Algorithms for Fitting the Space-Time ETAS Model to Earthquake Catalog Data: A Comparative Study

Abstract

The space-time epidemic-type aftershock sequence (space-time ETAS) is a standard model for the analysis of earthquake catalogs. The model considers a semi-parametric conditional intensity function consisting of a semi-parametric background rate and a parametric aftershock rate. For the estimation procedure, the optimization employs an iterative algorithm where the nonparametric and parametric components are estimated iteratively using, respectively, kernel density estimation and maximum likelihood technique. ETAS and etasFLP are the two R packages that implement such a procedure with different techniques for estimating both the nonparametric and parametric components. The two packages have been studied from different directions and have not been evaluated together. This study examines the common features of the models and algorithms generated from the packages, and then evaluates their performance through simulation study and application to the Sumatran earthquake. For the analysis involving small or medium number of earthquakes, the etasFLP outperforms ETAS in terms of parameter estimation and computing time. For the application, we identify three main areas of high seismic risk: Simeulue Island, Nias Island, and southeast of Siberut Island.