Analysing the interevent time distribution to identify seismicity phases: a Bayesian nonparametric approach to the multiple-changepoint problem

In the study of earthquakes, several aspects of the underlying physical pro cess, such as the time non-stationarity of the process, are not yet well un derstood, because we lack clear indications about its evolution in time. Ta king as our point of departure the theory that the seismic process evolves in phases with different activity patterns, we have attempted to identify t hese phases through the variations in the interevent time probability distr ibution within the framework of the multiple-changepoint problem. In a nonp arametric Bayesian setting, the distribution under examination has been con sidered a random realization from a mixture of Dirichlet processes, the par ameter of which is proportional to a generalized gamma distribution. In thi s way we could avoid making precise assumptions about the functional form o f the distribution. The number and location in time of the phases are unkno wn and are estimated at the same time as the interevent time distributions. We have analysed the sequence of main shocks that occurred in Irpinia, a p articularly active area in southern Italy: the method consistently identifi es changepoints at times when strong stress releases were recorded. The est imation problem can be solved by stochastic simulation methods based on Mar kov chains, the implementation of which is improved, in this case, by the g ood analytical properties of the Dirichlet process.