A system consisting of three bott0m-moored 12 000-Hz CW beacons, each separated in frequency by 40 Hz, and separated in space by about 8 k.m, has been used to track the motion of ship-suspended, ship-mounted, sonobuoy-deployed, and bottom-moored hydrophones to an accuracy of 4 cm. The system uses Doppler tracking of the beacon signals to provide real-time estimation of hydrophone velocity and displacement. Factors that m'•,ht compromise system performance, such as surface, bottom or forward volume scattering, ot multipath effects, were found to be negligible. Random phase fluctuations in beacon signals due to these phenomena are small compared with those due to hydrophone motion. Two tests of the system, near Eleuthera Island and near Bermuda, were made in September-October 1972. [This work was performed under U.S. Office of Naval Research Contract No. N00014-72-C-0205.].

Phase fluctuations of underwater sound (406 Hz) transmitted between a fixed source and deep free-drifting hydrophones have been obtained for transmission ranges of 200 km. Phase variations due to hydrophone drift are removed by a bottom-moored, CW tracking system that corrects for motion-induced phase variations of 0.06 rad or larger. Most of the energy traveled along refracted paths, eliminating much of the phase fluctuation due to bottom and surface scatter. Residual surface scatter effects are removed by narrow-band filtering. Maximum observed phase fluctuations are 15 cycles over 3 h on the deepest hydrophones (1500 m). The mean-square phase spectrum has a slope of --2 for frequencies between 0.4 and 40 cycles/h. The shallow hydrophone (300 m) data contain half the phase fluctuation of the deep hydrophones. Depth dependence of the fluctuations is attributed to internal gravity waves. Subject Classification: 30.20, 30.80.

Fluctuations in the amplitude and phase of low-frequency sound propagated to long range in the ocean are predicted. Phase fluctuations are attributed to the passage of acoustic radiation through the internal gravity-wave field; predictions are based on measured and modeled internal wave spectra. Ray theory is used to determine phase and amplitude variations as a function of time, space, and acoustic frequency. It is shown and experimentally verified that mean-square phase fluctuations are depth dependent.Subject Classification: 30.20. A b E(ot, w•.) ß g(z), M no, R,T S acoustic signed amplitude internal-wave stratification depth sound velocity internal-wave energy density internal-wave displacement, acoustic thickness, and phase spectral densities acceleration of gravity horizontal distance, travel time from depth z to the r•earest upper turning point eigenray order complex ampiRude of the acousticthickness wave internal-wave peak buoyancy frequency, buoyancy-frequency depth distribution acoustic ray cycle length, travel time acoustic-internal-wave correlation factor temperature, adiabatic temperature, potential temperature, and salinity gradients internal-wave period Z(z) B, ß 6o 0 p, p•, 0), O.)i, O)g Turner number or temperature-salinity relationship normalized wave function internal-wave horizontal wavenumber linearized salinity, temperature coefficients from Wilson's equation {ndex of refraction sound velocity/internal wave interaction parameter internal-wave displacement Dirac delta function time-and space-varying acoustic thickness acoustic phase acoustic, internal wavelength wavenumber cutoff coefficient potential density horizontal acoustic ray angie in interhal-wave layer acoustic field acoustic, inertial, internal-wave frequency

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Passage of an acoustic signal through an internal wave field results in the presence of amplitude and phase fluctuations at the receiver. The acoustic-internal wave interaction has been discussed previously using ray techniques [R. P. Porter, R. C. Spindel, and R. J. Jaffee, J. Acoust. Soc. Am. 56, 1426–1436 (1974)]. We report here on wave techniques describing the interaction phenomenon. The Rytov perturbation approach is applied to a horizontally stratified medium which is perturbed by the internal wave field. Statistical expressions for the acoustic fluctuations are obtained based upon a postulated internal wave model [C. Garrett and W. Munk, Geophys. Fluid Dynam. 2, 225–264 (1972)]. It is shown that for internal wavelengths comparable to acoustic ray cycle distances a resonant condition exists leading to large acoustic fluctuations. The validity and limitations of the perturbation technique applied to the horizontally stratified medium are discussed.