## The Annals of Applied Statistics

### Nonstationary ETAS models for nonstandard earthquakes

#### 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.

#### Article information

Source
Ann. Appl. Stat., Volume 8, Number 3 (2014), 1825-1852.

Dates
First available in Project Euclid: 23 October 2014

https://projecteuclid.org/euclid.aoas/1414091236

Digital Object Identifier
doi:10.1214/14-AOAS759

Mathematical Reviews number (MathSciNet)
MR3271355

Zentralblatt MATH identifier
1304.86011

#### Citation

Kumazawa, Takao; Ogata, Yosihiko. Nonstationary ETAS models for nonstandard earthquakes. Ann. Appl. Stat. 8 (2014), no. 3, 1825--1852. doi:10.1214/14-AOAS759. https://projecteuclid.org/euclid.aoas/1414091236

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