Study of the Operator Expansion Method and its Application to Scattering fromRandomly Rough Dirichlet Surfaces

摘要

The Operator Expansion (OE) method, a new approximation introduced by Milder forcomputing wave scattering from rough surfaces, is applied to acoustic scattering from one-dimensional randomly rough pressure release (Dirichlet) surfaces. The accuracy of the OE series solution is evaluated through comparison with exact numerical results obtained by solution of an integral equation. Studies of scattering from moderately rough surfaces with a Gaussian spectrum indicate that the first order OE solution is accurate when either small perturbation theory or the Kirchhoff approximation is accurate. The first order OE solution is also accurate in some cases when neither classical method is valid. In this moderate roughness regime, the OE series converges rapidly over all scattering angles for a broad range of incident angles, and numerical studies indicate that rapid convergence is always associated with an accurate solution. As roughness is increased, the OE series solution converges less rapidly overall but remains accurate for a wide range of scattering regimes, including some cases just rough enough to support backscattering enhancement.