APPLICATION OF THE OPERATOR EXPANSION METHOD TO SCATTERING FROM ONE-DIMENSIONAL MODERATELY ROUGH DIRICHLET RANDOM SURFACES

A new method for computing wave scattering from rough surfaces, called the operator expansion (OE) method, has been proposed by D. M. Milder [J. Acoust. Soc. Am. 89(2), 529-541 (1991)]. In this paper, the OE method is examined in its application to acoustic scattering from one-dimensional randomly rough surfaces with Gaussian and Pierson-Moskowitz roughness spectra satisfying the pressure release (Dirichlet) boundary condition. The operator expansion solution, which is expressed in a systematic series, is found to converge rapidly and monotonically for moderately rough surfaces, that is, for surfaces whose slope-height roughness parameter khs, given by the product of acoustic wave number k, rms surface height h, and rms surface slope s, is less than about 0.25. Through comparison with a numerically exact integral equation solution, the OE method is found to be accurate over a wide range of incident and scattering angles. The method is currently used in a Monte Carlo computation of the scattering cross section, in which scattering is computed from one surface realization at a time and then averaged over 50 realizations. Nevertheless, its efficiency and accuracy in one-dimensional tests suggest that the operator expansion would be a useful method for computing scattering from two-dimensional surfaces in roughness regimes encountered in scattering of low-frequency sound from the ocean surface.