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This article proposes a spatiotemporal point process model that enhances theclassical Epidemic-Type Aftershock Sequence (ETAS) model by incorporating arenewal main-shock arrival process, which we term the renewal ETAS (RETAS)model. This modification is similar in spirit to the renewal Hawkes (RHawkes)process but the conditional intensity process supports a spatial domain. Itempowers the main-shock intensity with the capability to reset upon the arrivalof main-shocks and therefore allows for heavier clustering of earthquakes thanthe spatiotemporal ETAS model introduced by Ogata (1998). We introduce alikelihood evaluation algorithm for parameter estimation and provide a novelprocedure to evaluated the fitted model's goodness-of-fit based on a sequentialapplication of the Rosenblatt transformation. A simulation algorithm for theRETAS model is developed and applied to validate the numerical performance ofthe likelihood evaluation algorithm and goodness of fit test procedure. Weillustrate the proposed model and procedures on various earthquake catalogsaround the world each with distinctly different seismic activity. Thesecatalogs will demonstrate that the RETAS model affords additional flexibilityin comparison to the classical spatiotemporal ETAS model and has the potentialfor superior modeling and forecasting of seismicity.

Spatiotemporal ETAS model with a renewal main-shock arrival process