Forward propagation in a half-space with an irregular boundary

The parabolic wave equation (PWE) has been used extensively for modeling the propagation of narrow beams in weakly inhomogeneous random media. Corrections have been developed to accommodate wider scattering angles and boundaries have been introduced. Nonetheless, the formalism remains approximate and irregular surfaces with general boundary conditions present difficulties that have yet to be overcome. This paper presents an alternative approach to the entire class of propagation problems that strictly involve forward propagation. Forward-backward iteration has been shown to be a powerful procedure for computing the source functions that support propagation over irregular boundaries at low grazing angles. We show that the source functions for any unidirectional sweep can be computed by using a marching solution. This is not only more efficient than the single-sweep computation, but it facilitates accommodation of inhomogeneities in the propagation media. An exact equation for forward propagation in unbounded inhomogeneous media is used to derive a correction term that is applied at each forward-marching step. Results that combine ducting atmospheres and rough-surface scattering effects are presented for both the Dirichlet and Neumann boundary conditions.