An empirical study of instability and improvement of absorbing boundary conditions for the elastic wave equation

Abstract

One of the persistent problems with numerical solutions to the elastic wave equation is the finite size of the numerical grid. As with a physical body, the grid boundaries will reflect incident energy. If not eliminated or reduced substantially, these reflections will invade the grid interior and interfere with the desired solution. One method for eliminating reflections is creating a large and/or expanding grid. This method may be impractical since it can be quite costly in both computer time and memory. Another method is making the grid boundary “transparent” to outgoing energy. This method is ideally done by designing absorbing or nonreflecting boundaries which are mathematically equivalent to a one‐way, or outgoing, elastic wave equation only. In practice, an outgoing elastic wave equation is an approximation since the wave equation is not generally separable into outgoing and incoming parts. Two absorbing boundary condition approximations commonly used are those from Reynolds (Reynolds, 1978) and Clayton and Engquist, (Clayton and Engquist, 1977).