Earthquake nucleation is traditionally described using cascading or slow pre-slip models. In the latter, nucleation occurs as the sudden transition from quasi-static slip growth to dynamic rupture propagation. This typically occurs when a region of the fault of critical size Lc, often called nucleation length, is sliding. This transition is relatively well-understood in the context of homogeneous faults. Yet, faults exhibit multiple scales of heterogeneities that may emerge from local changes in lithologies or from its self-affine roughness. How these multiscale heterogeneities impact the overall fault stability is still an open question. Combining the nucleation theory of [Uenishi and Rice, JGR, 2003] and concepts borrowed from statistical physics, we propose a theoretical framework to predict the influence of brittle/ductile asperities on the nucleation length Lc for simple linear slip-dependent friction laws. Model predictions are benchmarked on two-dimensional dynamic simulations of rupture nucleation along planar heterogeneous faults. Our results show that the interplay between frictional properties and the asperity size gives birth to three (in)stability regimes: (i) a local regime, where fault stability is controlled by the local frictional properties, (ii) an extremal regime, where it is governed by the most brittle asperities, and (iii) a homogenized regime, in which the fault behaves at the macroscale as if it was homogeneous and the influence of small-scale asperities can be averaged.
Using this model, we explore the overall stability of rough faults, featuring multiscale distributions of frictional properties. We also investigate the stability of velocity-neutral faults that features brittle asperities. Overall, our model provides a theoretical basis to discriminate which heterogeneity scales should be explicitly described in a comprehensive modelling of earthquake nucleation, and which scales can be averaged.