Spontaneous growth and autonomous contraction of a two-dimensional earthquake fault

Abstract

We numerically study a model of an earthquake as a spontaneous rupture on a fault. We assume that a two-dimensional antiplane shear crack initiates at a point in an infinite, homogeneous and isotropic elastic medium and subsequently propagates with variable velocity under the influence of nonuniform stress drop on the crack and nonuniform cohesive resistance at the crack edges. To begin with, we analyze the dynamical rupture process immediately after nucleation. We determine the subsequent extension of each edge by solving an ordinary differential equation of the first order, as well as the dynamical stress in the regions between each edge and the nearest wave front. Application of this procedure to both edges of the crack in an alternating manner yields the complete history of extension of the crack. We use the critical stress-intensity fracture criterion to determine the conditions on propagation and arrest of the crack. To verify the accuracy and the stability of our numerical technique we compare it with some special cases in which analytical solutions are available. The comparison indicates that the numerical results are in good agreement with the analytical ones obtained previously by Knopoff and Chatterjee (1982) and Chatterjee and Knopoff (1983). We apply this technique to the computation of the dynamical extension of the crack for several representative cases. Among them are: 1. (1) uniform stress drop but nonuniform cohesion (a barrier model), 2. (2) nonuniform stress drop but uniform cohesion (an asperity model) and 3. (3) nonuniform stress drop and nonuniform cohesion (a combination of both the barrier and the asperity models). The numerical results indicate that the heterogeneities of both the stress drop and the cohesion are the main factors which control the growth, cessation and healing of the crack, and that the complexities in the seismic radiation are caused by the complex healing process as well as by the complex rupture propagation. In contrast to the asperity model, the barrier model is characterized by abrupt changes in the slope of the source-time function and the theoretical seismogram. The collision of the stress pulses from each pair of barriers is the potential source of the crack fission. In the general model, the fission process occurs in a complex sequence, and the effects of this process have to be taken into account in the interpretation of observations.