A condition for super-shear rupture propagation in a heterogeneous stress field

We have used numerical simulations with the boundary integral equation method to investigate a mechanism to excite super-shear rupture velocities in a homogeneous stress field including an asperity of increased initial stress. When the rupture, with the slip-weakening distance selected to generate sub-Rayleigh speed, encounters the asperity it either accelerates to super-shear velocities or maintains the sub-Rayleigh speed, dependent on the size and amplitude of the asperity. Three classes of rupture propagation are identified: the velocity (a) for the most narrow asperities increases slowly towards the Rayleigh wave speed, (b) for intermediate width of the asperities jumps to super-shear values for a short distance but then decreases to sub-Rayleigh wave speeds, and (c) for the widest asperities jumps to supershear values and pertains to values between the S- and P-wave velocities. The transitions between the three classes of rupture propagation are characterized by very narrow (critical) ranges of rupture resistance. If the size of the initial asperity is smaller than critical, it becomes difficult for rupture to propagate with super-shear velocities even if the initial stress level is high. Our results suggest that stress variation along the rupture path helps homogenize the rupture velocity and propagate with sub-Rayleigh wave speeds.