Including stress relaxation in point-process model for seismic occurrence

Physics-based and statistic-based models for describing seismic occurrence are two sides of the same coin. In this paper, we compare the temporal organization of events obtained in a spring-block model for the seismic fault with the one predicted by probabilistic models for seismic occurrence. Thanks to the optimization of the parameters, by means of a Maximum Likelihood Estimation, it is possible to identify the statistical model which fits better the physical one. The results show that the best statistical model must take into account the non-trivial interplay between temporal clustering, related to aftershock occurrence, and the stress discharge following the occurrence of high magnitude main shocks. The two mechanisms contribute in different ways according to the minimum magnitude considered in the data fitting catalogue.