Investigation on the key parameters of slip weakening law in dynamic rupture simulations

How the crack propagates on the fault plane when an earthquake happens is a fundamental problem in earthquake studies. To understand the dynamics of a spontaneously propagating crack various constitutive laws for friction, e.g., slip weakening, slip rate weakening, effective temperature and rate-and-state laws, which define the relationship between the instantaneous stress and slip (or slip rate) on the fault have been widely used in various rupture simulations. One crucial aspect of the variety of rupture models is to to quantify how the main parameters characterizing a certain law affect the rupture process. We chose the slip weakening law and then massively computed a large suite of dynamic rupture simulations on a rectangular fault embedded in 3-D isotropic homogeneous medium. The simulations included hundreds of different sets of parameters varying Dc, the critical slip weakening distance and Te the initial stress. All are spatially constant except in a rectangular asperity, where the rupture is triggered. With the same parameter set we used several different discretizations to avoid the numerical effects. Computationally we use the boundary integral method. We have also given definitions of rupture status: non-growth rupture, growth rupture, subshear rupture and supershear rupture. With all of the simulations we construct a phase-diagram on which different rupture states locate in different parameter-set zones (phase boundary lines with errors less than 0.1%) We find that (1) In the areas with smaller Dc, phase boundary lines seems to fit the ones Madariaga (1998) predicted using non- dimensionalized parameter κ, but not for the whole phase line. (2) When Dc reaches a particular size, none of the ruptures will propagate regardless of the value of the initial stress on the fault. (3) Some transitional states may occur where a rupture propagates only 2-4 times the initial asperity size and then stops spontaneously.