Crack Models of Repeating Earthquakes Predict Observed Moment-Recurrence Scaling

Abstract

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 ∼M 1/6 , contrasts with expectation assuming constant stress drop and no aseismic slip (T r ∼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 (R ∞ < R < 2R ∞ , 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 ∼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∞