Basic Models of Seismicity: Temporal Models

In this and subsequent articles, we present an overview of some models of seismicity that have been developed to describe, analyze and forecast the probabilities of earthquake occurrences. The models that we focus on are not only instrumental in the understanding of seismicity patterns, but also important tools for time-independent and time-dependent seismic hazard analysis. We intend to provide a general and probabilistic framework for the occurrence of earthquakes. In this article, we begin with a survey of simple, one-dimensional temporal models such as the Poisson and renewal models. Despite their simplicity, they remain highly relevant to studies of the recurrence of large earthquakes on individual faults, to the debate about the existence of seismic gaps, and also to probabilistic seismic hazard analysis. We then continue with more general temporal occurrence models such as the stress-release model, the Omori-Utsu formula, and the ETAS (Epidemic Type Aftershock Sequence) model.