Self-similar asymptotics of rate-strengthening faults

Robert C. Viesca, & Pierre Dublanchet

Published August 12, 2016, SCEC Contribution #6658, 2016 SCEC Annual Meeting Poster #068

We examine how slow slip progresses on rate-strengthening faults. We consider that the source of rate-strengthening may be a linear or non-linear viscous fault rheology, a logarithmic rate-dependence, or a Dieterich-Ruina dependence on slip rate and its history. We show the existence of self-similar asymptotic solutions for slip rate of the form V = t^alpha f(x/t^beta). The exponent beta is determined by the nature of the elastic interaction (for slip between elastic half-spaces in contact, beta = 1; and for a layer sliding above a substrate, beta = 1/2). The similarity exponent alpha is determined by the type of initial or boundary conditions. Such conditions may be, for example, (i) a sudden change in stress on the fault or (ii) an imposed boundary slip rate. We consider in-plane or anti-plane slip for examples (i) and (ii) and present the asymptotic solutions thereof, which may be found numerically or in closed form. The self-similar behavior of scenario (i) is, for a step increase in stress, that of an initially elevated slip rate decaying in time while spreading in space; and of scenario (ii) is that an elevated slip rate propagating along the fault. Under scenario (i) we show that the disparate fault rheologies share a common closed-form similarity solution for the decay of slip rate following the initial stress change. For comparison, we compute numerical solutions to the evolution equation for slip rate (and state, when applicable) and find precise agreement with the above analysis.

Key Words
post-seismic slip, propagating slow slip

Citation
Viesca, R. C., & Dublanchet, P. (2016, 08). Self-similar asymptotics of rate-strengthening faults. Poster Presentation at 2016 SCEC Annual Meeting.

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