Stochastic declustering of earthquakes with the spatiotemporal RETAS model

Epidemic-Type Aftershock Sequence (ETAS) models are point processes that have found prominence in seismological modeling. Its success has led to the development of a number of different versions of the ETAS model. Among these extensions is the RETAS model which has shown potential to improve the modeling capabilities of the ETAS class of models. 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. This article solves this problem by developing an iterative algorithm to calculate the smoothed main and aftershock probabilities conditional on all available information contained in the catalog. Consequently, an objective estimate of the spatial intensity function can be obtained and an iterative semi-parametric approach is implemented to estimate model parameters with information criteria used for tuning the smoothing parameters. The methods proposed herein are illustrated on simulated data and a New Zealand earthquake catalog.