A new estimation of the decay of aftershock density with distance to the mainshock

Abstract

We investigate how aftershocks are spatially distributed relative to the mainshock. Compared to previous studies, ours focuses on earthquakes causally related to the mainshock rather than on aftershocks of previous aftershocks. We show that this distinction can be made objectively but becomes uncertain at long time scales and large distances. Analyzing a regional earthquake data set, it is found that, at time t following a mainshock of magnitude m, the probability of finding an aftershock at distance r relative to the mainshock fault decays as r−γ, where γ is typically between 1.7 and 2.1 for 3 ≤ m < 6 and is independent of m, for r less than 10 to 20 km and t less than 1 day. Uncertainties on this probability at larger r and t do not allow for a correct estimation of this spatial decay. We further show that a static stress model coupled with a rate‐and‐state friction model predicts a similar decay, with an exponent γ = 2.2, in the same space and time intervals. This suggests that static stress changes could explain the repartition of aftershocks around the mainshock even at distances larger than 10 times the rupture length.