Finite-difference treatment of a time-domain parabolic equation: Theory

Abstract

A time-domain parabolic wave equation is derived from the usual acoustic wave equation used to describe underwater propagation. Using well-known finite-difference approximations, equations describing the pressure field within layers are derived. Discontinuities of sound speed and density at layer interfaces are properly accounted for by requiring continuity of pressure and particle velocity. The resulting tridiagonal systems of equations can be solved by standard methods.