A finite-difference treatment of interface conditions for the parabolic wave equation: The horizontal interface

Abstract

An elegant finite-difference technique applicable to the parabolic wave equation is developed to handle the boundary conditions at the interface between two media with different sound speeds and densities. Continuity of pressure and continuity of the normal component of particle velocity are preserved at the interface. The method is designed to be implicit and is unconditionally stable. A complete mathematical treatment for the case of a horizontal interface is described.