A higher-order parabolic equation for wave propagation in an ocean overlying an elastic bottom

Abstract

A higher-order elastic parabolic equation (HEPE) is derived for wave propagation in depth-dependent and weakly range-dependent fluid/solid media. Galerkin’s method is used to discretize the depth operators in the HEPE within layers in which depth variations in the Lamé constants and density are continuous. Discontinuities in material properties are handled with centered differences for the interface conditions between layers. The numerical solution of the HEPE also involves the method of alternating directions and Crank–Nicolson integration. The HEPE is applied to underwater wave propagation problems involving a water column over an elastic bottom including a weakly range-dependent problem. The accuracy of the HEPE is demonstrated with benchmark calculations.