Dilatant Strengthening as a Mechanism for Slow Slip Events

Paul Segall, Allan M. Rubin, Albert M. Bradley, & James R. Rice

Published 2010, SCEC Contribution #1362

Transient slow slip events (SSE) have been observed in a number of subduction zones, yet their mechanics remain poorly understood. We suggest that dilatancy stabilizes sliding during SSE; specifically that unstable rate-state friction nucleates transients under drained conditions but that as slip accelerates dilatancy induced reductions in pore-pressure $ quench the instability. Accelerating slip leads to shear heating and consequent thermal pressurization which is destabilizing. Competition between thermal weakening and dilatant strengthening may control whether slip is fast or slow. We model SSE with 2D elasticity, rate-state friction and a dilatancy/compaction law in which inelastic porosity $\phi$ evolves toward steady-state over the frictional slip scale, $.
Laboratory data show $\phi_{ss} \simeq \epsilon \ln (v/v_0)$, with $\epsilon \sim 10^{-4}$. We consider two diffusion models: In {\em membrane diffusion} the diffusive term is approximated by $-(p- p^{\infty})/{t_f} $ where $ and ^{\infty}$ are the fault zone and remote pore-pressures, respectively, and $ is a characteristic diffusion time. {\em Homogeneous diffusion} more accurately models flow normal to the fault with
diffusivity $ c_{hyd}$, using a finite difference scheme. For membrane diffusion, a linearized stability analysis shows that $\cE = 1-a/b$ defines a boundary between slow and fast slip, where $\cE \equiv f_0 \epsilon/ \beta b (\sigma - p^{\infty})$, $ f_0$ is nominal friction, $ and $ are rate-state parameters,
and $\beta$ is compressibility. Simulations with $\cE < 1-a/b$ accelerate to radiation damping for sufficiently large slip zones, whereas for $\cE > 1-a/b$ the maximum slip-speeds are quasi-static. For homogeneous diffusion the non-dimensional dilatancy efficiency is $ E_p \equiv {\epsilon h}/ ( {\beta (\sigma - p^{\infty})} \sqrt{ { v^{\infty}} / { c_{hyd} d_c} }),$ where $ is the shear zone thickness,
and ^{\infty}$ is the plate velocity. Slow slip is thus favored by strong dilatancy $\epsilon h$, low effective stress, compressibility, and diffusivity. The ratio of $ to thermal pressurization efficiency scales inversely with effective stress showing that low $(\sigma - p^{\infty})$ favors SSE, consistent with seismic observations. For \sim 10^{-3}$ simulated transient slip-rates, repeat times, average slip, and stress drops are comparable to that observed in Cascadia. Model propagation speeds in
the dip-direction are comparable to those observed along-strike. For a broad range of parameters simulations exhibit slow phases driven by down-dip, steady plate motion and faster phases that relax the accumulated stress. The faster phases are assumed to model geodetically observable SSE; the slow phases may help to explain tremor observed between strong SSE. Slow slip accommodates only a fraction of the net relative plate
motion, implying that the remaining deficit is made up during coseismic or post-seismic slip.

Citation
Segall, P., Rubin, A. M., Bradley, A. M., & Rice, J. R. (2010). Dilatant Strengthening as a Mechanism for Slow Slip Events. Journal of Geophysical Research, 115, B12305 (37 pages). doi: 10.1029/2010JB007449.