Stochastic declustering of space-time earthquake occurrences

This article is concerned with objective estimation of the spatial intensity function of the background earthquake occurrences from an earthquake catalog that includes numerous clustered events in space and time, and also with an algorithm for producing declustered catalogs from the original catalog. A space-time branching process model (the ETAS model) is used for describing how each event generates offspring events. It is shown that the background intensity function can be evaluated if the total spatial seismicity intensity and the branching structure can be estimated. In fact, the whole space-time process is split into two subprocesses, the background events and the clustered events. The proposed algorithm combines a parametric maximum likelihood estimate for the clustering structures using the space-time ETAS model and a nonparametric estimate of the background seismicity that we call a variable weighted kernel estimate. To demonstrate the present methods, we estimate the background seismic activities in the central region of New Zealand and in the central and western regions of Japan, then use these estimates to produce catalogs of background events.