Recent experimental results (F. E. Boyle and N. P. Chotiros, J. Acoust Soc. Am. 91, 2615-2619, 1992; N. P. Chotiros, J. Acoust Soc. Am. 97, 199-214, 1995) reveal acoustic penetration from water into sandy sediments at grazing angles below the compressional critical angle in relation to the mean surface. These authors interpret their results to indicate the excitation of a Biot slow wave in the sediment. Another explanation is considered here. Modeling the ocean as a homogenous fluid, and the sediment as a lossy homogenous fluid, computer simulations of these experiments based on analytical derivations in this work show that roughness of the water-sediment interface causes propagation of acoustical energy from water into the sediment at grazing angles below the compressional critical grazing angle; these simulations indicate that their experimental results can be explained in terms of diffraction of an ordinary longitudinal wave. These simulations use an analytical expression for the time-dependent mean square incoherent field scattered through (and from) a rough 2-D fluid-fluid interface that is derived in terms of the bistatic scattering cross section per unit area per unit solid area (differential cross section) of the rough interface. First-order perturbation theory is used to derive an expression for the differential cross section. The coherent field is calculated using the flat-surface result (zero-order perturbation theory) and compared to the coherent component of the second-order perturbation theory result. Effects of sound-speed gradients on the field scattered from the rough water-sediment interface are also shown using the first-order perturbation derivations.
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