Citation/Abstract

In this dissertation an elastic parabolic wave equation which approximates the linear elastic wave equations in a depth-dependent medium with fluid/solid interface is considered. A Galerkin Finite Element Method is developed for the discretization in the depth dimension with particular emphasis on the interface. A high-order implicit Runge-Kutta method is adapted to discretize the equations in the marching direction. A finite element function-space is developed which guarantees that the numerical solutions satisfy an extensive system of boundary and interface conditions. The resulting discrete linear system is shown to be non-singular.