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