Stochastic declustering of earthquakes with the spatiotemporal renewal ETAS model

Abstract

Modeling and forecasting earthquakes is challenging due to the complex interplay and clustering of main-shocks and aftershocks. The epidemic-type aftershock sequence (ETAS) model represents the conditional intensity of earthquakes as the superposition of a background and aftershock rate which allows for the declustering of the earthquakes. Its success has led to the development of numerous versions of the ETAS model. Among these extensions is the renewal ETAS (RETAS) model, which has shown promising potential. The RETAS model endows the main-shock arrival process with a renewal process, which serves as an alternative to the homogeneous Poisson process. Model fitting is performed using likelihood-based estimation by directly optimizing the exact likelihood. However, inferring the branching structure from the fitted RETAS model remains a challenging task since the declustering algorithm that is currently available for the ETAS model is not directly applicable. Therefore, this article develops an iterative algorithm to calculate the smoothed main- and aftershock probabilities, conditional on all available information contained in the catalog. Consequently, an estimate of the background spatial intensity function and model parameters can be obtained using an iterative semiparametric procedure with the smoothing parameters selected using information criteria. The methods proposed herein are illustrated on simulated data and a New Zealand earthquake catalog.