Non-Poissonian Earthquake Occurrence Probability through Empirical Survival Functions

Earthquake engineering normally describes earthquake activity as a Poissonian process. This approximation is simple, but not entirely satisfactory. In this paper, a method for evaluating the non-Poissonian occurrence probability of seismic events, through empirical survival probability functions, is proposed. This method takes into account the previous history of the system. It seems robust enough to be applied to scant datasets, such as the Italian historical earthquake catalog, comprising 64 events with M ≥ 6.00 since 1600. The requirements to apply this method are (1) an acceptable knowledge of the event rate, and (2) the timing of the last two events with magnitude above the required threshold. I also show that it is necessary to consider all the events available, which means that de-clustering is not acceptable. Whenever applied, the method yields a time-varying probability of occurrence in the area of interest. Real cases in Italy show that large events obviously tend to occur in periods of higher probability.