Math Geosci (2013) 45:149–164 DOI 10.1007/s11004-012-9438-x Comparing the Hawkes and Trigger Process Models for Aftershock Sequences Following the 2005 Kashmir Earthquake K. Türkyilmaz · M.N.M. van Lieshout · A. Stein Received: 25 January 2012 / Accepted: 6 December 2012 / Published online: 15 January 2013 © International Association for Mathematical Geosciences 2013 Abstract 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 dis- aster 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 after- shock 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 under- stood as a mixture of two bivariate normal distributions centered around two major shocks and estimate the parameters. Keywords Cluster process · EM method · Minimum contrast method · Mixture model · Nearest neighbor distance distribution function · Pair correlation function 1 Introduction Due to the orogenic belt caused by the collision of the Indo-Australian continental plate and the Eurasian plate, Pakistan is vulnerable to earthquakes. This vulnera- bility varies across the country (Van Lieshout and Stein 2012); a hot spot occurs K. Türkyilmaz · M.N.M. van Lieshout Probability, Networks and Algorithms, CWI, Amsterdam, The Netherlands A. Stein ( ) Faculty of Geo-Information Science and Earth Observation (ITC), University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands e-mail: a.stein@utwente.nl