Generalized Additive Poisson Models for Quantifying Geological Factors Effect on the Earthquake Risk Mapping

Cluster-type point process models are the popular model for modeling the arrangement of locations of earthquake occurrences. When a spatial trend is presence due to e.g. geological factors, the log-linear intensity of the point process is often considered to exploit inhomogeneity due to such factors. However, this could be a major drawback, especially in seismology when the relation between the intensity of earthquake occurrences and environmental covariates is not log-linear. In this paper, we consider the Cauchy cluster process with a log-additive intensity model to quantify two effects in modeling the distribution of locations of major earthquakes in Sulawesi-Maluku: (1) spatial trend due to geological covariates such as subduction zones, faults, and volcanoes and (2) clustering effect due to seismic activities. The Cauchy cluster process could detect the clustering effect even when the aftershocks are extremely distant to the mainshocks while log-additive intensity is a more flexible model to study inhomogeneity due to the environment. To estimate the parameters, we apply two-step estimation procedure, in the first step, we estimate the regression parameter corresponding to effects of the geological variables by maximum composite likelihood by involving penalized iteratively re-weighted least squares (PIRLS) technique, and in the second step, we obtain the cluster estimates by maximum second order composite likelihood. The results show that the active faults and volcanoes are significant covariates that trigger earthquakes, the estimated mainshock intensity is around 78, and the aftershocks are distributed around it with a distance of 15.2 km due to mainshock activity.