Kay theory for pre-stressed media

Because of the similarity between the equations of motion governing infinitesimal vibration due to a small perturbing force superimposed on an already existing state of finite stress and the equations of linear anisotropic elasticity, methods of analysis used in one may be extended to the second. In particular, in this paper, the technique of ray expansions is considered. .Methods for calculation of rays and amplitude coefficients of the ray series are given. A seismic ray is described by a system of ordinary differential equations of first order which can be solved by standard numerical techniques. Another system of ordinary differential equations is introduced to compute amplitude coefficients