A simple stick-slip and creep-slip model for repeating earthquakes and its implication for microearthquakes at Parkfield

repeating earthquakes are represented by circular ruptures, have constant stress drops, and experience no aseismic slip, then their recurrence times should vary with seismic moment as t(r) proportional to M-0(1/3). In contrast, the observed variation for small, characteristic repeating earthquakes along a creeping segment of the San Andreas fault at Parkfield (Nadeau and Johnson, 1998) is much weaker. Also, the Parkfield repeating earthquakes have much longer recurrence intervals than expected if the static stress drop is 10 MPa and if the loading velocity V-L is assumed equal to the geodetically inferred slip rate of the fault V-f. To resolve these discrepancies, previous studies have assumed no aseismic slip during the interseismic period, implying either high stress drop or V-L not equal V-f. In this study, we show that a model that includes aseismic slip provides a plausible alternative explanation for the Parkfield repeating earthquakes. Our model of a repeating earthquake is a fixed-area fault patch that is allowed to continuously creep and strain harden until reaching a failure threshold stress. The strain hardening is represented by a linear coefficient C, which when much greater than the elastic loading stiffness k leads to relatively small interseismic slip (stick-slip). When C and k are of similar size creep-slip occurs, in which relatively large aseismic slip accrues prior to failure. Because fault-patch stiffness varies with patch radius, if C is independent of radius, then the model predicts that the relative amount of seismic to total slip increases with increasing radius or M-0, consistent with variations in slip required to explain the Parkfield data. The model predicts a weak variation in t(r) with M-0 similar to the Parkfield data.