Parabolic equation method approximation for high-frequency diffraction by an elongated body

The problem of high-frequency diffraction by a strongly elongated body is considered. The surface is supposed to be well approximated by a spheroidal surface. The asymptotic approximation for the induced currents is constructed by means of the parabolic equation method under the assumption that the wave-size of the body in the longitudinal direction is of the order of the square of its wave-size in transverse direction. We analyze the formulas from the point of view of waves attenuation and find that the attenuation is only logarithmically large with respect to the asymptotic parameter.