EXACT, NONREFLECTING BOUNDARY CONDITIONS FOR PARABOLIC-TYPE APPROXIMATIONS IN UNDERWATER ACOUSTICS

Abstract

In the different parabolic approximations to the reduced wave equation which model acoustic propagation in the ocean, the bottom is usually modeled as an interface and the domain of propagation includes an absorbing layer below the bottom interface. Thus the boundary value problem to be solved has zero boundary conditions at the surface as well as at the bottom boundary. In this paper exact boundary conditions are developed and numerically implemented along the physical bottom boundary if it is horizontal, otherwise, along an artificially placed horizontal computational boundary inside the bottom. These boundary conditions are nonlocal but integrable and can be incorporated in finite difference schemes for the parabolic equations.