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

Abstract 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).