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## Crack Models of Repeating Earthquakes Predict Observed Moment‐Recurrence Scaling

Camilla Cattania, & Paul Segall

Published January 30, 2019, SCEC Contribution #8999

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 in a velocity-strengthening fault predict the 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, 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 2Ri < R <~ 6 Ri simulations exhibit simple cycles with ruptures nucleating from the edge. Asperities with R >~ 6Ri 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 Dtau, nucleation length and creep rate Vpl is the same across all regimes: Tr ~ (Ri^(1/2) Dtau^(5/6) M0^(1/6)/Vpl. This supports the use of repeating earthquakes as creepmeters, and provides a physical interpretation for the scaling observed in nature.

Citation
Cattania, C., & Segall, P. (2019). Crack Models of Repeating Earthquakes Predict Observed Moment‐Recurrence Scaling. Journal of Geophysical Research: Solid Earth, 124(1), 476-503. doi: 10.1029/2018JB016056.

Related Projects & Working Groups
Fault and Rupture Mechanics (FARM)