Assessing the dependency between the magnitudes of earthquakes and the magnitudes of their aftershocks

Current assumptions on the level of inter-dependency between the magnitudes of earthquakes and the magnitudes of their aftershocks vary significantly, ranging from assumed independence for models like epidemic type aftershock-sequence (ETAS) to assumed positive correlation, at least for the events leading up to the largest earthquakes, for models like accelerated moment release. Recently, a method was developed by Marsan and Lengline for model independent stochastic de-clustering (MISD) of a multidimensional Hawkes self-exciting process, or as is the case here, earthquake activity. After expanding the algorithm to allow for a spatially dependent background rate (henceforth SDMISD), repeated application of SDMISD to a global earthquake catalog allows for estimates with confidence bounds for the average magnitude of an aftershock conditioned upon the magnitude(s) of the earthquake(s) that caused the aftershock. 15 years of data on M 5.3 earthquakes from the global Centroid Moment Tensor earthquake catalog indicate that the magnitudes of aftershocks are dependent on the magnitudes of the earthquakes that cause them, and indeed, larger than average earthquakes are more likely to trigger larger than average aftershocks. Copyright © 2014 John Wiley & Sons, Ltd.