Rough surface backscatter and statistics via extended parabolic integral equation

TL;DR

This paper extends the parabolic integral equation method to include backscatter from rough surfaces by applying a novel splitting technique, enabling efficient numerical evaluation and analytical backscatter corrections.

Contribution

It introduces a new approach to incorporate backscatter into the parabolic integral equation method using left-right splitting and series of Volterra operators.

Findings

Efficient numerical evaluation of backscatter from rough surfaces.

Analytical expressions for mean field and autocorrelation with backscatter corrections.

Extension of parabolic integral equation method to include backscatter effects.

Abstract

This paper extends the parabolic integral equation method, which is very effective for forward scattering from rough surfaces, to include backscatter. This is done by applying left-right splitting to a modified two-way governing integral operator, to express the solution as a series of Volterra operators; this series describes successively higher-order surface interactions between forward and backward going components, and allows highly efficient numerical evaluation. This and equivalent methods such as ordered multiple interactions have been developed for the full Helmholtz integral equations, but not previously applied to the parabolic Green's function. In addition, the form of this Green's function allows the mean field and autocorrelation to be found analytically to second order in surface height. These may be regarded as backscatter corrections to the standard parabolic integral equation method.