Bayesian ETAS: Towards Improved Earthquake Rate Models in the Pacific Northwest

Abstract:

The Pacific Northwest (PNW) has substantial earthquake risk, both due to the Cascadia megathrust fault and but also crustal faults that lie under population centers such as Seattle. Stable models of its earthquake rates and clustering parameters are thus key to probabilistic seismic hazard assessment and aftershock forecasts for the continental PNW. The Epidemic-Type Aftershock Sequence model (ETAS) is a spatiotemporal point process model which parameterizes the rates of earthquakes and aftershocks within a seismic region, using a catalog of its past earthquakes. Typically, maximum likelihood estimation is used to fit ETAS to an earthquake catalog; however, the ETAS likelihood suffers from flatness near its optima, parameter correlation and numerical instability. We present a Bayesian procedure to estimate ETAS parameters, such that parameters can be reliably estimated and their uncertainties resolved. The procedure is conditional on knowing which earthquakes triggered which aftershocks; this latent structure and the ETAS parameters are estimated stepwise, similar to the expectation-maximization algorithm. The procedure uses a Gibbs sampler to conditionally estimate the posterior distributions of each part of the model. We experiment with several prior distributions, which represent different hypotheses on aftershock properties. We simulate several synthetic catalogs and test the modelling procedure, showing posterior distributions that are well-centered on true values and follow previously reported patterns. We also demonstrate the procedure on a new catalog for the continental PNW. This catalog is merged from three existing catalogs with automated procedures for duplicate detection and identification of earthquake swarms. More detailed information about PNW aftershocks can be estimated using Bayesian ETAS than using simpler seismicity models.