A finite‐difference treatment of interface conditions for the parabolic wave equation: The irregular interface

A finite‐difference solution to the parabolic wave equation is extended to treat an irregular interface. Interface conditions are developed to preserve continuity of pressure and continuity of the normal component of particle velocity at the boundary between media having different sound speeds and densities. A complete mathematical treatment for the case of an irregular interface is presented. To demonstrate the method, numerical results are obtained for sound propagation from deep to shallow water.