Playing against nature: improving earthquake hazard assessment & mitigationSeth Stein, Earth & Planetary Sciences, Northwestern University Jerome Stein, Applied Mathematics, Brown UniversityG52A-04Tohoku, 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 gapGeller 2011

Tohoku earthquake broke many segments2011 Tohoku Earthquake 450 km long fault, M 9.1 (Aftershock map from USGS)J. MoriExpected 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 tsunamiMitigation planning assumed maximum magnitude 8 Seawalls 5-10 m highCNNNYTStein & Okal, 2011

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

2008 Wenchuan earthquake (Mw 7.9) was not expected: map showed low hazard based on lack of recent earthquakesDidnt use GPS data showing 1-2 mm/yr (~Wasatch)Stein et al., 2012

Haiti2001 hazard maphttp://www.oas.org/cdmp/document/seismap/haiti_dr.htm2010 M7 earthquake shaking much greater than predicted for next 500 yearsMap didnt 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?

NY Times 11/2/2011Choosing mitigation policy involves hazard assessment, economics, politicsToo 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 EarthquakesMajor 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 faultsLoading rate on a given fault is slow & may not be constantEarthquakes can cluster on a fault for a while then shiftPast can be poor predictorStein, Liu & Wang 2009

OrdosPlateauShanxi GrabenBohai BayBeijing1303 HongtongM 8.0Liu, Stein & Wang 2011Weihi rift

OrdosPlateauShanxi GrabenBohai BayBeijing1556 HuaxianM 8.3Weihi riftLiu, Stein & Wang 2011

OrdosPlateauShanxi GrabenBohai BayBeijing1668 TanchengM 8.5Weihi riftLiu, Stein & Wang 2011

OrdosPlateauShanxi GrabenBohai BayBeijing1679 SanheM 8.0Weihi riftLiu, Stein & Wang 2011

OrdosPlateauShanxi GrabenBohai BayBeijing1966 XingtaiM 7.21976 TangshanM 7.81975 HaichengM 7.3Weihi riftLiu, Stein & Wang 2011

No large (M>7) events ruptured the same fault segment twice in past 2000 yearsIn past 200 years, quakes migrated from Shanxi Graben to N. China PlainShanxi GrabenWeihi rift

Newman et al., 2001180%275%Hazard maps involve assumptions about- Mmax of largest future eventsGround motion modelTiming of future earthquakes (time-independent or time-dependent)Since all have large uncertainties, wide range of plausible hazard models

154%%106Hazard maps involve assumptions about- Mmax of largest future eventsGround motion modelTiming of future earthquakes (time-independent or time-dependent)Since all have large uncertainties, wide range of plausible hazard models

Stein et al, 2012Stein et al., 2012Uncertainty typically factor of 3-4 Often cant 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 challengesShort 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, 2010Before 2010 Haiti M7After 2010 Haiti M74X

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 fitQuadratic fit

Consider map as means, not end

Assess maps 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 lossExpected 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 costStein & Stein, 2012For 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 caseCurrent mitigation10-100 fatalities~ $100B damageExamine range of parameters & use to find optimumhttp://earthquake.usgs.gov/earthquakes/eqarchives/poster/2011/20110516.php

Present Value of Future LossesExpected average loss over T years is LTInterest rate iPVFL = 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 largeFor 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

SummaryLimitations in our knowledge about earthquakes, notably space-time variability, limit how accurately hazard maps can be madeAlthough uncertain maps likely produce nonoptimal mitigation, they still do some good if theyre not too badTesting maps & quantifying uncertainties will help someNeed to recognize & accept uncertainties

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