1. 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

2. 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 2

3. Tohoku earthquake broke many segments
450 km long fault, M 9.1
Expected Earthquake Sources
50 to 150 km segments
M7.5 to 8.2
(Headquarters for Earthquake Research Promotion)
(Aftershock map from USGS)
J. Mori

4. 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

5. 180/300 km swept away or destroyed
Expensive seawalls - longer than Great Wall of China -proved ineffective
180/300 km swept away or destroyed
In some cases discouraged evacuation
NY Times 3/31/2011

6. 2008 Wenchuan earthquake (Mw 7
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 6

7. 2010 M7 earthquake shaking much greater than predicted for next 500 years
Haiti
2001 hazard map
Map didn’t use GPS data

8. 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?

9. 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.”
NY Times 11/2/2011

10. Hazard maps are hard to get right: successfully predicting future shaking depends on accuracy of four assumptions over 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

11. Plate Boundary Earthquakes
Major fault loaded rapidly at constant rate
Earthquakes spatially focused & temporally quasi-periodic
Past is fair predictor
Plate A
Plate B
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

12. Earthquakes in North China
Liu, Stein & Wang 2011
during the period
prior to the period
instrumental events
Earthquakes in North China
Large events often pop up where there was little seismicity!
Beijing
Bohai Bay
Ordos
Plateau
Shanxi Graben
1303 Hongtong
M 8.0
Weihi rift

13. Earthquakes in North China
Liu, Stein & Wang 2011
during the period
prior to the period
instrumental events
Earthquakes in North China
Large events often pop up where there was little seismicity!
Beijing
Bohai Bay
Ordos
Plateau
Shanxi Graben
Weihi rift
1556 Huaxian
M 8.3

14. Earthquakes in North China
Liu, Stein & Wang 2011
during the period
prior to the period
instrumental events
Earthquakes in North China
Large events often pop up where there was little seismicity!
Beijing
Bohai Bay
Ordos
Plateau
Shanxi Graben
Weihi rift
1668 Tancheng
M 8.5

15. Earthquakes in North China
Liu, Stein & Wang 2011
during the period
prior to the period
instrumental events
Earthquakes in North China
Large events often pop up where there was little seismicity!
1679 Sanhe
M 8.0
Beijing
Bohai Bay
Ordos
Plateau
Shanxi Graben
Weihi rift

16. Earthquakes in North China
Liu, Stein & Wang 2011
during the period
prior to the period
instrumental events
Earthquakes in North China
Large events often pop up where there was little seismicity!
1975 Haicheng
M 7.3
Beijing
Bohai Bay
1976 Tangshan
M 7.8
Ordos
Plateau
Shanxi Graben
1966 Xingtai
M 7.2
Weihi rift

17. No large (M>7) events ruptured the same fault segment twice in past 2000 years
Historical
Instrumental
Shanxi Graben
Weihi rift
In past 200 years, quakes migrated from Shanxi Graben to N. China Plain

18. 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
180%
275%
Newman et al., 2001

19. 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
%106
154% 19

20. 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

21. 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

22. Some testing challenges
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.

23. 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

24. Linear fit
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 future ones than a smoothed map How much detail is useful?
Quadratic fit

25. 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

26. 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
More mitigation gives less expected loss but higher total cost
Optimum
Stein & Stein, 2012

27. 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
fatalities
~ $100B damage
Examine range of parameters & use to find optimum

28. 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) /(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.

29. 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

30. Within range, inaccurate hazard maps produce nonoptimal mitigation,
raising cost, but still do some good (net benefit)
Inaccurate loss estimates have same effect

31. Testing maps & quantifying uncertainties will help some
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