On the Earthquake Distribution Modeling in Sumatra by Cauchy Cluster Process: Comparing Log-Linear and Log-Additive Intensity Models

Abstract

Inhomogeneous cluster point processes have been considered for modeling the distribution of earthquake epicenters with the spatial trend and clustering patterns. In particular, the spatial trend is assessed by the intensity model involving geological variables. However, for intensity with a log-linear form, it may be too restrictive and not appropriate for earthquake distribution. In this study, we consider the Cauchy cluster process with the log-additive intensity model to analyze the distribution of major earthquake occurrences in Sumatra, Indonesia. The estimation procedure follows the standard two-step estimation technique, where the first step adapts the method for the Generalized Additive Models (GAMs) using penalized iteratively reweighted least squares (PIRLS) algorithm, and the second step employs the second-order composite likelihood. For the earthquake analysis in Sumatra, the log-additive intensity shows more flexibility to determine the contribution of each geological factor, especially to capture the effect of the nearest distance to the fault which is far from log-linear. In addition, compared to the log-linear model, the Cauchy cluster process with a log-additive intensity model performs better with a smaller Akaike Information Criterion’s (AIC) value and a sharper envelope K-function. The estimated number of mainshocks is around 114 with aftershocks spread by 14 km around the mainshocks. We detect three hotspots for the major earthquake in Sumatra: the northern part (Aceh and North Sumatra), the western part (Mentawai, Nias, and Simeulue), and Bengkulu.