A New Unified Theory for Scattering of A Bounded Acoustic Beam from A Liquid-solid interface Near the Rayleigh Angle

For scattering of a bounded acoustic beam from a liquid-solid interface, the principal difficulty comes from the treatment of tie plane wave reflection coefficient. In the present paper, following the Singularity Expansion Method, we expand the reflection coifficient into the sum of an analytic function (constant 1) and the principal part of the Laurent expansion in a neighborhood of the Rayleigh pole. The scattered field is now evaluated by a double integral in the wave number and interface planes. The constant 1 produces a rigid boundary geometrical reflected beam, and the expansions at the Rayleigh poles yield the leaky Rayleigh waves. It is particularly proved that the residues of the poles are nearly proportional to the imaginary parts of the poles for most liquid-solid interfaces. Therefore, the complex pole may determine the whole behavior of the leaky Rayleigh wave, including the excitation and reradiation efficiencies. For the backscattered field, since the negative Rayleigh pole plays a major role, a backward leaky Rayleigh wave will appear naturally.