This paper concerns the theory of acoustic reflection from a two-layered marine sediment, the upper layer of which consists of a fine-grained material (mud). The seawater above and basement below the layer are treated as homogeneous half-spaces. Within the mud layer, the density is taken to be constant, and three sound speed profiles are considered: uniform, linear, and inverse-square. The reflection coefficient exhibits a background component that is similar in all three cases, exhibiting only a weak sensitivity to the gradient of the profile, the frequency, and the depth of the layer. Additionally, the two profiles with a non-zero gradient, linear and inverse-square, exhibit a sequence across grazing angle of narrow spikes of total reflection. The angular distribution of this acoustic glint is highly sensitive to the frequency and depth of the layer, and mildly so to the gradient. As the gradient approaches zero, the glint vanishes and the reflection coefficient reduces identically to the form of a uniform sound speed profile. If it were detectable, the angular distribution of the glint, observed at several frequencies, could constitute a unique, sensitive set of "fingerprints," allowing the depth and sound speed gradient of the mud layer to be inferred.
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