Acoustic double-reflection and transmission at a rough water–solid interface

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The double interaction of a wave with a rough interface is important in many acoustic measurements. An acoustic beam that reflects twice from a rough water–solid interface is considered. The second reflection from the rough surface is accomplished after the transducer’s buffer rod is used as an acoustic mirror. Changes in the spatially averaged specular reflection are related to the phenomenon of ‘‘enhanced backscatter,’’ previously observed for diffuse scattering. Simple, approximate closed-form analytic formulas for the strength of the specular double reflections are given as a function of frequency and the stand-off distance of the transducer. As one application of the analytic results, a method is proposed for determining the surface correlation function from the specular double reflections. The same physics (and appropriately modified analytic formulas) apply to doubly transmitted waves. Experimental measurements have been made of acoustic double reflection with a normally oriented broadband piezoelectric transducer near a rough water–solid interface. Measurements of (1) the wave reflected once from the rough interface, and (2) the wave reflected twice from the rough interface are given. The strength of the specular reflections was measured as a function of frequency and the transducer’s distance from the surface. It was observed that for large distances between the transducer and the rough surface and at low frequencies the scattering-induced loss of the doubly reflected wave was twice the loss of a singly reflected wave. However, for small distances between the transducer and the surface and at high frequencies the scattering-induced loss of the doubly reflected wave was four times the loss of a singly reflected wave.