Numerical modeling of waves incident on slip discontinuities

Interfaces in elastic media need not be in welded contact. For instance, fractures allow a small amount of slip to occur along their surfaces during the passage of a seismic wave. By slip, we mean that the displacement across the interface can be discontinuous. Reflection and transmission of plane waves in this case are frequency dependent. Previous numerical studies have chosen the finite-difference method to simulate slip discontinuities. The approach suffers from difficulties in incorporating boundary conditions into the strong form of the equations of motion. We show in detail that only a finite-element formulation of the σ-v (stress and velocity) equations can overcome these problems. Numerical examples illustrate the method for an SH-wave normally incident on a slip discontinuity and a P -wave incident at an angle.