Nonstationary ETAS models for nonstandard earthquakes

TL;DR

This paper introduces nonstationary extensions of the ETAS model to better fit nonstandard earthquake swarms caused by transient stress changes, using empirical Bayes estimation and demonstrated on a 2011 Tohoku-Oki swarm.

Contribution

It develops time-dependent parameter models for nonstandard earthquakes and applies empirical Bayes for robust estimation, improving fit over stationary models.

Findings

Nonstationary ETAS models better fit transient earthquake swarms.

Empirical Bayes method provides robust parameter estimation.

Model successfully applied to 2011 Tohoku-Oki earthquake swarm.

Abstract

The conditional intensity function of a point process is a useful tool for generating probability forecasts of earthquakes. The epidemic-type aftershock sequence (ETAS) model is defined by a conditional intensity function, and the corresponding point process is equivalent to a branching process, assuming that an earthquake generates a cluster of offspring earthquakes (triggered earthquakes or so-called aftershocks). Further, the size of the first-generation cluster depends on the magnitude of the triggering (parent) earthquake. The ETAS model provides a good fit to standard earthquake occurrences. However, there are nonstandard earthquake series that appear under transient stress changes caused by aseismic forces such as volcanic magma or fluid intrusions. These events trigger transient nonstandard earthquake swarms, and they are poorly fitted by the stationary ETAS model. In this study, we examine nonstationary extensions of the ETAS model that cover nonstandard cases. These models allow the parameters to be time-dependent and can be estimated by the empirical Bayes method. The best model is selected among the competing models to provide the inversion solutions of nonstationary changes. To address issues of the uniqueness and robustness of the inversion procedure, this method is demonstrated on an inland swarm activity induced by the 2011 Tohoku-Oki, Japan earthquake of magnitude 9.0.