Careful developments of a number of approximate solutions of the problem of point source acoustic scattering from the ocean surface are presented. The regime of interest is the small-waveheight regime, where the rms waveheight of the ocean surface is small compared to the acoustic wavelength and the correlation length of the ocean surface. The approximate solutions fall into two categories: those derived by utilizing the Kirchhoff approximation and those based on a small-waveheight perturbation expansion. It is shown that within the small-waveheight regime the small-perturbation solution is superior to any solution based on the Kirchhoff approximation, the former being uniformly valid in the ratio of acoustic wavelength to surface-wave wavelength. In that portion of the small-waveheight regime where the ratio of acoustic wavelength to surface-wave wavelength is small, all approximate solutions are shown to be in agreement. Pitfalls which can and have occurred in the misapplication of the Kirchhoff approximation are pointed out.
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Labianca et al. (1977) studied this question.