Comparing the Hawkes and Trigger process models for aftershock sequences following the 2005 Kashmir earthquake

In an earlier study (Van Lieshout and Stein in Math Gesoci 44(3):309–326, 2012) we postulated the existence of two major earthquakes in the 2005 Kashmir disaster instead of a single one, based upon the pattern of aftershocks. In this study, we explore this hypothesis further by fitting several spatial point pattern models. In particular, we discuss the Hawkes and the trigger process models for earthquake aftershock sequences following the Kashmir catastrophe in 2005. The minimum contrast method is used for estimation of the parameters. The study shows that the trigger model fits better than the Hawkes model. The most likely number of main shocks is rounded to 2 generating the almost 200 aftershocks, whereas the Hawkes model would estimate a parent process of approximately 18 parents with on average about 10 descendants. We conclude that the spatial pattern of aftershocks can best be understood as a mixture of two bivariate normal distributions centered around two major shocks and estimate the parameters.