A Simple Discrete Elastic Model Exhibits Both the Statistical Properties and Migration Patterns of Slow Slip
Ling Xia, & Allan M. RubinSubmitted August 30, 2026, SCEC Contribution #15118, 2026 SCEC Annual Meeting Poster #TBD
25 years after their discovery, the physical mechanisms of slow earthquakes remain enigmatic. Here we develop a simple quasi-static elastic model that reproduces both the migration patterns of elastic/frictional models, and the statistical properties of Brownian models. Fault elements are either slipping or locked, with locked elements having either a fully healed static strength τ_p, or a reduced static strength if they slipped recently. By adjusting τ_p, the fixed slip speed V_slip, and the grid spacing Δx, the model generates characteristic events with recurrence intervals of about 1 year and propagation speeds of about 10 km/day, consistent with observations in Cascadia as well as analytical estimates derived from fracture mechanics. The simulated events also exhibit a constant scaled energy (that is, a proportionality between squared moment acceleration and moment rate, with the former being a proxy for energy rate), and an amplitude spectrum decaying as 1/f at high frequencies, matching both observations and Brownian walk models. We approximate the simulated moment rate functions using a linear birth-death process, with birth and death rates estimated from properly weighted elastic interaction kernels and the reduced static strength, and obtain analytical estimates of the equilibrium moment rate, the scaled energy, and the lower corner frequency of the amplitude spectrum, all in good agreement with the simulations.
However, this simple model generates secondary slip fronts without an obvious preferred propagation direction, unlike the backward-propagating rapid tremor reversals (RTRs) that are observed. In addition, the scaled energy is roughly 5-6 orders of magnitude lower than observed values, and the simulated moment rate function lacks the intermittency seen in tremor records. To address these limitations, we are extending the study using RSQSim, which incorporates a simplified rate- and state-dependent friction law, specifically including logarithmic-with-time fault re-strengthening when “locked”, and exponential self-acceleration to instability during nucleation. Preliminary results suggest that the time-dependent healing in RSQSim simulations generates secondary slip fronts with a more consistent backward propagation direction. The moment rate within individual events also exhibits greater temporal variability, suggesting that the self-acceleration to instability in RSQSim may better reproduce the intermittency observed in tremor records.
Key Words
slow slip and tremor, stochastic processes
Citation
Xia, L., & Rubin, A. M. (2026, 08). A Simple Discrete Elastic Model Exhibits Both the Statistical Properties and Migration Patterns of Slow Slip. Poster Presentation at 2026 SCEC Annual Meeting.
Related Projects & Working Groups
Fault and Rupture Mechanics (FARM)
