Dynamical model of faulting in two dimensions and self-healing of large fractures

We describe a model for the simulation of extended two-dimensional in-plane dynamical ruptures and for the rapid calculation of statistical properties of repeated model-seismicity events. The discretization involves first- and second-nearest neighbors and is isotropic in both compression and shear properties. All rupture events obey a fracture criterion in the appropriate coordinate frame and numerical oscillations in slip velocity at crack tips due to discretization are minimized. The rupture velocities of fractures, in cases of homogeneous stress drop equal to the strength, are the supershear P-wave velocity in the direction of the prestress and the S-wave velocity in the perpendicular direction. We use the model to study the growth and healing of individual faults to understand the formation of propagating slip pulses. We confirm two mechanisms for the generation of isolated rupture pulses that have been proposed, namely, (1) a decrease in the dynamical friction with accelerating slip and (2) the encounter of the growing crack with extended regions of large difference between the threshold fracture stress and the prestress. We describe a third mechanism which is that of a velocity-dependent friction that operates equally on both the phases of increasing and decreasing slip velocities and has a characteristic length scale. It is a proxy for energy loss by radiation in a three-dimensional medium. In the case of an elongated rectangular model fault with an upper free surface and lower rigid boundary, pulses develop due to the influence of stress waves reflected from the rigid bottom boundary. In general, the excess of strength over stress drop controls crack fracture speeds; if it is too large, the crack stops. Under homogeneous stress conditions, isolated slip pulses are controlled by the spatial distribution of heterogeneities and by the velocity-dependent friction parametrization.