A vast literature already existed on sea surface and seabed scattering as of 1982, and over the intervening thirty years that literature has steadily increased in size. We focus here on just four developments that we believe have been of particular importance over the past thirty years. First, numerical methods have been developed for obtaining rigorous solutions to certain simplified scattering problems, and this has led to a better understanding of the accuracy of rough surface scattering theory, and in particular of the two classical approximations: the Kirchhoff approximation and small-height perturbation theory. Second, a more general scattering theory approximation, the small-slope approximation, has been obtained which reduces smoothly to the two classical approximations in the appropriate limits, a long soughtafter goal. Third, modeling seabed scattering has been significantly improved by taking into account a more realistic description of the seabed, including, for example, volume heterogeneity, layering, and shear. Finally, methods are presently being developed for modeling reverberation that account for sea surface forward scattering, which can have important effects on the reverberation level.

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