Transport theoretic boundary conditions are derived for acoustic wave reflection and transmission at a rough interface with small random fluctuations. The Wigner distribution is used to go from waves to energy transport in the high frequency limit, and the Born expansion is used to calculate the effect of the random rough surface. The smoothing method is also used to remove the grazing angle singularity due to the Born approximation. The results are presented in a form that is convenient both for theoretical analysis and for numerical computations.
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Bal et al. (1999) studied this question.