Including Foreshocks and Aftershocks in Time-Independent Probabilistic Seismic-Hazard Analyses

Time-independent probabilistic seismic-hazard analysis treats each source as being temporally and spatially independent; hence foreshocks and aftershocks, which are both spatially and temporally dependent on the mainshock, are removed from earthquake catalogs. Yet, intuitively, these earthquakes should be considered part of the seismic hazard, capable of producing damaging ground motions. In this study, I consider the mainshock and its dependents as a time-independent cluster, each cluster being temporally and spatially independent from any other. The cluster has a recurrence time of the mainshock; and, by considering the earthquakes in the cluster as a union of events, dependent events have an opportunity to contribute to seismic ground motions and hazard. Based on the methods of the U. S. Geological Survey for a high-hazard site, the inclusion of dependent events causes ground motions that are exceeded at probability levels of engineering interest to increase by about 10% but could be as high as 20% if variations in aftershock productivity can be accounted for reliably.