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Bulletin of the Seismological Society of America; October 1982; v. 72; no. 5; p. 1689-1705
© 1982 Seismological Society of America
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Bayesian analysis of extreme earthquake occurrences. Part I. Probabilistic hazard model

KENNETH W. CAMPBELL

TERA CORPORATION, 2150 SHATTUCK AVENUE, BERKELEY, CALIFORNIA 94704

Abstract

Bayesian probability theory in conjunction with the model of extremes is used to develop a Bayesian distribution of extreme earthquake occurrences by assuming that earthquakes represent a Poisson process with exponential distribution of magnitudes. The Bayesian distribution represents the probability that Mmax, the largest earthquake expected to occur within a period of t years, will exceed some specified magnitude m, and may be computed from the relationship,


Formula

where n'' and t'' represent updated (posterior) Bayesian estimates of the number of earthquakes and the time period of observation, respectively, and F{bsim}(m) is the Bayesian distribution of magnitudes, each updated from prior estimates of seismicity using historical observations of earthquake occurrences. Through the application of Bayesian probability theory, the above distribution contains two features that make it more powerful and reliable than the conventional extreme-value distribution. First, it incorporates statistical uncertainty in the estimation of seismicity in addition to the inherent uncertainty associated with the random nature of earthquake occurrences. Second, it provides a rigorous means of combining prior information on seismicity, such as geologica data, with available historical observations of earthquake occurrences. The last feature represents a major step toward the ability of earthquake engineers to systematically use information from geologists and seismologists, regarding the seismic potential of faults and small regions, in the probabilistic assessment of seismic hazards and provides a means of periodically updating estimates of earthquake occurrence probabilities as new seismicity data become available.




This article has been cited by other articles:


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 Seismological Research LettersHome page
K. K. S. Thingbaijam, P. Chingtham, and S. K. Nath
Seismicity in the North-West Frontier Province at the Indian-Eurasian Plate Convergence
Seismological Research Letters, July 1, 2009; 80(4): 599 - 608.
[Full Text] [PDF]

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 Bulletin of the Seismological Society of AmericaHome page
K. W. CAMPBELL
Bayesian analysis of extreme earthquake occurrences. Part II. Application to the San Jacinto fault zone of southern California
Bulletin of the Seismological Society of America, August 1, 1983; 73(4): 1099 - 1115.
[Abstract] [PDF]


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