  The transition from quasi-static slip growth to dynamic rupture propagation
constitutes one possible scenario to describe earthquake nucleation. If this
transition is rather well understood for homogeneous faults, how the friction
properties of multiscale asperities may influence the overall stability of
seismogenic faults remains largely unclear. Combining classical nucleation
theory and concepts borrowed from condensed matter physics, we propose a
comprehensive analytical framework that predicts the influence of
heterogeneities of weakening rate on the nucleation length $L_c$ for linearly
slip-dependent friction laws. Model predictions are compared to nucleation
lengths measured from 2D dynamic simulations of earthquake nucleation along
heterogeneous faults. Our results show that the interplay between frictional
properties and the asperity size gives birth to three instability regimes
(local, extremal, and homogenized), each related to different nucleation
scenarios, and that the influence of heterogeneities at a scale far lower than
the nucleation length can be averaged.
