Scattering of an acoustic axially symmetric surface wave propagating to the vertex of a right-circular impedance cone

The work deals with the scattering of an incident surface wave propagating to the vertex of a circular impedance cone. Diffraction of the incident surface wave by the vertex gives rise to the reflected surface wave as well to the spherical wave from the vertex of the cone in the far-field approximation. The study is based on the Sommerfeld integrals, Fourier transform and on the incomplete separation of the spherical variables for the problem at hand. The analytic formulas for the reflected surface wave and for the diffraction coefficient of the spherical wave are obtained.