A Coupled Etas - I 2 Gmm Point Process with Applications to Seismic Fault Detection

Epidemic-type aftershock sequence (ETAS) point processes are a common model for the occurrence of earthquake events. ETAS models consist of a stationary background Poisson process modeling spontaneous earthquakes and a triggering kernel representing the space-time-magnitude distribution of aftershocks. Two popular non-parametric methods for estimation of the background intensity include histograms and kernel density estimators. While these methods are able to capture local spatial heterogeneity in the intensity of spontaneous events, they do not capture patterns resulting from fault-line structure over larger spatial scales. Here we propose a two-layer infinite Gaussian mixture model for clustering of earthquake events into fault-like groups over intermediate spatial scales. We introduce a Monte-Carlo expectation-maximization (EM) algorithm for joint inference of the ETAS-IGMM model and then apply the model to the Southern California earthquake Catalog. We illustrate the advantages of the ETAS-IGMM model in terms of both goodness of fit of the intensity and recovery of fault line clusters in the Community Fault Model 3.0 from earthquake occurrence data.