Experiments from several shallow water areas are summarized and coherent sound transmission results, wavenumber spectra, are compared to range dependent calculations that use oceanographic and geophysical characteristics from measurements and archives as bounded inputs to the propagation codes. In general excellent agreement was obtained between the measured and calculated results for both narrow- and broad- band transmissions between 50 Hz and 1 kHz to ranges of 40 km. A relative signal gain, rsg, method for the estimation of horizontal coherence length was applied to measured rsg results and yielded coherence lengths on the order of 30 λ @ 400 Hz at distances of 40 km. Perturbation theory was applied to the shallow water waveguide under the condition of adiabatic normal modes and expressions were derived for the phase structure function that was simplified by the use of Gaussian correlation functions. These analytical results with estimates of the variances of the environmental variables permitted the estimation of the coherence function and the rsg. The calculated coherence function and rsg were found to be consistent with measured rsg and replica correlation results. The fluctuations in the oceanic water volume were found to be the dominant factor in the loss of coherence.
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