THEORETICAL-STUDY OF NONLINEAR ELASTIC-WAVE PROPAGATION

A theoretical study of the propagation of a plane wave in a material w ith nonlinear response is presented. We start with the wave equation f or an isotropic, homogeneous, elastic solid with cubic anharmonicity i n 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 f ield at distance x from the source. We examine the influence of propag ation distance, source frequency spectrum, source displacement amplitu de, attenuation, and nonlinear coefficient on the spectrum of a propag ating wave. The displacement field for various source functions is cal culated using parameters typical of rocks.