
doi: 10.1121/1.3248705
Strictly reverberation consists of all the back-scattered contributions from many locations that arrive at one absolute time regardless of their respective travel times. However, for calculation purposes, particularly at long range, it is often more convenient to assume the scatterers to be close together at a single location with corresponding propagation loss for the outward and return paths. It would be useful to know whether the latter approximation is a safe one or not. An analytical method of calculating reverberation either at a fixed time or at a fixed range will be presented. The ratio of these quantities is found to depend on the (vertical) angular spread of the contributing paths. In isovelocity water at long ranges, mode-stripping reduces the angular spread to the point where fixed-range reverberation is indistinguishable from fixed-time. The greatest effect is at shorter ranges where there is no significant mode-stripping, and the ratio rises to roughly 1 plus 0.855 times the square of the critical angle (in radians). Thus the effect is typically less than 1 dB at any range.
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