AN INVESTIGATION OF THE SMALL SLOPE APPROXIMATION FOR SCATTERING FROMROUGH SURFACES .2. NUMERICAL-STUDIES

The small slope approximation (SSA) of Voronovich [Sov. Phys. JETP 62, 65-70 (1985)] is a promising method for modeling wave scattering from rough surfaces. The SSA T-matrix series, which can be interpreted as an expansion in a generalized surface slope, satisfies the appropriate reciprocity condition at each order and reduces to the standard pertu rbation series for small surface roughness. When the SSA T matrix is f ound to second order in generalized slope, it reduces to that of the K irchhoff approximation as the frequency is increased. In an earlier pa per [E. I. Thorsos and S. L. Broschat, J. Acoust. Soc. Am. 97, 2082-20 93 (1995)] the derivation of the SSA for surfaces subject to the Diric hlet boundary condition was examined in detail. In this paper the accu racy of the SSA for the Dirichlet problem is investigated through comp arison with exact results. Expressions for the first three terms of th e SSA incoherent bistatic scattering cross-section series are presente d, followed by numerical results for one-dimensional surfaces with Gau ssian statistics and a Gaussian roughness spectrum. Surfaces with rms slope angles up to 45 degrees are considered. It is found that, for th e numerous cases studied, the SSA results agree well with the exact re sults over a broad range of scattering angles. When the lowest-order r esults are inaccurate, successive addition of each higher-order term g enerally yields improvement. The range of scattering angles over which the SSA results are accurate depends on both the rms slope angle and the surface correlation length, as well as on the angle of incidence. A simple rule of thumb, however, is that for an incident angle of 45 d egrees, the highest-order SSA scattering cross section examined here i s accurate to within +/-1 dB from backscatter to a forward grazing ang le of 5 degrees for rms slope angles less than about 30 degrees. When the surface roughness is such that perturbation theory is accurate, th e SSA is accurate over the full range of scattering angles for small t o moderate slopes. (C) 1997 Acoustical Society of America.