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Bayesian analysis of extreme earthquake occurrences. Part II. Application to the San Jacinto fault zone of southern California

TERA CORPORATION, 2150 SHATTUCK AVENUE, BERKELEY, CALIFORNIA 94704

Abstract

The Bayesian extreme-value distribution of earthquake occurrences developed in the first part of this study is tested and applied to the estimation of seismic hazards for the San jacinto fault zone of southern California. Prior estimates of seismicity are developed from seismotectonic data based on standard seismological relationships among seismic moment, slip rate, earthquake recurrence rate, and magnitude. These estimates are then updated using Bayes' theorem and historical estimates of seismicity associated with the San Jacinto fault zone. Bayesian extreme-value distributions available from the literature are found either to overestimate exceedance probabilities of earthquake occurrences or require more complex computations as compared to the distribution proposed in this study. On the other hand, the conventional extremevalue distribution of earthquake occurrences first proposed by Epstein and Lomnitz (1966) was found to give results consistent with the Bayesian distribution of this study, if updated estimates of the seismicity parameters are used and the standard deviations of these parameters are restricted to be less than about 25 per cent of their mean values.

The Bayesian analysis of extreme earthquake occurrences for the 300-km-long San Jacinto fault zone indicated a rather large sensitivity to the uncertainty associated with the prior seismotectonic estimate of seismicity. Using moderate estimates of this uncertainty, magnitudes of 6.2, 6.9, 7.1, 7.4, and 7.5 are found to be associated with return periods at 10, 50, 100, 500, and 1000 yr for an upper bound magnitude of 7.5 M_S on the fault zone. These estimates lie approximately midway between those based on historical and seismotectonic estimates of seismicity. Estimated magnitudes are reduced significantly for return periods of 50 to 1000 yr, if upper bound magnitude is restricted to a value of 7.0 M_S, closer to the largest historical earthquake observed on the zone. In this case, for example, the 100- and 1000-yr earthquakes have magnitudes of 6.8 and 7.0, respectively.