Elastic and Electromagnetic Wave Propagation in Horizontally Layered Media

Abstract

The mathematical similarity between electromagnetic and elastic wave propagation in layered media is well known (1, 2,3). By applying a combination of Fourier, Laplace and Bessel transforms to the different partial differential equations, we obtain a system of 2n linear ordinary differential equations where the coefficients are functions of the depth coordinate and the transformed time and horizontal space coordinates. The 2n × 2n coefficient matrix may be partitioned into 4 nxn submatrices. By a proper choice of variables the two diagonal submatrices are zero, and the off-diagonal submatrices are symmetric. This technique has been used by Richards (4) for plane P-SV waves. A similar equation has been considered by Reid (5) for an electromagnetic transmission line problem. By considering this general type of equation a number of results are derived. The wavefield is decomposed into upgoing and downgoing waves by an eigenvalue decomposition, which is much simplified compared with the general case of a full 2n × 2n coefficient matrix. The propagator matrix (6) for a stack of inhomogeneous layers is computed by a simplified method. For a stack of homogeneous layers we obtain recursive equations for the computation of the submatrices of the propagator matrix.