The intensity of the field generated by a point source and reflected from a rough surface

This paper studies the intensity of the acoustic field generated by a point source above a rough surface with the Dirichlet or Neumann boundary conditions. The derived equations are valid for arbitrary distances between the source, receiver and rough surface, including the case when these distances are smaller than the correlation radius of the surface roughness. It is believed that the proposed method is an improvement of the more conventional approach, which is based on integration over individual areas of the rough surface and that is valid when the source, receiver, and surface are at large distances from each other. The main limitation in deriving the expressions for the acoustic field intensity is the condition that the mutual shadowing of the surface points is small, which is close to the small slope approximation for the rough surface profile. The derivation includes the limiting cases which lead to the traditional small perturbation method and Kirchhoff approximation.