Theoretical bottom-reflection losses are computed using a multilayered model of the ocean bottom in which the layers are considered to be absorbing liquid sediments with velocity gradients. The sound velocity of each sediment layer is assumed to be a nearly linear function of depth z. In this case, the acoustic field in the sediment layers can be represented as a linear combination of Airy functions. Comparisons of theoretical and measured bottom-reflection losses are made for three areas at frequencies from 0.1 to 1.6 kHz.
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Halcyon E. Morris (1970) studied this question.