1. What to do given that earthquake hazard maps often fail
Seth Stein, Northwestern University Robert Geller, University of Tokyo Mian Liu, University of Missouri 
NY Times
CNN
Tohoku, Japan March 11, M 9.1

2. NY Times 3/31/2011

3. 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

4. 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 high
Stein & Stein, 2012

5. Including risk aversion & uncertainty
Consider marginal costs C’(n) & benefits Q’(n) (derivatives)
More mitigation costs more
But reduces loss
Optimum is where marginal curves are equal, n*
Benefit
(loss reduction)
cost
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
Stein & Stein, 2012

6. 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.”
NY Times 11/2/2011

7. 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!)

8. Detailed model of segments with 30 year probabilities
Off Sanriku-oki North ~M8 0.2 to 10%
Off Sanriku-oki Central ~M to 90%
Assumption:
No M > 8.2
Off Miyagi ~M7.5 > 90%
Off Fukushima ~M %
Off Ibaraki ~M6.7 – M %
Sanriku to Boso M8.2 (plate boundary)
20%
Sanriku to Boso M8.2 (Intraplate)
4-7%
Expected Earthquake Sources
50 to 150 km segments
M7.5 to 8.2
(Headquarters for Earthquake Research Promotion)
J. Mori 8

9. Giant earthquake broke five segments
2011 Tohoku Earthquake
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

10. 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

11. Didn’t consider historical record of large tsunamis
NYT 4/20/11

12. 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

13. NY Times 3/21/11
Why?

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

15. 2010 M7 earthquake shaking much greater than maximum predicted for next 500 years
2001 hazard map

16. 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

17. 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.

18. What to do
Continue 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

19. Comparing map predictions shows the large uncertainties (~3X) resulting from different assumptions
Stein et al, 2012
Newman et al, 2001

20. 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."

21. Test maps by comparison to what happened after they were published.
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

22. Avoid biases from new maps made after a large earthquake that earlier maps missed.
Before 2010 Haiti M7
After 2010 Haiti M7 4X
Frankel et al, 2010

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

24. 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