What is the Chance of an Earthquake
What is the chance that at least one earthquake of magnitude 6.7 or greater will occur before the year 2030 in the San Francisco Bay Area? The U.S. Geological Survey estimated the chance to be 0.7 +/- 0.1. In this paper, we try to interpret such probabilities. Making sense of earthquake forecasts is surprisingly difficult. In part, this is because the forecasts are based on a complicated mixture of geological maps, empirical rules of thumb, expert opinion, physical models, stochastic models, numerical simulations, as well as geodetic, seismic, and paleoseismic data. Even the concept of probability is hard to define in this context. We examine the problems in applying standard definitions of probability to earthquakes, taking the USGS forecast---the product of a particularly careful and ambitious study---as our lead example. The issues are general, and concern the interpretation more than the numerical values. Despite the work involved in the USGS forecast, the probability estimate is shaky, as is the estimate of its uncertainty.