On the scaling of the slip weakening rate of heterogeneous faults

Abstract

We present an attempt to describe the scaling law of the slip weakening rate at the onset of instability using a two‐dimensional fault model. A fault consists of a series of weak patches under slip weakening friction, separated by unbreakable barriers. A first group of faults contains an even distribution of patches of different scales conserving the same total slipping length, while a second group consists of various fractal Cantor sets. The global behavior of rupture is described by the exponential growth rate λ. For an infinite homogeneous fault, the coefficient λ is governed by the weakening rate of the friction law. We estimate the weakening rate of each individual fault in an heterogeneous fault system such that the rate of exponential growth λ of this fault network is identical to that of a single homogeneous fault. Using this homogenization procedure, we compute the weakening rate on the weak patches for faults with different scales of heterogeneity and a given λ. At large scales, the weakening rate is scale‐independent, the initiation process on a long patch being similar to the case of an infinite fault. At small scales and for all the different geometries considered here, the weakening rate varies as α = β*0/a, where a is the scale or half length of each elementary fault and β*0 ≃ 1.158. We discuss the physical implications of our results on the value of the slip weakening distance Dc and give a possible explanation of the scale dependence of this parameter.