Probabilistic forecasting of earthquakes

We present long-term and short-term forecasts for magnitude 5.8 and larger earthquakes. We discuss a method for optimizing both procedures and testing their forecasting effectiveness using the likelihood function. Our forecasts are expressed as the rate density (that is, the probability per unit area and time) anywhere on the Earth. Our forecasts are for scientific testing only; they are not to be construed as earthquake predictions or warnings, and they carry no official endorsement. For our long-term forecast we assume that the rate density is proportional to a smoothed version of past seismicity (using the Harvard CMT catalogue). This is in some ways antithetical to the seismic gap model, which assumes that recent earthquakes deter future ones. The estimated rate density depends linearly on the magnitude of past earthquakes and approximately on a negative power of the epicentral distance out to a few hundred kilometres. We assume no explicit time dependence, although the estimated rate density will vary slightly from day to day as earthquakes enter the catalogue. The forecast applies to the ensemble of earthquakes during the test period. It is not meant to predict any single earthquake, and no single earthquake or lack of one is adequate to evaluate such a hypothesis. We assume that 1 per cent of all earthquakes are surprises, assumed uniformly likely to occur in those areas with no earthquakes since 1977. We have made specific forecasts for the calendar year 1999 for the Northwest Pacific and Southwest Pacific regions, and we plan to expand the forecast to the whole Earth. We test the forecast against the earthquake catalogue using a likelihood test and present the results. Our short-term forecast, updated daily, makes explicit use of statistical models describing earthquake clustering. Like the long-term forecast, the short-term version is expressed as a rate density in location, magnitude and time. However, the shortterm forecasts will change significantly from day to day in response to recent earthquakes. The forecast applies to main shocks, aftershocks, aftershocks of aftershocks, and main shocks preceded by foreshocks. However, there is no need to label each event, and the method is completely automatic. According to the model, nearly 10 per cent of moderately sized earthquakes will be followed by larger ones within a few weeks.