A procedure to estimate the probability distribution of recurrence times in the west-northwestern Hellenic arc

Abstract

The determination of the probability distribution of recurrence times is the most important problem in the calculation of long-term conditional probabilities for the recurrence of large and great earthquakes. The principle of maximum entropy in conjunction with a goodness-of-fit test (chi-square or Kolmogorov-Smirnov test) may be employed to obtain estimates of these densities using recurrence data for some seismic regions. Four different distributions are characterized by the property of maximum entropy, as possible laws for recurrence times of the largest earthquakes: uniform, exponential, Gaussian and log-normal. To discriminate among these different probability distributions we use the probability theory and the chi-square test to check the goodness-of-fit to the distribution of recurrence time of shocks of magnitude 6.5 and largest occurred in the west-northwestern zone of the Hellenic arc from 1791 to 1983. It is found that the recurrence times data for the west-northwestern zone of the Hellenic arc cannot be represented by the uniform and the Gaussian probability densities. The recurrence times data for the west-northwestern zone of the Hellenic arc can be described accurately by the exponential and log-normal probability densities, which were predicted from the principle of maximum entropy. In other words, the principle of maximum entropy does not necessarily lead to a unique solution. In turn, the mathematical properties of these distributions could be used to derive different physical properties of the earthquake process in the west-northwestern zone of the Hellenic arc.