Surface Waves in a Laterally Varying Layered Structure

Sum17zur.y A kind of ray theory is developed for surface waves in a layered elastic medium in which there are gradual lateral variations in the thicknesses of the layers and in the elastic parameters characterizing each layer. An approximation equivalent to the JWKB approximation is used, and equations governing the slow variations in amplitude, frequency and wavenumber in a nearly uniform sinusoidal wavetrain are deduced. In the first approximation these equations are found to be those given by Whitham’s average Lagrangian method. An equation governing the slow variation in phase is also deduced. The solution of these equations by the method of characteristics gives ray-tracing equations and an amplitude equation similar to those given by standard ray theory for body waves. The analysis also leads to a straightforward method for finding the total energy flux and energy density of the waves without performing an integration over the depth co-ordinate.