Statistical identification of seismicity phases

We propose a statistical methodology to detect and quantify different seismicity phases on the basis of variations in certain characteristic features of seismic phenomenon, taking as examples two of the most studied aspects of seismicity: the occurrence rate and interevent time. Our objective is to provide an overall, compact picture of the activity, given a sufficiently long sequence of events, by identifying the flow of patterns that are singly described by well known physical models in limited time intervals. We assume that the sequence of events recorded in a seismically active region represents the set of an unknown number of consecutive phases, and that in each phase, the observations are the realization of a different version of the same stochastic process, in our case the Poisson or the Dirichlet process. The quantities to be estimated are the number of phases, the instants in which the system passes from one phase to another and the model parameters. We have formulated this problem in the framework of a multiple change-point problem. The inference is made possible by exploiting recently developed computer-intensive methods based on the stochastic simulation of Markov chains. The data analysed are from the region of Kresna in southwestern Bulgaria. This area was hit by two strong earthquakes in the last century, one of MS = 7.8 magnitude in 1904, and another of MS = 6.7 magnitude in 1931.