A ray model is presented for downwind propagation of sound in a layered atmosphere, with a logarithmic or a power profile of the sound speed. The model employs a new method to compute ray paths, which takes advantage of the fact that ray paths are ordered in groups of four. The paths are obtained from an iterative solution of an integral equation. This solution requires a very small computation time, compared with computation times of numerical ray models and wave models. Ground reflections are taken into account by either the plane wave reflection coefficient or the spherical wave reflection coefficient (a pseudoreflection coefficient for a point source above a ground surface). At high frequency both coefficients yield good agreement with numerical solutions of the Helmholtz equation. An empirical reflection coefficient is introduced to obtain good agreement at low frequency. The ray model is used to compute effects of atmospheric turbulence on the received sound spectrum. It is found that these effects are rather small for downwind sound propagation. The ray model is used further to compute the flow of acoustical energy along the different rays through the atmosphere. It is found that much of the energy flows along the highest rays, in particular at high frequency.
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Erik M. Salomons (1994) studied this question.