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## Slip partitioning and scaling relations of repeating earthquakes on rate-state faults

Camilla Cattania, Paul Segall, & Sebastian Hainzl

Published August 15, 2017, SCEC Contribution #7818, 2017 SCEC Annual Meeting Poster #166

Small repeating earthquakes, characterized by similar waveforms, are thought to represent the rupture of isolated asperities loaded by creep. They are very periodic, making them an ideal natural laboratory to study the factors determining the duration of a seismic cycle. An interesting observation is the scaling between recurrence interval and seismic moment: T~M^1/6, which contradicts what is expected from constant stress drop and stick-slip behavior (T~M^1/3).

We use numerical tools and ideas from fracture mechanics to study earthquake cycles on circular asperities (regions of velocity-weakening rate-state friction embedded in a velocity-strengthening fault). We aim to explain how the recurrence interval and the slip partitioning between phases of the seismic cycle vary with asperity radius.
After a seismic rupture, a creep front propagates inward from the edge; when it reaches a critical distance, slip accelerates. Numerical simulations present two regimes. Above a given asperity size, earthquakes nucleate near the edge, with each event preceded by few episodes of slip acceleration. The recurrence interval is explained by an energy criterion: the elastic energy release rate everywhere on the asperity needs to at least be equal to the fracture energy. For a circular asperity of radius R, this results in the scaling: T~R^1/2. In this regime stress drops are constant, so that M~R^3 leads to the observed T~M^1/6 scaling. For smaller faults, nucleation occurs when the creep front reaches the asperity center. The energy criterion is always satisfied, leading to a full rupture. We use a crack model to estimate the time required for the creep front to reach the center, and we find that it scales linearly with R. In this regime, however, the stress drop is not constant: smaller faults have lower stress drops, resulting in a scaling close to T~M^1/6. This behavior is due to the nucleation phase: on smaller faults, a larger fraction of slip is released aseismically during acceleration.

We suggest that the recurrence interval is determined by two timescales: the time required to accumulate enough elastic energy for full rupture, and the nucleation time, controlled by the propagation of a creep front. Depending on the asperity radius, the longest timescale determines T. Furthermore, our results suggest a breaking of self-similarity due to the existence of a finite nucleation size, as indicated by non-constant stress drops for small asperities.

Citation
Cattania, C., Segall, P., & Hainzl, S. (2017, 08). Slip partitioning and scaling relations of repeating earthquakes on rate-state faults. Poster Presentation at 2017 SCEC Annual Meeting.

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