# The physics of small earthquakes

Small repeating earthquakes are events characterized by very similar waveforms, and overlapping rupture areas. Unlike most other earthquakes, they are very periodic; they are commonly interpreted as rupturing an isolated asperity embedded in a velocity-strengthening (creeping) fault. Since they are driven by aseismic slip, they are an invaluable tool to probe creeping sections of a fault, and detect spatio-temporal variations in slip rate. I used simple crack models to derive analytical expressions for the recurrence interval as a function of asperity dimension and seismic moment. These expressions are in excellent agreement with the scaling between recurrence interval and seismic moment observed in the simulations: $T_r \sim M_0^{1/ 6}$ (see figure), consistent with observations.

While these results are based on a relatively simple model (circular, uniform asperities), they provide a useful framework to interpret the seismic behavior of small asperities. They make specific predictions, such as a dependence of stress drop on magnitude and a transition between central ruptures for small asperities to lateral ruptures for large asperities (where small and large is a well defined ratio between the asperitity radius and the nucleation radius); similarly, the occurrence of partial ruptures is expected for asperities exceeding a particular dimension.

Cattania, C. and P. Segall (2018), *Crack models of repeating earthquakes predict observed moment-recurrence scaling*, J. Geophys. Res. Solid Earth (
abstract;
article)

**Current and future efforts:** The results above imply a break of self-similarity near the nucleation dimension. Could this be seen in the data? To answer this question, we first need a theoretical source model for small earthquakes, which does not assume constant rupture velocity but instead considers the initial acceleration. I will present some preliminary results on this topic at the 2020 AGU Fall Meeting.