Yet another elastic plane-wave, layer-matrix algorithm

Abstract

Many techniques have been developed to calculate the elastodynamic response of a stack of plane layers to a plane, spectral wave. These variations on the original propagator matrix method, commonly called the Haskell matrix method, aim to improve the efficiency and numerical stability of the algorithm. In this note, a simple variant, based on the Langer block-diagonal decomposition and second-order minors, is presented. The method is valid in isotropic media and anisotropic media with up-down symmetry on vertical planes of symmetry. The method is efficient and extremely simple to program code in Matlab° is presented for the isotropic case.