A boundary integral equation method is described for the prediction of the acoustic field due to a point source in a homogeneous quiescent atmosphere, above a homogeneous rigid porous half-space containing a smooth rigid obstacle. The problem is initially stated as a boundary value problem and is subsequently reformulated as a boundary integral equation via Green's second theorem. It is shown that the boundary value problem and the boundary integral equation are equivalent. The numerical solution of the boundary integral equation by a simple boundary element method is then described. The solution method, which reduces to a system of linear equations with a block circulant coefficient matrix, is applicable to any obstacle which is axisymmetric about a vertical axis. The numerical solution shows good agreement with a known analytical solution—that of scattering of an incident plane wave by a rigid sphere in an infinite homogeneous medium, and with solutions for scattering due to a rigidly backed layer.
