Radiation Boundary Conditions for Elastic Wave Propagation

In this paper, a class of radiation boundary conditions for two-and three-dimensional elastic wave propagation is developed. The boundary conditions are based on compositions of simple first-order operators. Some recent empirical investigations have suggested that certain earlier radiation boundary conditions may be unstable if the ratio of P-wave velocity to S-wave velocity is sufficiently large. The boundary conditions developed in the present paper are stable for all values of the velocity ratio. The boundary operators used here are defined by relatively simple formulas that apply without modification to problems in both two and three dimensions. Given an arbitrary angle of incidence, some parameters in the boundary conditions can be adjusted to make the conditions perfectly absorbing for P- waves and/or S-waves traveling at that angle of incidence to the boundary.