We estimate long-term worldwide earthquake probabilities by extrapolating catalogs of seismic moment solutions. We base the forecast on correlations of seismic moment tensor solutions. The forecast is expressed as a map showing predicted rate densities for earthquake occurrence and for focal mechanism orientation. Focal mechanisms are used first to smooth seismicity maps to obtain expected hazard maps and then to forecast mechanisms for future earthquakes. Several types of smoothing kernels are used: in space domain we use the 1/distance kernel for the distribution of seismicity around any epicenter. The kernel is parameterized using two adjustable parameters: maximum distance and directivity (distribution of seismicity around an epicenter with regard to the focal mechanism of an earthquake). For temporal prediction we use the Poisson hypothesis of earthquake temporal behavior. We test these forecasts: we use the first half of a catalog to smooth seismicity level, and the second half of the catalog is used to validate and optimize the prediction. To illustrate the technique we use available data in the Harvard catalog of seismic moment solutions to evaluate seismicity maps for several seismic regions. The method can be used with similar catalogs. The technique is completely formal and does not require human operator intervention, hence the prediction results can be objectively tested. Moreover, the maps can be used as the Poisson null hypothesis for testing by the likelihood method against any other prediction model which shares the same sample space (the same zones, time window, and acceptance criteria).
