Flexible space-time process for seismic data

Abstract

Point processes are well studied objects in probability theory and a powerful tool in statistics for modelling and analyzing the distribution of real phenomena, such as the seismic one. Point processes can be specified mathematically in several ways, for instance, by considering the joint distributions of the counts of points in arbitrary sets or defining a complete intensity function. The conditional intensity function is a function of the point history and it is itself a stochastic process depending on the past up to time t. In this paper some techniques to estimate the intensity function of space-time point processes are developed, by following semi-parametric approaches and diagnostic methods to assess their goodness of fit. In particular, because of its particularly adaptive properties to anomalous behavior in data, in this paper a nonparametric estimation approach is used to interpret dependence features of seismic activity of a given area of observation; to justify the estimation approach a diagnostic method for space-time point processes is also revised.