Law of Total Probability of Aftershocks in Earthquake Insurance

Abstract. Seismic hazard expressed in annual rate of exceedance of a peak ground acceleration traditionally refers to mainshock. A similar seismic hazard, APSHA, has been adopted for aftershock probabilistic seismic hazard. Probabilistic seismic hazard assessment (PSHA) refers to a homogeneous Poisson process to describe mainshock while APSHA models aftershock occurrence as a nonhomogeneous Poisson process whose rate modeled as Omori law. It shown that the combination of PSHA and APSHA results seismic hazard for mainshock-aftershock seismic sequence/cluster (SPSHA/CPSHA). This study shows how to combine results of APSHA and PSHA and proposes a method for earthquake insurance. The study was carried out for West Java region with 206 occurrences consist of 11 clusters. One cluster with 74 aftershocks was chosen for further study. The parameters of SPSHA/CPSHA was estimated using maximum likelihood. The results of SPSHA/CPSHA combined with damage probability matrix (DPM) yields an expected annual damage ratio (EADR) as an indicator of earthquake insurance. The proposed method in this study can be used as a method for computing earthquake insurance premium. Due to limited data further study is needed to obtain accurate and reasonable results.