Probabilistic forecasting of earthquakes

We present longterm and shortterm forecasts for magnitude ( and larger earth quakes We discuss a method for optimizing both procedures and testing their fore casting effectiveness using the likelihood function ,ur forecasts are expressed as the rate density C40that is the probability per unit area and time / anywhere on the 1arth ,ur forecasts are for scienti®c testing only they are not to be construed as earthquake predictions or warnings and they carry no of®cial endorsement 3or our longterm forecast we assume that the rate density is proportional to a smoothed version of past seismicity C40using the 4arvard 5T 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 kilo metres 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 7t is not meant to predict any single earthquake and no single earthquake or lack of one is adequate to evaluat