plate boundaries, as seen from inspection of maps of earthquake locations. The most abundant (and obvious) example of earthquake clustering in time and space is the occurrence of aftershocks (see Chapter 4). Indeed, many complete catalogs of earthquakes are dominated by aftershocks of moderate to large events (210). Thus, the occurrence of a single earthquake greatly increases the probability of another event in the same location.

Although the physical origin of clustering behavior is not clear, it has important implications for models of earthquake occurrence. Clustering suggests a causality between earthquakes that could change many of the assumptions that underlie seismic hazard assessments. In short to intermediate time scales, the most dangerous regions may be those that have recently experienced large earthquakes, rather than the locked portions of seismically active faults.

Stress Interactions Identifying the origins of clustering, or distinguishing among different models of earthquake recurrence, will require an explicit physical theory of seismic activity. Important components of such a theory will include an explicit model for stress evolution on major faults due to tectonic stress accumulation, previous earthquakes, and inelastic stress relaxation as well as the evolution of frictional strength on faults, the mechanical strength of materials off the fault, and the rupture of virgin rock required to accomplish finite displacements in a brittle medium. Such a complete theory will be difficult to develop and difficult to confirm experimentally because it requires a long span of accurate earthquake information including focal mechanisms. Furthermore, the stress model must include tectonic stress accumulation, for which there is no definitive model at present. However, significant progress has been made on parts of the theory.

An important first step was the development of expressions to calculate stresses everywhere in a homogeneous elastic half-space due to an arbitrary dislocation (211). These expressions allow calculations of the change in stress across any existing fault due to earthquakes causing known displacements. With this model, it has become routine to calculate stress changes for all earthquakes above M 5 in populated regions. Using these methods to calculate tectonic stress accumulations is more complex because it requires assumptions about strain partitioning throughout fault and plate boundary zones.

Application to Seismic Hazard Analysis There have been continuing efforts to utilize the understanding of earthquake forecasting to improve the capabilities of PSHA. To this end, the recent USGS ground-motion mapping study incorporated characteristic earthquakes for a

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