Abstract

To invert the stationary Rayleigh-type vibrations we describe them in a matrix Sturm-Liouville form. Information on the elastic parameters and density as functions of depth is contained in the matrix potential of this problem. Understanding the potential structure is very important for an inversion. The paper presents a study of the Sturm-Liouville matrix equation which governs Rayleigh waves. The potential of the equation is proved to be, in general, a nonsymmetric matrix-function of a symmetric matrix depending on Lame's parameters. Consequently, the properties of Rayleigh waves are determined by the symmetric matrix and the boundary condition at the surface. We describe the structure of the matrix in terms of Lame's parameters, density, and frequency.