Propagation of Surface Waves at High Frequencies

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Abstract
An asymptotic theory is presented for the analysis of surface wave propagation at high frequencies. The theory is developed for scalar surface waves satisfying an impedance boundary condition on a surface, which may be curved and, whose impedance may be variable. A surface eikonal equation is derived for the phase of the surface wave field, and it is shown that the wave field propagates over the surface along the surface rays, which are the characteristics of the surface eikonal equation. The wave field in space is found by solving certain eikonal and transport equations with the aid of complex rays. The theory is then applied to several examples: axial waves on a circular cylinder, spherically symmetric waves on a sphere, waves on a circular cone with a variable impedance, and waves on the plane boundary of an inhomogeneous medium. In each case it is found that the asymptotic expansion of the exact solution agrees with the asymptotic solution.

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