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A stochastic model for spatially and temporally dependent earthquakes

Jack R. Benjamin and Associates, Inc., 444 Castro Street, Suite 501, Mountain View, California, 94041
Stanford University Department of Civil Engineering, Stanford, California 94305

Abstract

Site-specific hazard estimation requires modeling the occurrences of earthquakes on faults that can potentially impact the site. Evidence for large-magnitude earthquakes (approximately moment magnitude 6.5 and above) occurring infrequently on long faults indicates that the assumptions of temporal and spatial independence are not valid. Thus, a new stochastic model that captures the temporal and spatial characteristics of earthquake recurrence is introduced. This model uses a generalized semi-Markovian process (GSMP) to provide the complex framework required for describing space-time earthquake dependence. The objective of this model is to estimate the hazard over time periods of engineering significance (e.g., 50 to 200 yr).

The model is applied to the northern San Andreas Fault (the portion of the fault that ruptured in 1906). Mean recurrence rates obtained from the model application are in good agreement with actual observations. Events are also simulated over a long time period to observe the fault behavior. Based on the results obtained from the simulation, two distinct processes are observed to be at work in that section of the San Andreas. The North Coast segment generates large earthquakes (approximately moment magnitude 7.7 to 8.1), and the South Santa Cruz Mountains segment generates somewhat smaller earthquakes (approximately moment magnitude 6.8 to 7.4). The San Francisco Peninsula segment represents a transition between these two behaviors. Sensitivity studies of the model parameters reveal that the results are relatively sensitive primarily to the slip rate and the mean and standard deviation of the interarrival time distribution. The model appears to be relatively insensitive to the remaining parameters of the model.