Edward M. Brooks

Metrics for Assessing Earthquake-Hazard Map Performance

Recent large earthquakes that caused great damage in areas predicted to be relatively safe, illustrate the importance of criteria that assess how well earthquake hazard maps used to develop codes for earthquake‐resistant construction are actually performing. At present, there is no agreed‐upon way of assessing how well a map performed and thus determining whether one map performed better than another. The fractional site exceedance metric implicit in current maps, that during the chosen time interval the predicted ground motion will be exceeded only at a specific fraction of the sites, is useful but permits maps to be nominally successful even if they significantly underpredict or overpredict shaking, or permits them to be nominally unsuccessful but do well in terms of predicting shaking. We explore some possible metrics that better measure the effects of overprediction and underprediction and can be weighted to reflect the two differently and to reflect differences in populations and property at risk. Although no single metric alone fully characterizes map behavior, using several metrics can provide useful insight for comparing and improving hazard maps. For example, both probabilistic and deterministic hazard maps for Italy dramatically overpredict the recorded shaking in a 2200‐yr‐long historical intensity catalog, illustrating problems in the data (most likely), models, or both.

Comparing the Performance of Japan’s Earthquake Hazard Maps to Uniform and Randomized Maps

Following the 2011 magnitude 9.1 Tohoku earthquake, Geller (2011) argued that “all of Japan is at risk from earthquakes, and the present state of seismological science does not allow us to reliably differentiate the risk level in particular geographic areas,” so a map showing uniform hazard would be preferable to the existing map. We explore this by comparing how well a 510‐yr‐long record of earthquake shaking in Japan is described by the Japanese national‐hazard (JNH) maps, uniform maps, and randomized maps. Surprisingly, as measured by the metric implicit in the JNH maps (i.e., a metric that requires only a specific fraction of the sites during the chosen time interval to exceed the predicted ground motion), both uniform and randomized maps do better compared with the actual maps. However, using the squared misfit between maximum observed shaking and the predicted shaking as a metric, the JNH maps do better compared with the uniform or randomized maps. These results indicate that (1)xa0the JNH maps are not performing as well as expected, (2)xa0identification of the factors controlling map performance is complicated, and (3)xa0learning more about how maps perform and why would be valuable in making more effective policy.

Should All of Nepal Be Treated as Having the Same Earthquake Hazard

Current earthquake hazard maps for Nepal predict substantial variations in hazard within the nation, with noticeable differences between maps. We thus suggest that given present knowledge, all of Nepal may be better regarded as equally hazardous and perhaps vulnerable to much larger earthquakes than those currently known because of their long recurrence times. This proposal is based on the limitations of the historical earthquake record, the recognized deficit in seismic moment release, and GPS data showing a similar level of coupling along the arc. Support for using smoother maps can be had from analysis for Japan, which is also located on and parallel to a subduction boundary, showing that in some ways the hazard maps may be overparameterized, in that including too high a level of detail may lower the maps’ ability to predict shaking. Treating Nepal’s hazard as uniform and developing mitigation strategies accordingly may help reduce damage in future earthquakes.

Investigating the effects of smoothing on the performance of earthquake hazard maps

We explore whether less detailed probabilistic hazard maps might perform better by assessing how smoothing Japans national earthquake hazard maps affects their fit to a 510-year record of shaking. As measured by the fractional exceedance metric implicit in such probabilistic hazard maps, simple smoothing over progressively larger areas improves the maps performance such that in the limit a uniform map performs best. However, using the squared misfit between maximum observed shaking and that predicted as a metric, map performance improves up to a ~75-150 km smoothing window, and then decreases with further smoothing. This result suggests that the probabilistic hazard models and the resulting maps may be over-parameterized, in that including too high a level of detail to describe past and future earthquakes may lower the maps ability to predict future shaking.

Should Fermi Have Secured His Water Heater

A common student response to quantitative questions without obvious answers is “I have no idea.” Often these questions can be addressed by Fermi estimation, in which a difficult‐to‐estimate quantity is estimated by combining order of magnitude estimates of easier‐to‐estimate quantities. Although this approach is commonly used for numerical estimates, it can be applied to issues combining science and policy. Either application involves dividing an issue into tractable components and addressing them separately. To learn this method, our natural hazards seminar considered a statement by the Illinois Emergency Management Agency that homeowners should secure water heaters to prevent them from being damaged by earthquakes. We divided this question into subtopics, researched each, and discussed them to reach a synthesis. We estimated the net benefit: the difference between the expected value of damage and the cost of securing. This benefit is positive, indicating that securing is worthwhile, only if the probability of damage during the heater’s life is relatively large, approximately 1%–10%. To assess whether the actual probability is likely to be this high, we assume that major heater damage is likely only for shaking with modified Mercalli intensity VIII (“heavy furniture overturned”) or greater. Intensity data for 200 years of Illinois earthquakes show that this level was reached only in the southernmost part of the state for the 1811–1812 New Madrid earthquakes. As expected, the highest known shaking generally decreases northward toward Chicago, consistent with the fact that we find no cases of earthquake‐toppled water heaters in Illinois. We compared the rate of return on securing a water heater in Chicago to buying a lottery ticket when the jackpot is large and found the latter a better investment. This project let us explore ideas that might otherwise have seemed abstract and difficult to grasp, and suggests that other courses might consider similar projects.