bay
Ordos
Plateau
Weihi rift
Large events often pop up where there was little seismicity!
Liu, Stein & Wang 2011
during the period
prior to the period
instrumental events
Earthquakes in North China
1975 Haicheng
M 7.3
Beijing
1976 TangshanBohai Bay
M 7.8
Ordos
Plateau
1966 Xingtai
M 7.2
Weihi rift
Large events often pop up where there was little seismicity!
No large (M>7) events ruptured the same
fault segment twice in past 2000 years
Historical
Instrumental
Weihi rift
In past 200 years, quakes migrated from Shanxi Graben to N. China Plain
Hazard maps involve
assumptions about
- Mmax of largest
future events
180%
-Ground motion model
-Timing of future
earthquakes (timeindependent or timedependent)
Since all have large
uncertainties, wide
range of plausible
hazard models
275%
Newman et
al., 2001
Hazard maps involve
assumptions about
- Mmax of largest
future events
-Ground motion model
-Timing of future
earthquakes (timeindependent or timedependent)
%106
Since all have large
uncertainties, wide
range of plausible
hazard models
154%
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
Stein et al, 2012
Stein et al., 2012
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.
Before 2010 Haiti M7
After 2010 Haiti M7
4X
Frankel et al, 2010
4) Overparameterized model
(overfit data):
Given a trend with scatter,
fitting a higher order
polynomial can give
Linear
fit
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 future
ones than a smoothed map
How much detail is useful?
Quadratic
fit
Societal assessment of hazard maps
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
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)
For earthquake, mitigation level is construction code
Loss depends on earthquake & mitigation level
Compared to optimum
Less mitigation decreases
construction costs but increases
expected loss and thus total cost
Optimum
Stein & Stein, 2012
More mitigation gives less
expected loss but higher total cost
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/eqar
chives/poster/2011/20110516.php
Present Value of Future Losses
Expected 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