A method due to Urusovskii [Sov. Phys. Acoust. 5, 362–369 (1959)] is applied to predict the field scattered by rough pressure release surfaces. Comparison of the predictions of this theory for scattering from a sinusoidal surface shows that his method yields results closer to an exact solution than do other approximations. When applied to predict the coherent field scattered by a random rough surface, the predictions agree well with those of the Kirchhoff approximation provided that the horizontal wave-number component of the incident field is much greater than the wave numbers at which the spectral decomposition of the surface irregularities attains its maximum value. For high-frequency scatter near the forward direction, Urusovskii’s theory yields a new result that provides a significant improvement to the Kirchhoff approximation.
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Suzanne T. McDaniel (1994) studied this question.