What to do given that earthquake hazard maps often

fail

Tohoku, Japan March 11, 2011 M 9.1NY Times CNN

Seth Stein, Northwestern University Robert Geller, University of Tokyo

Mian Liu, University of Missouri 

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NY Times 3/31/2011

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

Hazard map crucial for mitigation strategy

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)

Less mitigation decreases construction costs but increases expected loss and thus total cost

More mitigation gives less expected loss but higher total cost

Because assumed probability taken from hazard map, inaccurate map biases mitigation - too low

or too highStein & Stein, 2012

Including risk aversion & uncertainty

Consider marginal costs C’(n) & benefits Q’(n) (derivatives)

Stein & Stein, 2012

More mitigation costs more

But reduces loss

Optimum is where marginal curves are equal, n*

Uncertainty in hazard model causes uncertainty in expected loss. We are risk averse, so add risk term R(n) proportional to uncertainty in loss, yielding higher mitigation level n**

Crucial to understand hazard model uncertainty

cost

Benefit

(loss reduction)

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NY Times 11/2/2011

Too expensive to rebuild for 2011 sized tsunami

Choosing policy involves politics, economics, geoscience

“In 30 years there might be nothing left there but fancy breakwaters and empty houses.”

Hazard maps fail because of

- bad physics (incorrect description of earthquake processes)

-bad assumptions (mapmakers’ choice of poorly known parameters)

- bad data (lacking, incomplete, or underappreciated)

- bad luck (low probability events)

and combinations of these (Tohoku!)

Expected Earthquake Sources 50 to 150 km segments M7.5 to 8.2(Headquarters for Earthquake Research Promotion)

Off Sanriku-oki North ~M8 0.2 to 10%

Off Sanriku-oki Central ~M7.7 80 to 90%

Off Fukushima ~M7.4 7%

Off Ibaraki ~M6.7 – M7.2 90%

Detailed model of segments with 30 year probabilities

Sanriku to Boso M8.2 (plate boundary)20%

Sanriku to Boso M8.2 (Intraplate)4-7%

Off Miyagi ~M7.5 > 90%

J. Mori

Assumption:

No M > 8.2

Giant earthquake broke five 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

Planning assumed maximum magnitude 8 Seawalls 5-10 m high

CNN

NYTStein & Okal, 2011

Didn’t consider historical record of large tsunamis

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NYT 4/20/11

Lack of M9s in record seemed consistent with model that M9s only occur where lithosphere younger than 80 Myr subducts faster than 50

mm/yr (Ruff and Kanamori, 1980) Disproved by Sumatra 2004 M9.3

and dataset

reanalysis (Stein & Okal, 2007)

Short record at most SZs didn’t include rarer, larger

multisegment

ruptures

Stein & Okal, 2011

NY Times 3/21/11

Why?

Hazard maps are hard to get right: success 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 & map failure often result because these are often hard to assess

2001 hazard map

http://www.oas.org/cdmp/document/seismap/haiti_dr.htm

2010 M7 earthquake shaking much greater

than maximum predicted for next

500 years

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

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Maps are like ‘Whack-a-mole’ - you wait for the mole to come up where it went down, but it’s

likely to pop up somewhere else.

What to doContinue research on fundamental scientific questions (geoscience community’s job!)

Realistically assess map uncertainties and present them to help users decide how much credence to place in maps

Develop methods to objectively test hazard maps - which hasn’t been done despite their wide use - and thus guide future improvements

Comparing map predictions shows the large uncertainties (~3X) resulting from different

assumptions

Stein et al, 2012

Newman et al, 2001

Testing analogy: evidence-based medicine objectively evaluates widely used treatments, often with embarrassing

results

Although more than 650,000 arthroscopic knee surgeries at a cost of roughly $5,000 each were being performed each year, a controlled experiment showed that "the outcomes were no

better than a placebo procedure."

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Bad luck or bad map?

Compare maximum acceleration observed to that predicted by both map and null hypotheses.

A simple null hypothesis is regionally uniformly distributed hazard.

Japanese map seems to be doing worse than this null hypothesis.

Geller 2011

Test maps by comparison to what happened after they were

published.

Avoid biases from new maps made after a large earthquake that

earlier maps missed.

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Frankel et al, 2010

Before 2010 Haiti M7 After 2010 Haiti M7

4X

A posteriori changes to a model are "Texas sharpshooting:” shoot at the barn and then draw circles around

the bullet holes.

Challenge: Users want predictions even if they’re poor

Future Nobel Prize winner Kenneth Arrow served as a military weather forecaster. As he

described,

“my colleagues had the responsibility of preparing long-range weather forecasts, i.e., for the following month. The statisticians

among us subjected these forecasts to verification and found they differed in no way from chance. The forecasters themselves were convinced and requested that the forecasts be

discontinued.

The reply read approximately: "The commanding general is well aware that the forecasts are no good. However, he needs them for planning

purposes."

Gardner, D., Future Babble: Why Expert Predictions Fail - and Why We Believe Them Anyway, 2010