Matching Boundary Condition for Elastic Waves in Two Space Dimensions

ABSTRACT Based on Matching Boundary Conditions (MBCs) for the linear wave equation and Helmholtz decomposition, we design MBCs to treat elastic wave propagation in a two‐dimensional unbounded domain. MBCs are designed to effectively absorb waves traveling in specific directions. High‐order MBCs are derived from the product of MBC operators. Reflection coefficients are calculated, rigorously proving that P‐ and S‐waves have the same form of reflection coefficients as those for the wave equation, and no wave conversion occurs. The MBCs are implemented using a staggered grid, under finite difference semi‐discretization and the velocity Verlet scheme for time integration. Numerical experiments are conducted to demonstrate the performance of the scheme.