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

Abstract

Abstract-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 of 0.1 and 1 m and a correlation length 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 ( m), the SSA and PT give the same results for frequencies up to almost 1 kHz for both backscattering and bistatic scattering. For 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.

A scaled tank experiment for layered stochastic rough interface scattering reflection coefficient

“…Robert [3] improved the component description of the seafloor scattering interface and was superior to the perturbation theory. Yang [4] improved the perturbation method and small-slope approximation to theoretically derive and study the wave scattering of layered structures with rough interfaces of any number of layers. It gave us the transfer model between different layers.…”

Research on the acoustic scattering function and coherence properties from rough seafloor based on finite element model

“…Scattering problems are solved with theoretical models by making various assumptions in approximating the Helmholtz-Kirchhoff (HK) integral. The three well-known models are perturbation theory (PT) [1,2] in which the scattered pressure is expanded in a Taylor series; Kirchhoff approximation (KA) [3] in which the pressure and its normal derivative are calculated analytically from the incident pressure; and the hybrid model called small slope approximation (SSA), [4,5] which combines KA (most effective near the specular angle) and PT (more accurate away from specular). Some possible solutions from layered rough bottom scattering were further introduced into scattering.…”