##### Bayesian extreme values distribution for seismicity parameters assessment in South America

Authors:
O.C. Galanis, T.M. Tsapanos, G.A. Papadopoulos and A.A. Kiratzi

Journal name: Journal of the Balkan Geophysical Society

Issue: Vol 5, No 3, August 2002 pp. 77 - 86

Language: English

Info: Article, PDF ( 348.33Kb )

Summary:

Seismicity parameters in South America are estimated with the application of Bayesian statistics. The distribution is
named “distribution of extreme values”, because in order to compute the parameters of seismicity, the distribution of
maximum magnitude (i.e. an extreme value of magnitude in a given time span) is used. A concise analysis of the theory
applied is given. Some simple and generally accepted hypotheses, like the Poisson model for the temporal distribution of
earthquakes, as well as the exponential one for the distribution of the magnitudes of the earthquakes are adopted. Starting with
these initial hypotheses and by means of Bayesian statistics, the distribution of the maximum expected magnitude for a given
time span and the expected mean return period for a given magnitude are assessed. This is done in two steps. Firstly the
temporal distribution of earthquake is found, while in the second step their magnitude’s distribution is determined. Then
the parameters of the latter distributions are estimated. According to the methodology of Bayesian statistics, in order to start
with, prior values are assigned to the parameters. Utilising the conjugate distribution theory, the posterior values are
estimated using the prior values and the observational data. As these posterior parameters do not have an obvious physical
meaning, they are transformed to four familiar parameters of seismicity. These are the rate of occurrence of earthquakes,
*λ*, the parameter of the distribution of magnitude, *β*, and their respective standard deviations. Seismicity parameters
estimated and are expressed in terms of the probability of exceeding of a given magnitude in a given time span, and the
mean return period of a given magnitude. These parameters are useful for any seismic hazard assessment in this area.

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