A comparison of perturbation theory and the small-slope approximation for acoustic scattering from a rough interface for a Biot medium

In this paper, the lowest order small-slope approximation (SSA) scattering cross section for Biot theory is derived. Numerical results are obtained for both backscattering and bistatic scattering using a modified power law spectrum, and these results are compared with those of lowest order perturbation theory (PT). Frequencies ranging from 100 Hz to 3 kHz are used for surfaces with RMS heights h of 0.1 and 1 m and a correlation length l of 10 m. The angle of incidence for the bistatic results is limited to 45°. It is found that for the smaller surface height roughness (h = 0.1 m), the SSA and PT give the same results for frequencies up to almost 1 kHz for both backscattering and bistatic scattering. For h = 1 m, the SSA and PT backscatter results are in good agreement at all frequencies for incident grazing angles up to approximately 45°. For the bistatic results, the SSA and PT results agree only at low grazing angles of scatter. In the specular region, the results differ significantly.