Aftershocks Preferentially Occur in Previously Active Areas

The clearest statistical signal in aftershock locations is that most aftershocks occur close to their mainshocks. More precisely, aftershocks are triggered at distances following a power-law decay in distance (Felzer and Brodsky, 2006). This distance decay kernel is used in epidemic-type aftershock sequence (ETAS) modeling and is typically assumed to be isotropic, even though individual sequences show more clustered aftershock occurrence. The assumption of spatially isotropic triggering kernels can impact the estimation of ETAS parameters themselves, such as biasing the magnitude-productivity term, alpha, and assigning too much weight to secondary rather than primary (direct) triggering. Here we show that aftershock locations in southern California, at all mainshock–aftershock distances, preferentially occur in the areas of previous seismicity. For a given sequence, the scaling between aftershock rates and the previous seismicity rate is approximately linear. However, the total number of aftershocks observed for a given sequence is independent of background rate. We explain both of these observations within the framework of rate-and-state friction (Dieterich, 1994).