Testing Rate‐and‐State Predictions of Aftershock Decay with Distance

We analyze aftershocks of the 2019 M 7.1 Ridgecrest mainshock and isolated M 5–6 mainshocks in southern California to test predictions made by the rate‐and‐state friction model of Dieterich (1994). Rate‐and‐state friction predicts that the seismicity rate after a stress step follows Omori decay, where the Omori c‐value, which is the saturation in aftershock rate observed at small times, is larger for smaller stress steps. Put in the context of an aftershock sequence, this predicts that the Omori c‐value will be systematically larger at greater distances from the mainshock. To our knowledge, this predicted effect has not been observed. In part this may be because the Omori c‐value is difficult to measure because it often reflects short‐term catalog incompleteness rather than a true saturation in aftershock rate.

We explore the dependence of the Omori c‐value on the distance to the mainshock by applying the “a‐positive” method (van der Elst and Page, 2023). This method is insensitive to short‐term aftershock incompleteness and allows resolution of the true aftershock rate deep into the mainshock coda. For aftershocks of the Ridgecrest mainshock and stacked M 5–6 mainshocks, we observe systematic differences in early aftershock rates, relative to mainshock distance, consistent with the predictions of rate‐and‐state friction. Furthermore, for the larger Ridgecrest dataset, we observe that aftershocks nearer to the mainshock start earlier, and we resolve a flattening of the Omori curve consistent with a larger Omori c‐value for the farthest aftershocks, as predicted by Dieterich (1994).