Earthquake modelling at the country level using aggregated spatio-temporal point processes

The goal of this paper is to derive a hazard map for earthquake occurrences in Pakistan from a catalogue that contains spatial coordinates of shallow earthquakes of magnitude $4.5$ or larger aggregated over calendar years. We test relative temporal stationarity by the KPSS statistic and use the inhomogeneous J--function to test for inter-point interactions. We then formulate a cluster model, and deconvolve in order to calculate the hazard map, and verify that no particular year has an undue influence on the map. Within the borders of the single country, the KPSS test did not show any deviation from homogeneity in the spatial intensities. The inhomogeneous J-function indicated clustering that could not be attributed to inhomogeneity, and the analysis of aftershocks showed some evidence of two major shocks instead of one during the 2005 Kashmir earthquake disaster. Thus, the spatial point pattern analysis carried out for these data was insightful in various aspects and the hazard map that was obtained may lead to improved measures to protect the population against the disastrous effects of earthquakes.