The validity of the perturbation approximation for rough surface scattering using a Gaussian roughness spectrum

TLDR: In this article, the validity of low-order perturbation approximation for rough surface scattering is examined by comparison with exact results obtained by solving an integral equation and through comparison of low • order perturbations with higher • order predictions.

Abstract: The validity of the perturbation approximation for rough surface scattering is examined (1) by comparison with exact results obtained by solving an integral equation and (2) through comparison of low‐order perturbation predictions with higher‐order predictions. The pressure release boundary condition is assumed, and the field quantity calculated is the bistatic scattering cross section. A Gaussian roughness spectrum is used, and the surfaces have height variations in only one direction. It is found, in general, that the condition kh≪1 (k is the acoustic wavenumber, h is the rms surface height) is insufficient to guarantee the accuracy of first‐order (or higher‐order) perturbation theory. When the surface correlation length l becomes too large or too small with h held fixed, higher‐order perturbation terms can make larger contributions to the scattering cross section than lower‐order terms. An explanation for this result is given. The regions of validity for low‐order perturbation theory are also given. Th...