Abstract
A mathematical model is developed to describe sound propagation into the shadow zone below an isothermal layer by means of scattering from a rough surface. The model incorporates formula that describes the propagation losses within the duct to points from which the sound is scattered. The Beckmann theory is then used to estimate the scattered intensities at the various angles that correspond to ray paths leading from the surface to a point in the shadow zone. Reasonable agreement is found between the theoretical results and observations made at 5 kHz in a moderately rough sea. The theory indicates that most of the scattering occurs in a narrow region of the surface between 200 and 1200 yd from the point of observation in the shadow zone.
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