Second-order Small-slope Approximation Research Articles

On the high-frequency limit of the second-order small-slope approximation

Small-slope approximation (SSA) is a scattering theory that is supposed to unify both the small-perturbation model and the Kirchhoff approximation (KA). We study and compute the second-order small-slope approximation (SSA2) in a high-frequency approximation (SSA2-hf) that makes it proportional to the first-order term, with a roughness-independent factor. For the 3D electromagnetic problem we show analytically that SSA2-hf actually meets KA in the case of perfectly conducting surfaces. This no longer holds in the dielectric case but we give numerical evidence that the two methods remain extremely close to each other for moderate scattering angles. We discuss the potential applications of SSA2-hf and give some 2D numerical comparison with rigorous computations.

On bistatic sea surface scattering: Field measurements and modeling

The bistatic scattering cross section of the sea surface, σ, is studied, along with a model for σ and its comparison with field data. The data are horizontal spatial coherence and ensemble-averaged intensity, which represent integral measures of sea surface bistatic scattering, and the model for σ is used to generate these same properties for comparison with the field data. The data are from an experiment conducted in shallow waters off southern Florida, using a sound frequency of 30 kHz. Directional wave measurements were made with a wave buoy positioned within 100 m of the acoustic measurements, with the environment characterized by rms wave heights of O(10) cm and wind speeds of 1–4 m/s. In the model σ is divided into two components: σr associated with scattering from the rough, air/sea interface, and σb associated with scattering from near-surface bubbles. The second-order small slope approximation is used to compute σr, which is a much improved approach over the traditionally used composite roughness model. The primary advantage in the small slope approximation was the resulting smooth behavior in σr over a broad range of scattering angles. Directional wave data obtained by the wave buoy were converted to an estimate of the 2-D spatial correlation function of sea surface roughness, C(ξ,final_sigma), for use in the scattering calculations. An analysis of the effective correlation properties of C(ξ,final_sigma) suggested that an isotropic correlation function C(ρ), based on the directionally averaged wave-number spectrum, would be equally effective in the scattering calculations. Model-data agreement was quite satisfactory, regardless of whether C(ξ,final_sigma) or C(ρ) was used in the scattering calculations.

The small slope approximation reflection coefficient for scattering from a "Pierson-Moskowitz" sea surface

First- and second-order reflection coefficients are presented for the small slope approximation. The first-order reflection coefficient is identical to the Kirchhoff, or physical optics, result, and the second-order reflection coefficient reduces to those of perturbation theory and the Kirchhoff approximation in the appropriate limits. Numerical results are obtained for acoustic or TE-polarized electromagnetic scattering from one-dimensional, Pierson-Moskowitz sea surfaces at low grazing angles. Comparison with exact integral equation results shows that the second-order small slope approximation is extremely accurate and better than both the perturbation and Kirchhoff methods. >