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Nov 1976

Volume 60, Issue S1, pp. S1-S125

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back to top Session P. Underwater Acoustics III: Propagation and Fluctuations. Precis Poster Session
Poster Session
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Theory of pulse spreading in dispersive random sound channels (A)

F. D. Tappert and L. B. Dozier

J. Acoust. Soc. Am. Volume 60, Issue S1, pp. S33-S33 (1976); (1 page)

Online Publication Date: 11 Aug 2005

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The information‐carrying capacity of underwater sound channels using a normal‐mode, pulse‐coded modulation scheme has been theoretically calculated. The effects of random internal wave fluctuations on signal propagation are taken into account. A pulse compression scheme is proposed to intensify received signals. The limiting factor is found to be random coupling between the acoustic normal modes due to scattering from internal wave modes. [Work supported by ONR.]
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Coupling coefficients between acoustic wave normal modes and internal wave normal modes (A)

L. B. Dozier and F. D. Tappert

J. Acoust. Soc. Am. Volume 60, Issue S1, pp. S33-S33 (1976); (1 page)

Online Publication Date: 11 Aug 2005

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Theories of acoustic signal propagation in randomly fluctuating oceans using normal modes as a basis require knowledge of the coupling coefficients, or matrix elements, that connect the acoustic wave normal modes and internal wave normal modes. We have computed these coupling coefficients numerically using programs that generate both sets of normal modes from model sound velocity profiles and Brunt—Vaisala frequency profiles. Statistical properties of these random coupling coefficients have also been obtained. [Work supported by ONR.]
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Underwater sound wave propagation in the presence of a randomly perturbed profile (A)

I. M. Besieris and W. E. Kohler

J. Acoust. Soc. Am. Volume 60, Issue S1, pp. S33-S33 (1976); (1 page)

Online Publication Date: 11 Aug 2005

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The propagation of acoustic signals over long ranges in the deep ocean is influenced significantly by the following factors: (1) a deterministic sound speed profile possessing a “sound channel”; (b) highly anisotropic spatial random fluctuations; (3) temporal fluctuations due primarily to internal waves. The wave equation, with a randomly perturbed sound‐speed profile, is initially considered, and a scaling is introduced which is typical of the ocean environment. A space—time parabolic equation is then obtained for the random product of complex pressures at two spatial and temporal points. Finally, a transport equation is derived for a suitably chosen transform of the pressure correlation function. This transport equation is general in the sense that it can model the decorrelation of acoustic signals due to offsets in range, azimuth, depth, and time. [Work supported by ONR.]
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Coherent ray propagation through a Gulf Stream Ring (A)

N. L. Weinberg and X. Zabalgogeazcoa

J. Acoust. Soc. Am. Volume 60, Issue S1, pp. S33-S33 (1976); (1 page)

Online Publication Date: 11 Aug 2005

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Coherent ray‐tracing techniques were applied to describe acoustic propagation through a Gulf Stream Ring 320 km in diameter as measured in 1973. Rays were traced from a fixed source to a fixed receiver 445 km distant incorporating the profile variations of the Ring which had a forward movement of 4 km a day. This anomaly shifted the deep sound channel axis about 400 m and also decreased the minimum sound velocity. These profile variations caused significant changes in the arrival pattern of the ray types and number of cycles. A time history is presented of the relationships between the received signal variations and the passage of the Ring including the effects of the changes in multipath structure.
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Stochastic Green's function approach to acoustic propagation through a fluctuating medium (A)

David P. Vasholz

J. Acoust. Soc. Am. Volume 60, Issue S1, pp. S33-S33 (1976); (1 page)

Online Publication Date: 11 Aug 2005

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A general, Green's function‐based approach to the problem of acoustic wave propagation through a random medium is presented. Starting with the idea that stationarity should be preserved in the propagation from source to field point, the hypothesis that the moments of the stochastic Green's function G are invariant under arbitrary uniform translation of all time variables is proposed. Proceeding by analogy with quantum field theory the quantities G and M, related to the first and second moments of G, are defined. Various properties of G and M are discussed, and it is shown that they may be conveniently used to describe the principal physical effects induced by a fluctuating medium. An exactly soluble model which illustrates the general results is presented.
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Applications of a full diffraction theory numerical simulation of sound propagation in the ocean (A)

G. Fain and L. E. Estes

J. Acoust. Soc. Am. Volume 60, Issue S1, pp. S33-S33 (1976); (1 page)

Online Publication Date: 11 Aug 2005

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A review of this numerical technique and its physical basis is presented. A comparison of the technique and the parabolic approximation is made with particular attention paid to broad beam errors in the two approaches. The propagation is simulated in stepwise fashion with the range step sizes being limited by the Rayleigh length. The Rayleigh length is defined for a variety of different sound velocity profiles. The sensitivity of the technique to step size and sampling rates is examined by varying these parameters. The theory is extended to include smooth boundaries, sloping boundaries, and Snell's law bending in range (as well as depth). SOFAR channel, surface, duct, split beam shadow zone and sloping bottom are among the examples presented. [Work partially supported by the Office of Naval Research.]
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Exact relation between the solutions of the Helmholtz and parabolic equations (A)

J. A. DeSanto

J. Acoust. Soc. Am. Volume 60, Issue S1, pp. S33-S34 (1976); (2 pages)

Online Publication Date: 11 Aug 2005

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Given that the velocity potential Ψ satisfies the Helmholtz equation describing sound propagation in a waveguide with a depth and range dependent sound speed. Given that the function p satisfies a parabolic partial differential equation (which can be “derived” from the Ψ equation). What is the relation between Ψ and p? It is shown that Ψ can be expressed as an integral transform in range of p. For sound speeds which are only a function of depth, the integral transform is exact. This is explicitly shown using the normal mode expansion. For sound speeds which depend on both depth and range, the transform involves the solution of an auxiliary partial differential equation. In either case, a stationary phase approximation of the integral transform yields the usual parabolic approximation. Corrections to this stationary phase approximation will be discussed.
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Effect of Doppler on long‐range sound propagation (A)

Jerome A. Neubert

J. Acoust. Soc. Am. Volume 60, Issue S1, pp. S34-S34 (1976); (1 page)

Online Publication Date: 11 Aug 2005

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In this sound propagation study of the effect of Doppler on long‐range acoustic tracking, a method of modeling the effects of source and/or receiver motion has been developed. It is based on modifying the inputs to existing normal mode software so that the source and/or receiver trajectory and consequent Doppler effects of the given ocean experiment are properly modeled without requiring direct changes in the static software. From this the effects of the received signal after long range, multipath sound propagation from a moving source can be modeled and interpreted.
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Initial field for the parabolic equation method (A)

D. R. Palmer

J. Acoust. Soc. Am. Volume 60, Issue S1, pp. S34-S34 (1976); (1 page)

Online Publication Date: 11 Aug 2005

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One of the practical problems which anyone interested in using the parabolic equation method must face is the proper choice for an initial field. In this paper we propose the use of an initial field which is more physical than a Gaussian, far easier to construct numerically than a coherent sum of normal modes, and for which a detailed error analysis is possible.
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Future time prediction of transient signals from limited time measurements using the Prony method (A)

L. G. Beatty and A. Z. Robinson

J. Acoust. Soc. Am. Volume 60, Issue S1, pp. S34-S34 (1976); (1 page)

Online Publication Date: 11 Aug 2005

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Reflection interference associated with the reception of acoustic signals imposes low frequency limitations on the information which can be derived from the spectrum of the direct signal if the usual steady‐state or Fourier‐type processing is employed. To eliminate this interference it would be desirable to be able to predict the future of the direct signal from the measurement of a small number of time samples taken before the arrival of the unwanted echo. One approach to this problem is to seek a closed form solution of the transient wave form in terms of the poles told zeros of its Laplace transform from the time sample measurements. This procedure which is tantamount to expanding the waveform in a series of complex exponentials is called the Prony method. Theoretically this expansion should be possible for signals whose transforms have a finite number of poles and zeros. Results of a computer simulation of this process and its implication for underwater sound calibration are discussed. [Work supported in part by the Naval Electronic Systems Command.]
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Analysis of shallow water sound propagation by normal mode theory (A)

D. White and D. F. Gordon

J. Acoust. Soc. Am. Volume 60, Issue S1, pp. S34-S34 (1976); (1 page)

Online Publication Date: 11 Aug 2005

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Normal‐mode computations agree well with experimental sound propagation data observed in shallow water in the South China Sea. The sound‐speed profile has negative gradients in the water over a structured silt bottom. Determining a sufficient set of modes can be aided by the relationships between certain fundamental parameters of ray and mode theory. Interference distance between adjacent modes and ray theory loop length can be equated through their phase velocity. The ray theory accuracy can be improved by a frequency correction [E. L. Murphy and J. A. Davis, J. Acoust. Soc. Am. 56, 1747–1760 (1974)], Mode attenuation loss over one loop length can be attributed to the loss at one bottom reflection. A bottom reflected phase shift can also be derived from mode theory. Optimum propagation occurs at the lowest frequency that permits a mode to attain maximum loop length.
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Ray‐tracing technique adapted for rapid computation (A)

D. W. Princehouse and C. E. Lacy

J. Acoust. Soc. Am. Volume 60, Issue S1, pp. S34-S34 (1976); (1 page)

Online Publication Date: 11 Aug 2005

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REVGEN provides a computerized ocean acoustic environment for the development of a modern active sonar system. [D, W. Princehouse, “Real‐time reverberation generator,” J. Acoust. Soc. Am. 57, S68(A) (1975).] During an exercise, it is important that it run in as near to real time as possible. We have developed a method whereby the numerically difficult and time‐consuming portion of ray tracing can be performed before the exercise starts, and the results used rapidly when needed. We work in the limit of geometrical acoustics and assume that the sound velocity profile depends only on depth, not range or time. While many ray‐tracing techniques can be adapted, we have used those of NISSM II. [Henry Weinberg, Naval Underwater Systems Center, New London, CT 06320. NUSC Technical Report 4527.] A function of two variables is defined, range versus launch depth and vertex velocity. Knowledge of this function allows ray tracing to be performed. This function may be computed prior to its need, a lengthy process. By encoding it in an efficient fashion, however, it may be stored in computer memory for rapid access when needed. Examples of ray tracing, caustic detection, and multipath propagation will be shown.
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Separation of individual multipath arrivals—an experiment (A)

T. E. Ewart and J. E. Ehrenberg

J. Acoust. Soc. Am. Volume 60, Issue S1, pp. S34-S34 (1976); (1 page)

Online Publication Date: 11 Aug 2005

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During June 1976 an experiment was conducted in which acoustic pulses were transmitted from a fixed transmitter to a fixed receiver 1100 meters distant. A 2‐msec pulsed tone and 4‐msec Taylor weighted FM slide signals were sent at 2, 4, 8, and 16 kHz and the received signals were sampled every 15 msec. The sound velocity profile was such that two wholly refracted paths with a travel‐time difference of about 0.5 msec were received. Analysis of the data shows distinctly different behavior in the phases and amplitudes of the two arrivals. The vertical arrival angle of each ray has been computed from the data received at two vertically spaced transducers and the fluctuations in the angle are discussed. The signal‐processing techniques used to obtain the phase and amplitude estimates from the data are presented. The implication of this experiment toward understanding the relationship of multipath signals to the oceanographic environment (e.g., internal waves and fine structure) is discussed.
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Acoustic phase fluctuations induced by internal waves in the ocean (A)

Yves J. F. Desaubies

J. Acoust. Soc. Am. Volume 60, Issue S1, pp. S34-S34 (1976); (1 page)

Online Publication Date: 11 Aug 2005

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Acoustic phase fluctuations induced by internal waves in the ocean are calculated in the geometric approximation. The results compare favorably with available experimental data.
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Amplitude fluctuations of signals received from cw sources towed at long ranges in the deep ocean (A)

D. J. amsdale, K. D. Flowers, G. V. Frisk, and G. R. Giellis

J. Acoust. Soc. Am. Volume 60, Issue S1, pp. S35-S35 (1976); (1 page)

Online Publication Date: 11 Aug 2005

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In April 1974, three cw sources (9.807, 110, and 262 Hz) were towed for 16 days in the Atlantic along a track from Antigua to the Grand Banks of Newfoundland. Data from these sources were recorded near Bermuda, Puerto Rico, and Antigua on both bottom and suspended hydrophones. A 3‐h running average was subtracted from the amplitude data in order to remove long‐term deterministic trends. The remaining fluctuations were analyzed in fixed time segments to determine the correlation time, the density function and the associated first four moments. The variate difference technique was used to estimate the degree of randomness of the fluctuations. Finally, the effects of range, range‐rate, source frequency, and environment on the fluctuation statistics are discussed.
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Probability density functions for the amplitude of signals received from cw sources towed at long ranges in the deep ocean (A)

G. V. Frisk, G. R. Giellis, D. J. Ramsdale, and K. D. Flowers

J. Acoust. Soc. Am. Volume 60, Issue S1, pp. S35-S35 (1976); (1 page)

Online Publication Date: 11 Aug 2005

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The characteristics of the probability density functions for the cw tow data of the previous paper are discussed. Theoretical density functions which best fit the data and their physical interpretation are presented. The properties of the corresponding log transformed density functions are also discussed.
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Low‐frequency shallow water propagation in Barrow Strait, N.W.T., Canada (A)

R. F. MacKinnon and J. M. Ozard

J. Acoust. Soc. Am. Volume 60, Issue S1, pp. S35-S35 (1976); (1 page)

Online Publication Date: 11 Aug 2005

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A study is made of wave dispersion from explosive charges over ranges of 7–15 km in water of 150‐m depth at a location in the Canadian Arctic archipelago. At frequencies below 40 Hz, speeds are found to be as high as 7.4 km/sec and lower than 0.8 km/sec with a particularly large arrival occurring at a speed of 1.2 km/sec. At higher frequencies most energy travels at speeds near the speed of sound in water. Independent seismic surveys have shown the area of interest to be characterized by nearly horizontal strata in the bottom consisting of an extremely thin cover of unconsolidated sediment over layers of Paleozoic carbonates. General features of the observed wave trains are discussed on the basis of a theoretical three‐layer model with a bottom consisting of two elastic layers. Attenuation is observed to be severe generally and as a function of frequency possesses a maximum near 30 Hz.
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Sound transmission through the sea surface (A)

J. E. Barger, D. A. Sachs, and J. R. Nitsche

J. Acoust. Soc. Am. Volume 60, Issue S1, pp. S35-S35 (1976); (1 page)

Online Publication Date: 11 Aug 2005

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Under conditions of sea state 2.5–3 with significant swell, cw‐tone bursts from a helicopter‐borne calibrated acoustic horn were received by a vertical string of hydrophones, and the effect of the rough air—water interface on the acoustic transmission was measured. The experiments covered a range of parameters comparable to those previously reported at the 90th Meeting of the Acoustical Society for experiments with scaled sea surfaces [J. Acoust. Soc. Am. 58, S86(A) (1975)]; namely: acoustic source frequencies of 220, 450, and 1000 Hz, grazing angles from ∼3°–5° to ∼20°, and source heights from 50 to 4000 ft. The sound path was oriented parallel and antiparallel to the sea direction. Transmission losses relative to smooth surface transmission from 2 to 8 dB were observed at 220 and 450 Hz at heights up to 1000 ft. At 1000 Hz, transmission was generally close to or better than flat surface for source altitudes below 4000 ft. The transmission at all frequencies generally improved at the highest altitude. The data were found to compare well with the results of the scaled experiments under similar conditions. [Work supported by DARPA and monitored by ONR.]
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Sound attenuation by conglomerates of bubbles at low frequencies (A)

K. J. Diercks and W. B. Huckabay

J. Acoust. Soc. Am. Volume 60, Issue S1, pp. S35-S35 (1976); (1 page)

Online Publication Date: 11 Aug 2005

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Experimental measurements of sound attenuation in the frequency range from 0.5 to 10.0 kHz are described. Small plastic bubbles simulating in volume that of an adult anchovy swimbladder were used. Both signal enhancements and attenuations ranging from +5 to −25 dB, respectively, were observed. Effects of bubble location and population density upon the frequency and magnitude of the maximum enhancement or attenuation are described and a simple mathematical model relating these parameters is presented. [Work supported by NAVSEA.]
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Volume attenuation in the Labrador Basin (A)

I. A. Fraser and J. B. Franklin

J. Acoust. Soc. Am. Volume 60, Issue S1, pp. S35-S35 (1976); (1 page)

Online Publication Date: 11 Aug 2005

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Volume attenuation coefficients for one‐third octave frequency bands up to 400 Hz have been determined as part of an underwater sound propagation study conducted in the Labrador Basin in cooperation with the U. S. Naval Research Laboratory. Charge detonation depths, receiver depth and the sound channel axis depth were all roughly 200 m along the 1300‐km track. A late summer maximum in the near‐surface sound velocity and a water depth greater than 3000 m also helped to ensure nearly ideal measurement conditions. The deduced volume attenuation coefficients were greater than the Thorp predictions [W.H. Thorp, J. Acoust. Soc. Am. 42, 270 (1967)], with attenuation increasing toward both higher and lower frequencies from a minimum (0.002 dB/km) near 60 Hz. Comparisons with results from other areas will be made. Results on the low frequency dependence of propagation loss will also be discussed.
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Low‐frequency attenuation in the North Atlantic Ocean (A)

A. C. Kibblewhite, N. R. Bedford, and S. K. Mitchell

J. Acoust. Soc. Am. Volume 60, Issue S1, pp. S35-S35 (1976); (1 page)

Online Publication Date: 11 Aug 2005

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Several Pacific Ocean experiments have been reported in which the attenuation of underwater sound at low frequencies is apparently regionally dependent. An experiment conducted in the North Atlantic Ocean in 1973 has provided data for use in determining attenuation coefficients for frequencies below 300 Hz for that region. The methods used to obtain these coefficients, their values, and their relationship to previously reported data from other regions will be presented.
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Excess attenuation in a stochastic environment: theory, model, and experiment (A)

H. G. Schneider

J. Acoust. Soc. Am. Volume 60, Issue S1, pp. S35-S35 (1976); (1 page)

Online Publication Date: 11 Aug 2005

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A general scheme to explain the excess propagation loss in sound channels is outlined, in which the stochastic variability of the environment is combined with the usual deterministic effects on propagation loss. Then a method, previously reported by the author in Acustica [35 (1976)] to handle stochastic sound speed variations in ray tracing routines is applied to model the excess attenuation for the Hudson Bay data. Finally, results will be presented indicating that the excess attenuation in the sound channel is a function of both the variability of the environment and the bottom loss. [Work supported by NAVSEA.]
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Variability of low‐frequency sound absorption in the ocean: pH dependence (A)

R. H. Mellen and D. G. Browning

J. Acoust. Soc. Am. Volume 60, Issue S1, pp. S36-S36 (1976); (1 page)

Online Publication Date: 11 Aug 2005

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Measured values of absorption coefficients in sea water below 1 kHz show a marked regional dependence; for example, the value in the North Atlantic is found to be about twice that in the North Pacific. Recent laboratory measurements have demonstrated that the absorption mechanism is a boric acid—borate relaxation. Since this boric acid reaction acts as a buffer in sea water, the absorption coefficient is strongly pH dependent. Over the range of pH values encountered in the oceans (7.5–8.2), the absorption is a monotonically increasing function of pH and has a range of values of roughly 4:1. Comparison of experimental absorption coefficients and predictions based on reported local pH values show reasonably good agreement. [Work supported by NUSC.]
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Source‐speed effect on fluctuation time scale (A)

I. J. Rosenbaum

J. Acoust. Soc. Am. Volume 60, Issue S1, pp. S36-S36 (1976); (1 page)

Online Publication Date: 11 Aug 2005

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The time scale of acoustic fluctuations has been found to depend on source speed for a shallow‐receiver shallow‐sound source configuration in deep water off the coast of St. Croix, U. S. Virgin Islands Measurements were made of a 135‐Hz cw source towed at different speeds on a tangential track through a point 7.5 miles from the receiving hydrophones. Higher source speeds consistently gave rise to shorter correlation decay times. As the data integration period was increased from 5 to 100 sec, the measured correlation decay times increased as well, covering the range of 4–462 sec for various source‐speed—receiver‐depth combinations. The position of the receiver with respect to the thermal layer depth also plays a significant role.
Demonstration Paper
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Approximate ray angle diagram (A)

Henry Cox

J. Acoust. Soc. Am. Volume 60, Issue S1, pp. S36-S36 (1976); (1 page)

Online Publication Date: 11 Aug 2005

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The Ray Angle Diagram presents loci as a function of depth of the angles which selected rays make with the horizontal as sound propagates in the ocean. It provides useful qualitative information about deep ocean propagation and the vertical distribution of signal and ambient noise power. The loci are based on Snell's law. It is shown that an Approximate Ray Angle Diagram (ARAD) can be easily constructed directly from the Sound Velocity Profile since on an appropriate scale the loci of one minus the cosine of the ray angle versus depth are approximately mirror images of the Sound Velocity Profile. The approximations are shown to involve negligible errors for cases of interest in underwater acoustics. The use and construction of the ARAD are illustrated with examples. A simple graphical technique is presented for annotating the ARAD with range information from which rays may be plotted without the use of a computer.
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