Progression of spontaneous in-plane shear faults from sub-Rayleigh to compressional wave rupture speeds

Abstract

We investigate numerically the passage of spontaneous, dynamic in-plane shear ruptures from initiation to their final rupture speed, using very fine grids. By carrying out more than 120 simulations, we identify two different mechanisms controlling supershear transition. For relatively weaker faults, the rupture speed always passes smoothly and continuously through the range of speeds between the Rayleigh and shear wave speeds (the formerly considered forbidden zone of rupture speeds). This, however, occurs in a very short time, before the ruptures reach the compressional wave speed. The very short time spent in this range of speeds may explain why a jump over these speeds was seen in some earlier numerical and experimental studies and confirms that this speed range is an unstable range, as predicted analytically for steady state, singular cracks. On the other hand, for relatively stronger faults, we find that a daughter rupture is initiated by the main (mother) rupture, ahead of it. The mother rupture continues to propagate at sub-Rayleigh speed and eventually merges with the daughter rupture, whose speed jumps over the Rayleigh to shear wave speed range. We find that this daughter rupture is essentially a “pseudorupture,” in that the two sides of the fault are already separated, but the rupture has negligible slip and slip velocity. After the mother rupture merges with it, the slip, the slip velocity, and the rupture speed become dominated by those of the mother rupture. The results are independent of grid sizes and of methods used to nucleate the initial rupture.