Computation of Long-Range Propagation Losses in a Duct,
LITTLE (ARTHUR D) INC CAMBRIDGE MASS
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An acoustic ray shows the direction in which acoustic energy flows, but not the intensity of the resulting field. The conventional way to estimate intensity is to infer the cross-section of a narrow bundle of rays from the difference in the trajectories of a closely spaced pair of rays. Where the distance is long, the detailed sound velocity structure is uncertain, and multi-path propagation exists, there are both practical and theoretical objections to this procedure. As an alternative, one can seek the average intensity at a given depth over a range interval about a nominal range. The resulting expression involves no differencing of ray trajectory parameters, only summing, which is computationally preferable. To a first approximation, the resulting expression depends only on the velocity profiles at the source and receiver and the distance between them, but not on the detailed velocity structure between. This conceptually simple space average can be shown to be equivalent to the average of expected value resulting, by much more profound arguments, from uncertainty or from spatial or temporal fluctuations in the sound velocity structure.