Camilla Cattania, Paul Segall

Small repeating earthquakes are thought to represent rupture of isolated asperities loaded by surrounding creep.
The observed scaling between recurrence interval and seismic moment, Tr ~ M^(1/6), contrasts with expectation assuming constant stress drop and no aseismic slip (Tr ~ M^(1/3)). Here we demonstrate that simple crack models of velocity-weakening asperities embedded in a velocity-strengthening fault predict the Tr ~ M^(1/6) scaling; however, the mechanism depends on asperity radius, R.
For small asperities (Ri < R < 2Ri, where Ri is the nucleation radius) numerical simulations with rate-state friction show interseismic creep penetrating inwards from the edge, with earthquakes nucleating in the center and rupturing 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 due to the finite nucleation dimension.
For 2 Ri < R < 4.3 Ri simulations exhibit simple cycles with ruptures nucleating from the edge. Asperities with R > 4.3Ri exhibit complex cycles of partial and full ruptures. Here Tr is explained by an energy criterion: full rupture requires that the energy release rate everywhere on the asperity at least equals the fracture energy, leading to the scaling Tr ~ M^(1/6). Remarkably, in spite of the variability in behavior with source dimension, the scaling of Tr with stress drop \Delta\tau, nucleation length and creep rate Vpl is the same across all regimes: Tr ~ (Ri)^(1/2)\Delta\tau^(5/6)M^(1/6)/Vpl. This supports the use of repeating earthquakes as creepmeters, and provides a physical interpretation for the scaling observed in nature.