Crack models of repeating earthquakes predict observed moment-recurrence scaling

Camilla Cattania, & Paul Segall

Submitted August 15, 2018, SCEC Contribution #8749, 2018 SCEC Annual Meeting Poster #190

Small repeating earthquakes are highly periodic events, and they are thought to occur on velocity weakening (stick-slip) asperities embedded in a velocity strengthening (creeping) fault. In contrast, intermediate and large earthquakes (above ~ M4) do not exhibit such periodicity and characteristic ruptures. A puzzling observation is the scaling between the recurrence interval of small repeaters and seismic moment: a classical argument assuming constant stress drop and no interseismic slip on the asperity predicts Tr~ M0^(1/3), while the observed scaling is Tr~ M0^(1/6).

Here we use numerical simulations of rate-state faults and fracture mechanics concepts to understand how the seismic behaviour of isolated asperities loaded by creep varies depending on their dimension. We derive analytical expressions for the recurrence interval, which predict the Tr~ M0^(1/6) scaling over the entire range of R considered; however, the physical mechanism varies depending on the ratio of the asperity dimension to the critical nucleation radius Rc.

After a seismic rupture, creep penetrates inwards from the asperity boundary. We use an energy balance criterion to derive an equation of motion for the creep front and the time to nucleation, and identify two regimes: for R<2Rc, creep penetrates to the center of the asperity, where ruptures nucleate; the recurrence interval scales as Tr~ R, however the stress drop is not constant, due to the scale-dependence introduced by the finite nucleation radius. For 2Rc<R~<7Rc, simulations show simple cycles of ruptures nucleating near the edge and propagating laterally; stress drops are constant, and the Tr~ M0^(1/6) scaling is predicted by how the propagation of the creep front depends on R, which results in Tr~ R^(1/2).

Finally, larger asperities exhibit a mixture of partial and full ruptures; we estimate the recurrence interval for full ruptures from the requirement that the energy release rate everywhere on the asperity at least equals the fracture energy. We show that this criterion results in the scaling Tr~ M0^(1/6). Our results explain the behavior of repeaters over a wide magnitude range, and predict potentially observable changes in the rupture style and seismic cycle of isolated asperities depending on R/Rc.

Key Words
repeating earthquakes, rupture mechanics, earthquake periodicity

Cattania, C., & Segall, P. (2018, 08). Crack models of repeating earthquakes predict observed moment-recurrence scaling. Poster Presentation at 2018 SCEC Annual Meeting.

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