Rex K. Andrew, Bruce M. Howe, James A. Mercer and the NPAL Group

Journal of the Acoustical Society of America special issue on NPAL

The theory of wave propagation in random media (WPRM) has had considerable success in its original context involving fields propagating through homogeneous turbulent media. Application to long-range propagation in the ocean requires modifications: the medium is a waveguide, the background sound speed is depth-dependent, and the sound speed fluctuations are inhomogeneous and anisotropic. Flatte and colleagues developed a theory (henceforth denoted as FDMWZ) for signal statistics that incorporated these additional features. Predictions based on FDMWZ theory have been compared to measurements from the straits of Florida, Cobb seamount, the Azores, and the Slice89 experiments. These experiments involved ranges up to 1000 kilometers and used single hydrophones or multiple hydrophones attached to vertical moorings (i.e., vertical arrays). The Acoustic Thermometry of Ocean / Climate (ATOC) Engineering Test (AET) experiment tested the theory over a much longer range of 3250 km, but again only vertical line arrays were used to sample the acoustic field.

Second moment measurements available with these configurations were temporal (time-time) correlations, frequency-frequency correlations and vertical spatial correlations. A measurement not available in these experiments due to equipment configurations was the horizontal second spatial moment --- i.e., the horizontal coherence. An opportunity to measure horizontal coherence at 75 Hz over multi-megameter paths arose during the ATOC and follow-on North Pacific Acoustic Laboratory (NPAL) experiments. This page summarizes the results from two NPAL horizontal line array receivers at ranges from 2000 to 3000 km for measuring the transverse horizontal coherence.

FDMWZ theory is based on a path-integral treatment of the stochastic wave propagation problem. It incorporates the depth-dependent sound speed profile and waveguide characteristics of the ocean by constructing the deterministic eigenray from source to receiver and considering sound speed fluctuations along that path to be the primary contribution to the path integral calculation. (A ``deterministic eigenray" is conceptualized here as an eigenray traced through an ocean with internal waves turned off.) Inhomogeneous and anisotropic sound speed fluctuations are represented by the Garrett-Munk interval wave spectrum. Fluctuation calculations have been implemented numerically by the code ``Calculations of Acoustic Fluctuations due to Interval Waves" ( CAFI). The empirical measurements here are compared to FDMWZ predictions calculated by CAFI.

The Experiment:

The experiment geography is shown below. The Kauai source and receivers N and O were components of the larger NPAL experiment.

The Kauai acoustic source was deployed in July 1997 on the northeast slope of Kauai at 810~m depth. It is a pressure-compensated bender-bar/barrel-stave transducer designed for operation at depths to 1300 m and was built by Alliant Techsystems (Mukilteo, WA). At 810 m depth, it has a main resonant frequency of 65 Hz and a -3 dB bandwidth of 14 Hz.

The source transmitted m-sequence signals from August 1997 to October 1999, when the permit for its operation ended. Transmissions were nominally scheduled for every 4 hours every fourth day, but this scheme varied widely.

Receivers N and O are bottom-mounted horizontal line arrays. The receivers are cabled to shore where equipment designed, built and operated by the Applied Physics Laboratory, University of Washington (APL/UW), captured and processed the signals. These receivers are at ranges between 2 to 3 Mm.

Results:

A sample transmission reception is shown below, as a function of arrival time and azimuthal angle. Deterministic theory would predict 3 arrivals (or perhaps 3 pairs of arrivals) at about 10.2s, 11.0s and 11.5s. Instead, the acoustic field contains a speckle pattern clustered in these neighborhoods. This image was obtained by incoherently imaging over 40 pulses (about 20 minutes).

Raw intensity statistics for a single speckle region are shown below for the entire experiment (Kauai to site N, left, and Kauai to site O, right.) The empirical scintillation indices for these configurations was 1.53 and 1.69, Kauai-N and Kauai-O, respectively. This places the two signals into the partially saturated regime.

CAFI:

CAFI requires range-independent input sound speed and buoyancy profiles. Range-independent profiles were generated from the annual Levitus climatology by extracting temperature and salinity profiles every 100~km along each path, converting into sound speed and Brunt-Vaisala buoyancy frequency, and then averaging over the full range to yield the required input profiles. The non-dimensional index of refraction variance is then computed from these profiles: the profiles for these two paths are shown below:

Using these profiles, CAFI predictions for the spatial coherence at the two receivers is shown below. The empirical results are shown are shown as the grey-shaded region, which reflects a 60% confidence interval around the average solution. The CAFI prediction is seen to be quite close to the measured data. Note also that the spatial coherence is worse (drops off faster) for the Kauai-O path than the Kauai-N path. As the Kauai-O path is shorter than the Kauai-N path, an argument based solely on range would presume the spatial coherence to be better (i.e., drop off more slowly) on the shorter path. However, the index of refraction variations are more intense along the shorter path, and this cases greater decoherence along the shorter path. This effect is predicted by theory and observed in the data.

CAFI's predictions for scintillation index were 1.47 and 1.32 for Kauai-N and Kauai-O, respectively. CAFI predicts both signals to be in the fully saturated statistical regime.

Summary:

Overall, the comparisons between measurement and theoretical prediction of the second moment were quite good. Computations from CAFI were remarkably close, with predictions of horizontal coherence lengths about 400 m and scintillation index of about 1.3 to 1.5. A decrease in the measured coherence on the shorter Kauai-O path was successfully predicted by CAFI. Measurements similar to these, but in the fully-ensonified portion of the water column, preferably at multiple ranges, would augment the results reported here.

Empirical intensity statistics yield a parameterization of the scattering regime that is not well characterized in current theories. This is due to weaknesses in treatment of the multiple forward scattering problem. The empirical scintillation indices, around 1.5 to 1.6, were quite a bit above the saturation limit of 1.0, but CAFI still identified the fluctuation regime as fully saturated. Further exploration and characterization of this these scattering regimes is still needed.