On Mainshock Focal Mechanisms and the Spatial Distribution of Aftershocks

Despite previous observations that aftershocks lie preferentially along the fault planes of mainshocks, many branching models for earthquake occurrences do not directly incorporate information on the moment tensors of mainshocks in forecasting the spatial distribution of aftershocks, or do so in a very simplistic way using spatial kernels which have not been rigorously tested on earthquake data to date. We revisit the relationship between the mainshock moment tensor and aftershock location, analyzing strike-slip events in Southern California. Using data from the SCEDC catalog, we find ample evidence suggesting that the fault plane azimuth of a strike-slip earthquake has the highest concentration of aftershocks, a finding that is consistent with previous efforts. We propose a joint distribution to model the aftershock locations that is parameterized in terms of the distance and relative angle to the aftershocks. This model is compared to previously proposed models based on the normal distribution and the squared cosine function. Using residual analysis and weighted K-function as diagnostic measures, we find that both the normal and squared cosine models suffer from several serious problems, and that the joint distribution we propose has features similar to both alternative models but fits much better to Southern California earthquake data.