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 1 of 10 m. The angle of incidence for the bistatic results is limited to 45degrees. 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 45degrees. 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.