On the scaling of the slip weakening rate of heterogeneous faults

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 D c and give a possible explanation of the scale dependence of this parameter.