Theoretical study of nonlinear elastic wave propagation

K. R. McCall
Earth and Environmental Sciences Division,
Los Alamos National Laboratory, Los Alamos, New Mexico


A theoretical study of the propagation of a plane wave in a material with nonlinear response is presented. We start with the wave equation for an isotropic, homogeneous, elastic solid with cubic anharmonicity in the moduli, accounting for attenuation by introducing complex linear and nonlinear moduli. A heirarchy of equations, ordered in powers of the displacement field, is developed. Using a Green function technique, we solve this set of equations systematically for the displacement field at distance x from the source. We examine the influence of propagation distance, source frequency spectrum, source displacement amplitude, attenuation, and nonlinear coefficient on the spectrum of a propagating wave. The displacement field for various source functions is calculated using parameters typical of rocks.