Local absorbing boundary conditions for the elastic wave equation

We compare and analyze absorbing boundary conditions for the elastic wave equations. We concentrate on the first order extensions to Clayton–Engquist and show the relationship of the Lysmer–Kuhlemeyer ABC to these generalizations. We derive conditions for the reflection coefficient to have the same accuracy for near normal waves as in the acoustic wave case. Extensions to the first order system, spherical coordinates, higher order boundary conditions and frequency domain are derived. We extend Stacey's absorbing boundary condition (ABC) to all six sides of a cubic domain, and show that Stacey's ABC provide good numerical results.