Handbook of mathematical tables: Charles D. Hodgeman, S. Selby, R. C. Weast and R. S. Shankland (Eds.): Blackwell Scientific Publications, Oxford, 1962. 579 pp. 70s

Abstract

This paper presents the reverberation matrix method for wave propagation in a multi-layered liquid. First the local scattering matrix and phase matrix for the reflected and refracted waves are derived at each interface of two layers in terms of local co-ordinates. The local matrices of all layers are then stacked to form global scattering and global phase matrices. The product of these two matrices together with a global permutation matrix gives rise to the reverberation matrix R which represents the propagation of steady state waves through the multi-layered medium. By expanding the matrix [I–R]−1into a power series and applying the inverse Fourier transform, we then derive the ray integrals for transient waves generated by a column of point sources and propagating through multi-reflected and refracted paths in the medium. The ray integrals so derived are particularly suitable for numerical calculations by applying the Cagniard method.