A full wave solution for propagation in horizontally stratified elastic media with range variation

The purpose of this note is to outline a numerically efficient procedure for finding complete solutions to wave propagation problems in elastic media whose parameters (density, sound speed, etc.) depend on depth only, but where one of the interfaces (water/ air, or deep water/solid ocean bottom) is allowed to vary (under some restrictions) with range. This procedure is a straight forward modification to the method proposed in [1],[2] (which allows no range variation at all); the latter is summarized in the next section, and the former is explained in the following one. In the last section, this procedure is extended to allow the rough interface to move (again, under some restrictions) with time, thus allowing a rapid complete solution of the wave equation.