Pj. Kaczkowski et Ei. Thorsos, APPLICATION OF THE OPERATOR EXPANSION METHOD TO SCATTERING FROM ONE-DIMENSIONAL MODERATELY ROUGH DIRICHLET RANDOM SURFACES, The Journal of the Acoustical Society of America, 96(2), 1994, pp. 957-972
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 me
thod is examined in its application to acoustic scattering from one-di
mensional 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 s
ystematic series, is found to converge rapidly and monotonically for m
oderately rough surfaces, that is, for surfaces whose slope-height rou
ghness 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 soluti
on, the OE method is found to be accurate over a wide range of inciden
t and scattering angles. The method is currently used in a Monte Carlo
computation of the scattering cross section, in which scattering is c
omputed from one surface realization at a time and then averaged over
50 realizations. Nevertheless, its efficiency and accuracy in one-dime
nsional tests suggest that the operator expansion would be a useful me
thod for computing scattering from two-dimensional surfaces in roughne
ss regimes encountered in scattering of low-frequency sound from the o
cean surface.