A Nonparametric Bayesian Approach to Seismic Hazard Modeling Using the ETAS Framework

Abstract:

The epidemic-type aftershock sequence (ETAS) model is one of the most popular tools for modeling seismicity and quantifying risk in earthquake-prone regions. Under the ETAS model, the occurrence times of earthquakes are treated as a self-exciting Poisson process where each earthquake briefly increases the probability of subsequent earthquakes occurring soon afterwards, which captures the fact that large mainshocks tend to produce long sequences of aftershocks. A triggering kernel controls the amount by which the probability increases based on the magnitude of each earthquake, and the rate at which it then decays over time. 

This triggering kernel is usually chosen heuristically, to match the parametric form of the modified Omori law for aftershock decay. However recent work has questioned whether this is an appropriate choice. Since the choice of kernel has a large impact on the predictions made by the ETAS model, avoiding misspecification is crucially important.

We present a novel nonparametric version of ETAS which avoids making parametric assumptions, and instead learns the correct specification from the data itself. Our approach is based on the Dirichlet process, which is a modern class of Bayesian prior distribution which allows for efficient inference over an infinite dimensional space of functions. We show how our nonparametric ETAS model can be fit to data, and present results demonstrating that the fit is greatly improved compared to the standard parametric specification. Additionally, we explain how our model can be used to perform probabilistic declustering of earthquake catalogs, to classify earthquakes as being either aftershocks or mainshocks. and to learn the causal relations between pairs of earthquakes.

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