Dynamics of a velocity strengthening fault region: Implications for slow earthquakes and postseismic slip

We consider the effect of permanent stress changes on a velocity strengthening rate-and-state fault, through numerical simulations and analytical results on 1D, 2D and 3D models. We show that slip transients can be triggered by perturbations of size roughly larger than Lb = Gdc/bσ, where G is the shear modulus, dc and b are respectively the characteristic slip distance and the coefficient of the evolution effect of rate-and-state friction, and σ is the effective normal stress. Perturbations that increase the Coulomb stress lead to the strongest transients, but creep bursts can also be triggered by perturbations that decrease the Coulomb stress. In the latter case peak slip velocity is attained long after the perturbation, so that it may be difficult in practice to identify their origin. The evolution of slip in a creep transient shares many features with the nucleation process of a rate-and-state weakening fault: slip initially localizes over a region of size not smaller than Lb, then accelerates transiently and finally expands as a quasi-static propagating crack. The characteristic size Lb implies a constraint on the grid resolution of numerical models, even on strengthening faults, that is more stringent than classical criteria. In the transition zone between the velocity weakening and strengthening regions, the peak slip velocity may be arbitrary large and may approach seismic slip velocities. Postseismic slip may represent the response of the creeping parts of the fault to a stress perturbation of large scale (comparable to the extent of the mainshock rupture) and high amplitude, while slow earthquakes may represent the response of the creeping zones to a more localized stress perturbation. Our results indicate that superficial afterslip, observed at usually seismogenic depths, is governed by a rate-strengthening rheology and is not likely to correspond to stable weakening zones. The predictions of the full rate-and-state framework reduce to a pure velocity strengthening law on a time-scale longer than the duration of the acceleration transient, only when the triggering perturbation extends over length scales much larger than Lb.