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Some bounds for seismic risk

STATISTICS DEPARTMENT UNIVERSITY OF CALIFORNIA, BERKELEY, CALIFORNIA 94702

Abstract

The seismic risk at a site may be defined as the probability that a given threshold level is exceeded by a chosen variate within a time period of interest, as a result of nearby seismic events. Typically, the probability has been evaluated assuming that the sequence of origin times of earthquakes felt at the site is Poisson. This paper presents bounds for the probability that apply to a general distribution of origin times. In particular, the expected value of a particular counting variate is seen to provide an upper bound for the risk. The results are discussed for some specific marked point processes. Exact expressions for the risk are set down using the conditional intensity function.

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