Entropy of acoustical beams in a random ocean

Scattering by small scale ocean processes like internal waves imposes the ultimate limitations on large scale ocean acoustic remote sensing. Recent progress in utilizing ray methods to understand scattering processes in long range acoustic propagation suggest there is an exponential sensitivity to initial conditions and a rapid growth of acoustic field complexity with a scale of a few hundred kilometers; a result which casts some doubt on the effectiveness of long range acoustic remote sensing. However, as is well known in other fields of wave propagation, finite frequency effects can slow, suppress or mask this complexity. We have performed parabolic equation numerical simulations for acoustical beams which mimic a narrow bundle of ray paths and which traverse random realizations of internal wave sound speed perturbations obeying the Garrett-Munk internal wave spectrum. The variability of these beams as a function of range and beam angle are analyzed in terms of information theory using the Shannon entropy and in terms of the relative intensity variance or scintillation index. We find that the finite frequency beams do not increase in complexity exponentially and that very near the saturation range a constant non-maximal entropy is obtained. These results suggest that acoustic remote sensing is more robust than is implied by the ray scattering results.