Open Access
September 2014 Nonstationary ETAS models for nonstandard earthquakes
Takao Kumazawa, Yosihiko Ogata
Ann. Appl. Stat. 8(3): 1825-1852 (September 2014). DOI: 10.1214/14-AOAS759


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.


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Takao Kumazawa. Yosihiko Ogata. "Nonstationary ETAS models for nonstandard earthquakes." Ann. Appl. Stat. 8 (3) 1825 - 1852, September 2014.


Published: September 2014
First available in Project Euclid: 23 October 2014

zbMATH: 1304.86011
MathSciNet: MR3271355
Digital Object Identifier: 10.1214/14-AOAS759

Keywords: Akaike Bayesian Information Criterion , change point , induced seismic activity , time-dependent parameters , two-stage ETAS model

Rights: Copyright © 2014 Institute of Mathematical Statistics

Vol.8 • No. 3 • September 2014
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