Stephen A. Reynolds

Path‐integral treatment of acoustic mutual coherence functions for rays in a sound channel

The mutual coherence function (MCF) of the acoustic wavefunction from a point source is derived by the path‐integral technique for transmission in the presence of a sound channel. Separations in time, transverse horizontal position, vertical position, and acoustic frequency are treated. Approximate coherence times, lengths, and bandwidths due to internal‐wave fluctuations are derived. The MCF of frequency is explicitly evaluated for fluctuations due to internal waves. The shape of an ensemble‐averaged pulse is derived from the MCF of frequency.

The Mid‐Ocean Acoustic Transmission Experiment, MATE

An experiment to measure phase (travel time) and intensity fluctuations in sound pulses transmitted at 2, 4, 8, and 13 kHz over an 18.1 km wholly refracted Fermat path is discussed. Simultaneously with the acoustic monitoring the index of refraction fluctuations were measured in space and time with sufficient resolution to determine the correlation function of the medium. The site was the Cobb Seamount in the northeast Pacific (46°46′N, 130°47′ W), and the time period was 30 days in June–July, 1977. In terms of both the quality and quantity of acoustic and oceanographic measurements, this experiment represents a significant improvement over an earlier experiment in the same location [J. Acoust. Soc. Am. 60, 46–59 (1976)]. The acoustic measurements cover a wider range of acoustic frequencies and more closely represent measurements from a single Fermat path. Approximately 25% of the acoustic data are discussed here; the representations of the correlation function of the index of refraction are based on all ...

Effects of internal waves and turbulence on a horizontal aperture sonar

Random variability in the water column will affect the operation of a horizontal aperture sonar. Two sources of variability in shallow water are turbulence and internal waves. In a modeling study, the effects of turbulence and internal waves on a shallow-water imaging system are compared. The operational principles of a large aperture imaging system are first reviewed. A shallow-water internal wave model is developed by modifying the Garrett-Munk model. The internal waves are assumed to dissipate and drive the small-scale turbulence. The two phenomena are predicted to have markedly different effects on a system. Turbulence has short spatial correlation scales whose primary effects will be manifested in the variance of the acoustic phase. By contrast, internal waves will have much larger scattering but also a longer correlation scale. The primary acoustic quantity of interest for internal waves is shown to be the curvature of the phase as observed along the aperture. Properties of shallow-water internal waves are shown to preclude the use of standard acoustic calculations based on the Markov approximation. Using archival environmental data, sample calculations are presented for the site of a planned August 1996 experiment.

Internal wave effects on high-frequency acoustic propagation to horizontal arrays-experiment and implications to imaging

An experiment was carried out over a nine day period from August 18 to 27, 1996 to examine acoustic wave propagation in random media at frequencies applicable to synthetic aperture sonar. The objective was to test experimentally the hypothesized imaging effects of variations in the sound speed along two different acoustic paths as put forth by F.S. Henyey et al. (1997). The focus of this paper is on describing the experiment and carrying out an initial analysis of the data in the context of the effect of ocean internal waves on imaging resolution. The oceanography is summarized to the extent needed to discuss important aspects relative to the acoustics experiment. In the acoustics experiment transmissions at 6, 20, 75, and 129 kHz between sources and receiver arrays were carried out. Source to receiver separation was about 815 m. All sources and receivers were mounted on bottom-deployed towers and were at least 9 m off the seafloor. The analysis concentrates on the 75-kHz data acquired during one day of the experiment. The time span examined Is sufficient to examine a diurnal tidal cycle of the oceanographic conditions. The results indicate the IW phase perturbations would have a significant effect on imaging for even the most benign conditions of the experiment if no autofocusing scheme is used. Also, though autofocusing should be useful in recovering the focus for these conditions, there are conditions (e.g., for the path that has a turning point at the thermocline and during times when solibores are present), where more sophisticated compensation schemes would be needed.

AFAR measurements of acoustic mutual coherence functions of time and frequency

A joint acoustic–oceanographic experiment was performed near the Azores in 1975. Frequencies from 400–4670 Hz were transmitted over a 35‐km wholly refracted path. In addition, a separate data set was gathered over a 3‐km path in 1973. Measurements of the mutual coherence function of time and frequency, and measurements of the acoustic phase structure function are presented and compared with predictions of fluctuations due to internal waves.

Path‐integral treatment of intensity behavior for rays in a sound channel

The intensity coherence function (ICF) of the acoustic wavefunction from a point source is derived by the path‐integral technique for transmission through internal waves in the presence of a sound channel. Separations in time are emphasized, although separations in transverse horizontal position, vertical position, and acoustic frequency are discussed. Approximate intensity coherence times, lengths, and bandwidths due to internal‐wave fluctuations are derived. Analytic approximations suitable for computer coding are presented for the micropath focusing parameter γ, which controls the deviation of higher intensity moments from the Rayleigh‐distribution values.

Transport Theory for Shallow Water Propagation with Rough Boundaries

At frequencies of about 1 kHz and higher, forward scattering from a rough sea surface (and/or a rough bottom) can strongly affect shallow water propagation and reverberation. The need exists for a fast, yet accurate method for modeling such propagation where multiple forward scattering occurs. A transport theory method based on mode coupling is described that yields the first and second moments of the field. This approach shows promise for accurately treating multiple forward scattering in one‐way propagation. The method is presently formulated in two space dimensions, and Monte‐Carlo rough surface PE simulations are used for assessing the accuracy of transport theory results.

Determining an ocean internal wave model using acoustic log-amplitude and phase: A Rytov inverse

The feasibility of inverting acoustic field statistics to obtain the parameters of a stochastic internal wave model is demonstrated using numerical simulations. For weak scattering satisfying the Rytov approximation, the parameters of a generalized form of the Garrett–Munk internal wave model can be obtained. A hierarchy of experiment scenarios has been studied. Scenarios range from a densely populated vertical receiving array to single-point measurements. In each case, the intrinsic range-averaging of acoustic measurements provides integral constraints on the environmental model. The success of the inversion improves with increasing experimental complexity. With a vertical array, up to four parameters of the internal wave model can be recovered. For the simplest situation, two parameters can be fit with reasonable accuracy. The implications of these results for understanding oceanographic processes are discussed.

Instrumentation to Measure the Depth/Time Fluctuations in Acoustic Pulses Propagated through Arctic Internal Waves

Abstract Instrumentation for measuring the evolution of volume-scattered acoustic signals in both depth and time is described. Measurements were taken for 12 days during the spring of 1985 with transmitters and receivers suspended beneath arctic pack ice in the Beaufort Sea. These acoustic measurements were made simultaneously with extensive oceanographic measurements taken by other investigators during the Arctic Internal Wave Experiment (AIWEX). A depth cycling vertical array of three receivers and a single fixed horizontal receiver 100 m transverse to the propagation path were deployed 6.43 km from moored transmitters. A vertical depth cycle of 51 m produced a synthetic vertical aperture of 153 m. Pulses spanning three octaves in acoustic frequency (2, 4, 8, 16 kHz) were used. The scattered field was sampled more often at 8 and 16 kHz to assure sufficient sampling (better than Nyquist) of the space/time fluctuations. Ten Gbytes of acoustic pulse receptions were recorded on optical disk for later proces...

Observations of the phase and amplitude of individual Fermat paths in a multipath environment

FM slide and pulsed‐tone signals at 2, 4, 8, and 16 kHz were transmitted from a source to a receiver at the same depth 1100 m distant. Three wholly refracted paths were observed in the return signals, and a discussion of the six‐hour time series of the arrival times and amplitudes for each path is presented. Evidence is given of acoustic frequency‐dependent scattering, and scattering from oceanic fine structure is suggested as the most likely physical mechanism to explain the observations.