A useful test of discrete wavenumber modeling techniques is to model scattering from a sinusoidal free surface, while varying the maximum slope of the interface. Four discrete wavenumber methods, the Aki-Larner, the Waterman, the Waterman-Fourier, and the Campillo-Bouchon, are evaluated by testing for energy conservation and comparing displacement. Contrary to the claim of some authors (Varadan et al. 1987), the Waterman-Fourier shows no advantage over the Aki-Larner method for steep slopes. With the FFT to calculate the scattering matrix, the Waterman-Fourier method is as fast as Aki-Larner. The Campillo-Bouchon method is superior to the other methods in its ability to handle steep slopes, but it requires more wavenumber samples and is an order of magnitude slower.

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