Crack Models of Repeating Earthquakes Predict Observed Moment-Recurrence Scaling

Small repeating earthquakes are thought to represent rupture of isolated asperities loaded by surrounding creep. The observed scaling between recurrence interval and seismic moment, T-r approximate to M-1/6, contrasts with expectation assuming constant stress drop and no aseismic slip (T-r approximate to M-1/3). Here we demonstrate that simple crack models of velocity-weakening asperities in a velocity-strengthening fault predict the M-1/6 scaling; however, the mechanism depends on asperity radius, R. For small asperities ( , where R is the nucleation radius) numerical simulations with rate-state friction show interseismic creep penetrating inward from the edge, and earthquakes nucleate in the center and rupture the entire asperity. Creep penetration accounts for approximate to 25% of the slip budget, the nucleation phase takes up a larger fraction of slip. Stress drop increases with increasing R; the lack of self-similarity being due to the finite nucleation dimension. For 2R