Propagation of sound above a porous half-space

Abstract

An exact solution for the field due to a point source above a homogeneous and isotropic porous ground has been derived in terms of a single branch line integral and a pole residue. The expected properties of the porous ground lead to a less complex solution than that usual to geophysics or underwater acoustics. The method of steepest descents modified by subtraction of the pole enables the derivation of an approximate solution for an externally reacting boundary. The precise nature of the further approximations that follow the assumption of a locally reacting (or impedance) boundary is made explicit and the role of the surface wave pole is clarified. Finally, the existing solutions for a locally reacting boundary are compared, and with one exception they are shown to be identical.