The Bayesian probabilistic prediction of strong earthquakes in the Hellenic arc

Abstract

The Bayesian probability theory in conjunction with the Poisson process model is used to develop a Bayesian discrete distribution to estimate or predict the inter-arrival times ( T j ) for strong earthquakes in the Hellenic Arc. The Bayesian posterior probabilities may be computed from the relationship: P( T r M )= γT r e −γT r (1− e −γT r ) ∑ j=1 m γT j e −γT j (1−e −γT j ) where P( T r M ) , is the conditional probability of the event T r , given that an earthquake of magnitude M has occurred. The Bayesian discrete analysis is performed first by using the Poisson process to determine the prior probability distribution for T j , and the likelihood function. We can imagine the random earthquake experiment involved in the application of Bayes' theorem to earthquake prediction to be a two-stage experiment. The first stage was initiated a long time ago when the real time arrival dates of strong earthquakes were first recorded. The second stage was initiated in 1935 when the earthquake magnitude scale was introduced by Richter (1935), in southern California. Richter probably never thought that this measure of the earthquake magnitude then will be an experiment designed to give us information about the outcome of the earthquake inter-arrival times (the first stage). The earthquake data analyzed in this study have been taken from the earthquake catalog for the Hellenic Arc prepared by Ambraseys (1981). The discrete Bayesian analysis, suggests determining the most likely outcomes for the length of earthquake inter-arrival times, by using some maximum values of the final Bayesian probabilities. The following inferences concerning future strong earthquake occurrences in the Hellenic Arc area may be drawn: 1. (1) Our western-northwestern zone is a seismic region which approximately coincides with the region studied by Wyss and Baer. Therefore, we agree with the geographic location of the expected earthquake forecasted by Wyss and Baer (1981). 2. (2) Using probability theory (Bayes' theorem-Poisson process), we concluded that a period of strong earthquake activity is expected to occur in the same geographic location during the decade 1992–2002. This conclusion supports Ambraseys' conclusion. However, it should be noted that our conclusion indicates that the period of strong earthquake activity will occur anyway a decade later than predicted by Wyss and Baer.