Acoustic scattering by near-surface inhomogeneities in porous media.

Abstract

A theoretical and experimental investigation into the influence of nearsurface ihhomogeneities on the reflection of air-borne acoustic fields at a porous ground surface is conducted. Two theoretical approaches to the three-dimensional physical problem are presented, both being initially formulated as boundary value problems but with subsequent reformulation as boundary integral equations via Green’s Second Theorem. In the first near-surface inhomogeneity approach, a rigid inhomogeneity is embedded within the porous medium and the boundary value problem is formulated by assuming continuity of pressure and normal velocity at the ground surface, Sommerfeld’s radiation conditions, and the Neumann boundary condition on the surface of the inhomogeneity. In the second surface inhomogeneity approach, the boundary value problem is formulated by assuming an impedance boundary condition on the plane boundary. Any near-surface inhomogeneities are assumed to induce a local variation of surface impedance within the boundary, and analytical expressions for such induced variations in surface impedance are presented. The resultant integral equations require knowledge of the Green’s function for acoustic propagation in the presence of a plane boundary but in the absence of the inhomogeneity, and methods for calculating these Green’s functions are discussed.

The numerical solution of the boundary integral equations by a simple , boundary element method is described. The solution, which reduces to a system of linear equations with a block circulant coefficient matrix, is applicable to any inhomogeneity which is axisymmetric about a vertical axis; and for the near-surface inhomogeneity approach, the inhomogeneity must also be smooth. The numerical solutions have shown good agreement with classical results. The experimental measurements, presented in the form of spectra of the difference in sound pressure levels received at vertically separated points above surfaces of different media containing various scatterers, are in good agreement with the theoretical predictions.