A model for complex aftershock sequences

Abstract

The decay rate of aftershocks is commonly very well described by the modified Omori law, $n(t) \propto t^{-p}$, where n(t) is the number of aftershocks per unit time, t is the time after the main shock, and p is a constant in the range 0.9<p<1.5, and usually close to 1. But there are also more complex aftershock sequences for which the Omori law can be considered only as a first approximation. One of these complex aftershock sequences took place in the Eastern Pyrenees on February 18, 1996, and was described in detail by {\it Correig et al.} [1997]. In this paper, we propose a new model inspired by dynamic fiber-bundle models to interpret this type of complex aftershock sequences with sudden increases in the rate of aftershock production not directly related to the magnitude of the aftershocks (as in the epidemic-type aftershock sequences). The model is a simple, discrete, stochastic fracture model where the elements (asperities or barriers) break because of static fatigue, transfer stress according to a local load-sharing rule and then are regenerated. We find a very good agreement between the model and the Eastern Pyrenees aftershock sequence and we propose that the key mechanism for explaining aftershocks, apart from a time-dependent rock strength, is the presence of dynamic stress fluctuations which constantly reset the initial conditions for the next aftershock in the sequence.