Shear Stress and b-value Fluctuations in a Hierarchical Rate-and-State Asperity Model

The magnitude frequency distribution of earthquakes is generally observed to depend on regional differential stress. The typical signature is a decrease of the b-value with increasing differential stress, corresponding to an increased probability of larger events. At the scale of a seismogenic fault, regional stress changes translate into shear and normal stress variations that both influence the nucleation process and the maximum extent of earthquake ruptures. Recent models have shown that normal stress changes cannot explain the observed b-value dependency, suggesting that b-value is primarily controlled by shear stress conditions on faults resulting from regional loading. The relationship between shear stress and b-value is however still not clear. Here, I investigate numerically the shear stress contribution on magnitude statistics by analyzing the b-value evolution with shear stress changes along a planar rate-and-state interface containing hierechical asperities and forced by slow tectonic loading under constant normal stress. The b-value is shown to decrease from 1.2 to 0.7 when shear stress increases by 1 MPa which is in agreement with fracture mechanics predictions. An approximate expression relating shear stress and b value is proposed and validated by the simulations, where the rate of b-value decrease with shear stress is provided by the inverse stress drop of typical earthquakes. The effect of shear stress along a planar hierarchical interface is therefore too strong to explain current observations.