Validity of first-order perturbation theory for scattering from one-dimensional and two-dimensional rough surfaces described by power-law spectra

Abstract

First-order perturbation theory is a widely used model for estimating the backscatter of acoustic waves incident on a rough surface. The validity of perturbation theory for one-dimensional surfaces described by Gaussian spectra is well established. However, little has been done to confirm its range of validity when expanded to two-dimensional surfaces. Furthermore, the range of validity for surfaces described by power-law spectra has not been fully explored. This work seeks to benchmark first-order perturbation theory against a finite element method solution for scattering from one-dimensional and two-dimensional rough pressure-release surfaces described by power-law spectra. The relationship between ranges of validity of 1D and 2D surfaces will be considered. [Work sponsored by the Office of Naval Research, Ocean Acoustics.]