Interface scattering by poroelastic seafloors: First-order theory

Abstract

A perturbation model is developed for sound scattering by a poroelastic seafloor having roughness small compared to the acoustic wavelength. The sediment is assumed to be homogeneous and isotropic with wave propagation described by Biot’s equations. When applied to sandy sediments, the model predicts backscattering levels that are substantially lower than those of a fluid model having the same roughness, density, sound speed, and attenuation.

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

“…To facilitate comparison between this paper, the work of Williams et al [9], and previous papers on the SSA by Yang, Broschat, or Thorsos [12]- [16], the notation used in this paper follows that of Williams et al with the exception of the use of the -matrix and the use of and for the surface profile and its Fourier transform, respectively.…”

“…The zeroth-and first-order perturbation terms for the -matrix obtained by Williams et al are [9] (6) (7) where the final subscript 1 on the right-hand sides of these two equations indicates the first term of a 5 1 column vector. This term represents scattering into the upper half space, while the remaining four terms of the vector represent scattering into the Biot medium.…”

“…The -matrix can be expanded in a perturbation series in powers of where is the incident wavenumber. Williams et al used PT to obtain the first two series terms for the scattering amplitude which is directly related to the -matrix by [9] (5)…”

“…Williams et al [9] derived perturbation results based on Biot theory for scattering from randomly rough surfaces and obtained numerical results for a power law spectrum.…”

“…In addition to the compressional and shear waves occurring in an elastic solid, Biot theory predicts a third, or slow wave, in the sediment. The Biot model has been the subject of a number of studies [1]- [9], several of which concern scattering from an interface between a fluid and a Biot medium. Stoll and Kan [5] presented a comprehensive study on wave reflection in which they treated the ocean bottom as a flat interface between a fluid and Biot medium.…”