An eigenvalue decomposition method to construct absorbing boundary conditions for acoustic and elastic wave equations

Abstract

A new approach to constructing absorbing boundary conditions (ABCs) for acoustic and elastic wave equations (in transversely isotropic media) is presented. The eigenvalue decomposition method (ED method) is used to calculate the eigenvalues and eigenvectors of the coefficient matrix in the wave equations, which can be used to construct the outgoing and incoming waves along any direction. For different boundary regions, the outgoing waves are kept unchanged, but the amplitudes of the incoming waves are kept constant in time. As well as ABCs at the four lines in 2D and six surfaces in 3D, the ABCs at the four corners in 2D and eight corners and 12 lines in 3D are constructed. The vibration curves show that these conditions have nearly the same effect as perfectly matched layer (PML) absorbing boundary conditions, and are much better than Clayton-Enquist (CE) absorbing boundary conditions. © 2005 Nanjing Institute of Geophysical Prospecting.