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Dec 1977

Volume 62, Issue S1, pp. S1-S102

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back to top Session G. Underwater Acoustics I: Propagation (Precis‐Poster Session)
Precis‐Poster Papers
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Optical simulation of acoustic propagation in the ocean (A)

L. E. Estes and G. Fain

J. Acoust. Soc. Am. Volume 62, Issue S1, pp. S17-S17 (1977); (1 page)

Online Publication Date: 11 Aug 2005

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We have constructed, using lasers and optical components, a simulator for acoustic waves propagating in a nonhomogeneous two‐dimensional ocean. The resulting wavelength scaling provides for the contraction of tens of kilometer ocean distances to centimeter distances on the optical bench. Ocean velocity profiles which vary in range and depth are created by inducing a temperature distribution in a fluid with a high velocity‐temperature gradient. This is produced by imaging a transparency (with the desired distribution) using a high‐power‐pulse ruby laser onto the fluid. A blue dye in the fluid selectively absorbs the ruby light. The acoustic beam is simulated by a cw blue argon‐ion laser and the source and receiver patterns are generated via appropriate optics. Subwavelength‐size scatters make the blue beam visible from the side providing a photographic measure of sound intensity at all ranges and depths. A simultaneous measurement of the light velocity profile is made using a Michelson interferometer. The timing of the experiment consists of a 1‐msec ruby pulse immediately followed by a 1‐msec shuttering of the sound wave simulating and interferometer laser beams. [Work supported by the Office of Naval Research.]
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On the relationship between the geometric and parabolic propagation models and an extension of both (A)

John J. McCoy

J. Acoust. Soc. Am. Volume 62, Issue S1, pp. S17-S17 (1977); (1 page)

Online Publication Date: 11 Aug 2005

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A parabolic wave theory is considered in which the energy flux through an elemental aperture is required to lie in directions measured relative to a “local” principal propagation direction that can be termed narrow angled. This can be compared to the more commonly encountered theory in which a “global” principal propagation direction is used. A propagation model is then developed which is formulated in terms of an acoustic field measure termed the acoustic intensity angular spectral density. The relationship between this propagation model and the geometric theory is considered, with the latter being recovered in the appropriate limit. A sample calculation is carried out for the behavior of a beamed signal in the vicinity of a point caustic.
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Path integral approach to the parabolic approximation (A)

D. R. Palmer

J. Acoust. Soc. Am. Volume 62, Issue S1, pp. S17-S17 (1977); (1 page)

Online Publication Date: 11 Aug 2005

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We have examined the parabolic approximation using Fradkin's path integral formalism [E. S. Fradkin et al., Rev. Nuovo Cimento 2, 498–559 (1970)]. The results confirm a previous study [D.R. Palmer, J. Acoust. Soc. Am. 60, 343–354 (1976)] where the parabolic approximation was shown to be equivalent to two approximations: (1) a straight‐line geometric optics approximation applied in the horizontal plane (HGOA) and (2) a stationary‐phase approximation (SPA). For the random component of the sound speed we obtain the usual results [V.I. Klyatskin and V.I. Tatarskii, Sov. Phys. JETP 31, 335–339 (1970)]; namely, if the Markov approximation is satisfied, the first‐order correction to HGOA vanishes and SPA is valid. For the deterministic component of the sound speed we find the first‐order correction to HGOA does not, in general, vanish and SPA implies additional constraints which go beyond the Markov approximation. Moreover, we find, even in the simple situation considered by Klyatskin and Tatarskii, that range‐dependent terms appear in the first‐order correction to SPA and the parabolic approximation is equivalent to SPA only if the sound speed is range independent.
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Propagation in random oceans using a radiation transport code (A)

H. L. Wilson and F. D. Tappert

J. Acoust. Soc. Am. Volume 62, Issue S1, pp. S17-S18 (1977); (2 pages)

Online Publication Date: 11 Aug 2005

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A wave kinetic formulation of acoustic propagation in random media was recently developed by Besieris and Tappert [J. Math. Phys. 14, 1829 (1973); 17, 734 (1976)] which leads to an equation for the propagation of the mutual coherence function having the form of a radiation transport equation. A numerical method for solving such equations which has been successfully employed in other applications is described in Carter and Cashwell [“Particle Transport Simulation with the Monte Carlo Method,” ERDA Critical Rev. Ser., TID‐26607 (1975)]. We have adapted this technique and developed an acoustic propagation model that takes into account both scattering from rough surfaces and scattering from volume fluctuations. Code output was successfully compared to ray‐tracing predictions of transmission loss in the absence of scattering. We have used the code to calculate the effects of wind‐driven waves on scattering acoustic energy out of surface ducts and have compared to the results of measurements reported by Pedersen and Gordon [J. Acoust. Soc. Am. 37, 105 (1965)]. [Work supported by ONR]
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Pulse propagation in the ocean. I: The fast field program method (A)

Henry W. Kutschale and Fred D. Tappert

J. Acoust. Soc. Am. Volume 62, Issue S1, pp. S18-S18 (1977); (1 page)

Online Publication Date: 11 Aug 2005

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See Also: Erratum | Erratum

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Long‐range propagation experiments are often conducted in range‐dependent environments. The prediction of pulse propagation characteristics in such environments is possible with the parabolic equation (PE) method, using the Tappert—Hardin split‐step Fourier algorithm. A program has been developed to compute temporal waveforms from broadband sources as a function of range and depth, using Fourier synthesis to coherently add up the frequency response as obtained from the PE code at each range step. The effects of range‐dependent ice roughness are modeled by a modified formula of Marsh and Mellen, using as input the rms ice roughness along the propagation path. The computed waveforms have been tested against field data on SOFAR propagation in the central Arctic Ocean, and excellent agreement has been obtained. Numerical simulations of pulse compression in the Arctic channel using predistorted waveforms to match the dispersion of the channel at specified ranges show in detail the possibility of successfully achieving significant signal gain by pulse compression.
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Pulse propagation in the ocean. II: The parabolic equation method (A)

Henry W. Kutschale and Fred R. DiNapoli

J. Acoust. Soc. Am. Volume 62, Issue S1, pp. S18-S18 (1977); (1 page)

Online Publication Date: 11 Aug 2005

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The Fast Field Program (FFP) is a convenient method to compute the exact integral solution of the wave equation derived from harmonic sources in multilayered media. Solid layers as well as liquid layers may be included in the model. Thus, elastic subbottom layers are included in the model and, for Arctic propagation, an elastic ice sheet is also included. The sound field is computed as a function of range for each detector depth employing the fast Fourier transform (FFT) algorithm. The FFP has been extended to compute waveforms from broadband sources as a function of range and depth by Fourier synthesis employing the FFT algorithm. The input for this synthesis as a function of frequency is computed by the FFP. The computer program has been used to model SOFAR propagation in the central Arctic Ocean. Computed waveforms for the Arctic channel are in excellent agreement with field data. The computations clearly show the evolution in range of the dispersive signals observed in the Arctic channel. At any selected point in range and depth the waveform may be reversed in time and propagated back through the channel, showing the evolution of pulse compression to the range at which the ocean filter is matched and pulse spreading beyond this range.
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Stochastic Green's functions and random walks (A)

David P. Vazholz

J. Acoust. Soc. Am. Volume 62, Issue S1, pp. S18-S18 (1977); (1 page)

Online Publication Date: 11 Aug 2005

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In previous work [D. P. Vasholz, J. Acoust. Soc. Am. 60, S33(A) (1976)] a general black‐box approach to wave propagation through a randomly fluctuating medium based upon the stochastic Green's function G was presented. Motivated by parallels with quantum field theory the quantities G and M, related to the first and second moments of G, were defined. It was then shown how these quantities may be conveniently used to describe such effects as frequency broadening and coherence losses induced by the medium. In the present work it is pointed out that stochastic Green's functions readily lend themselves to interpretations of recent experimental work which have been made in terms of the random walk taken by the time‐varying transfer function in the complex plane [W. H. Munk and G. O. Williams, Nature 267, 775 (1977)]. In particular it is shown how these random walks arise in a stochastic Green's function formulation and how their principal parameters may be very simply expressed in terms of G and M.
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Mode coupling in a sound channel with range‐dependent parabolic velocity profile (A)

F. Chwieroth and H. Überall

J. Acoust. Soc. Am. Volume 62, Issue S1, pp. S18-S18 (1977); (1 page)

Online Publication Date: 11 Aug 2005

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The sound propagation problem is separable in a channel with adiabatic range dependence, and has been solved analytically to this approximation for the case of a parabolic sound velocity profile with linear range dependence [R. D. Graves, A. Nagl, H. Überall, and G. L. Zarur, Acustica (to be published)]. The depth functions are here Hermite functions, and the range functions Airy functions. For the nonadiabatic case (nongradual range dependence), the normal modes couple, and the coupling terms can be evaluated as the harmonic oscillator matrix elements of quantum mechanics. The coupled problem is then soluble in an almost exact fashion,. by carrying out a series of diagonalizations of the coupled range equations. We have evaluated the coupled range equations in this fashion, and examined the energy transfer between modes. The transmission loss was calculated and compared with that of the uncoupled case. [Supported in part by NRL Code 8120.]
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Coupled mode analysis of multiple‐rough‐surface scattering (A)

Alan Beills and Fred D. Tappert

J. Acoust. Soc. Am. Volume 62, Issue S1, pp. S18-S18 (1977); (1 page)

Online Publication Date: 11 Aug 2005

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The range‐dependent boundary condition imposed by a rough surface serves to couple the normal modes of an underwater acoustic field. Using a statistical analysis based on a model decomposition of the solution of the parabolic wave equation, we have derived a system of equations for the mean power in each mode describing the transfer of energy between modes. Explicit formulas for the coupling coefficients (transition probabilities) have been obtained in terms of the spectrum of the rough surface [W. J. Pierson, Jr. and L. Moskowitz, J. Geophys. Res. 69, No. 24, 5181–5190 (1964)]. Numerical solutions of the coupled power equations have been obtained for low‐frequency long‐range propagation and used to calculate the effects of rough‐surface scattering on the transmission loss as a function of range and depth. [Work supported by ONR.]
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Propagation of the mutual coherence function in a bounded waveguide (A)

John A. DeSanto

J. Acoust. Soc. Am. Volume 62, Issue S1, pp. S18-S19 (1977); (2 pages)

Online Publication Date: 11 Aug 2005

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The mutual coherence function Γ is defined as the product of the pressure field p times its complex conjugate evaluated at a different point. In three dimensions this is Γ  =  p(r,θ,z)p∗(r,math,math), where both pressure fields are restricted to the same range plane. Integral equations for Γ in a bounded waveguide are derived assuming p satisfies the usual parabolic equation, and using a Green′s function for the waveguide which satisfies a parabolic equation but with no sound‐speed term. The Green′s function thus depends only on the boundaries (its use is analogous to using the Laplace Green′s function). We derive the equation for the ensemble average of Γ for the case of a random sound speed. An example is presented for a flat waveguide with a sound‐speed field composed of refractive plus random parts, and the computability of such problems is discussed.
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Numerical studies of basin bathymetry on three‐dimensional ray traces (A)

R. N. DeWitt

J. Acoust. Soc. Am. Volume 62, Issue S1, pp. S19-S19 (1977); (1 page)

Online Publication Date: 11 Aug 2005

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Many ray‐tracing programs allow for a sloping or structured bottom. But when the normal to the bottom is tilted out of the vertical plane, a reflected ray is deviated from a straight‐line path as viewed from above. Thus if multiple reflections occur between the sea surface and the bottom, a general curving of the ray path is expected. For low frequencies when the bottom losses are small, this ray curving can persist through many reflections. A computer program has been written to study actual ray paths taken by such propagation. By digitizing basin bathymetry and velocity profiles, three‐dimensional ray traces are produced which display the effects of sea mounts, steep ridges, and curved basin walls. General characteristics of the computer program are addressed along with specific examples for certain areas in the Norwegian and Greenland Seas.
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Three‐dimensional ray paths in basins, troughs, and near sea mounts by use of ray invariants (A)

C. H. Harrison

J. Acoust. Soc. Am. Volume 62, Issue S1, pp. S19-S19 (1977); (1 page)

Online Publication Date: 11 Aug 2005

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Long‐range underwater sound propagation is often influenced by regions of repeated surface and bottom reflection. Under these conditions variations in water depth and bottom slope may produce a small change in ray heading after each bottom reflection, and the many resulting facets of the ray paths give the appearance of ray curvature in the horizontal plane. At low frequencies, where reflection losses are small, this curvature provides a mechanism for turning back rays from sea mounts or basin walls, and thus can introduce arbitrary increases in travel times and alterations in apparent bearing of sound sources. This paper uses ray invariants to derive analytical solutions for the horizontal projections of ray paths for many types of basins, troughs, sea mounts, or ridges. The isovelocity invariants for elevation angle and ray heading are extended to cover a basin with rotational symmetry as well as a trough of constant cross section, and the additional effects of refraction in a stratified medium are considered. Rough figures for the geometrical spreading loss and reflection loss at the edge of a basin are derived.
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Stochastic inputs for acoustic models (A)

A. E. Barnes and L. P. Solomon

J. Acoust. Soc. Am. Volume 62, Issue S1, pp. S19-S19 (1977); (1 page)

Online Publication Date: 11 Aug 2005

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Transmission loss depends on the sound velocity structure. Present models are deterministic, and require deterministic inputs. However, from a given set of sound velocity data generally only one sound velocity profile is generated. The resulting transmission‐loss curves are frequently compared to acoustic data for model evaluation purposes, sometimes unsuccessfully. A technique has been developed which, from a given data set, will generate many profiles, obeying certain vigorous mathematical constraints. Unfortunately each profile requires the acoustic model to be rerun, but the process generates transmission‐loss fields which can be statistically analyzed. The generation of such fields will allow more realistic appraisals of acoustic models when compared to acoustic data. The sensitivity of acoustic models to small perturbations in the sound velocity field is presented for certain special cases. The technique is applicable to all environmental inputs for any models requiring deterministic inputs.
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Comparison of experimental broadband and narrow‐band propagation‐loss data versus receiver depth (A)

E. P. Jensen and F. R. DiNapoli

J. Acoust. Soc. Am. Volume 62, Issue S1, pp. S19-S19 (1977); (1 page)

Online Publication Date: 11 Aug 2005

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In November 1973 a series of experiments were conducted in the Tongue of the Ocean, Bahama Islands, as part of Project BILL (Below and In Layer Propagation Loss). A 200–700‐Hz pseudorandom‐noise projector was slowly towed first in the surface duct at 76 m and then below the duct at 122 m. These runs were followed by a cw tow at 76 m during which the source was operated at 300 Hz. Ranged varied to 9 km and the transmitted signals were received at five hydrophones located in and below the surface duct for each of the tows. Comparisons of the results at the different receivers are made to show the effects of ln, cross, and below layer narrow‐and broadband propagation. Results obtained when the source and the receiver were at the same depth showed losses which were noticeably less than those obtained at other depths. For this situation model predictions required the inclusion of complex source angles in order to obtain better agreement. [Work supported by NUSC.]
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Effects of sound‐speed equations on critical depths in the oceans (A)

Kenneth V. Mackenzie

J. Acoust. Soc. Am. Volume 62, Issue S1, pp. S19-S19 (1977); (1 page)

Online Publication Date: 11 Aug 2005

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Critical depths (and consequently depth excesses required for convergence zone propagation) are generally computed from depth, temperature, and salinity data. In 1972, V. A. Del Grosso published a 19‐term formula that differs, up to 1.5 m/sec at depth, from the widely accepted 23‐term equation of W. D. Wilson (1960). A simple equation to determine sound speed from temperature, salinity, and depth, instead of pressure, was developed for computations, employing a pocket calculator [Joint Oceanographic Assembly, Edinburgh, Sept. 1976]. To generate a practical equation, 15 worldwide deep stations of high quality were selected, and depths corresponding to a number of pressures were computed for each profile. A polynomial of only nine terms fits Del Grosso sound speeds for all stations to depths of 8000 m with a standard deviation of only 0.07 m/sec. The simplified equation facilitates comparisons with Wilson, since depth, temperature, salinity, and Wilson sound speed appear in practically every profile tabulation. Results will be presented for a number of realistic situations.
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Quantitative model/measurement comparisons of propagation‐loss mean and fluctuating components (A)

R. B. Lauer

J. Acoust. Soc. Am. Volume 62, Issue S1, pp. S19-S19 (1977); (1 page)

Online Publication Date: 11 Aug 2005

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In November 1973 a propagation‐loss experiment was performed in the Tongue of the Ocean, Bahama Islands, under carefully monitored conditions with regard to environmental parameters and source/receiver geometry. A projector transmitting a 300‐H tone was towed at a depth of 76 m in the surface duct and receiver to a range of 9 km. A model, the Fast Field Program, was used to simulate propagation‐loss results using a measured sound‐speed profile and bottom parameters selected to achieve a good eyeball fit in the region dominated by bottom‐reflected energy. The measured and simulated results were then compared in terms of range‐dependent mean and range‐dependent standard deviation as obtained in moving windows. The mean level of the model oscillated with range in the bottom bounce region as contrasted to the measured data which exhibited an essentially constant mean level. Variability about the mean was greater for the simulated results than that of the measured data by 2–3 dB. This disparity is accounted for by fluctuation mechanisms shown to be present in the measured data besides multipath interference which is the sole cause of variability in the model simulated data. [Work supported by NUSC.]
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Doppler shift in a medium with velocity gradients (A)

R. Kolano and R. O. Rowlands

J. Acoust. Soc. Am. Volume 62, Issue S1, pp. S20-S20 (1977); (1 page)

Online Publication Date: 11 Aug 2005

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A basic formula for use in calculating Doppler shifts is shown to be dT/dt; this being the rate at which the travel time of the sound between source and receiver is changing. Examples of the application of this formula in a medium having velocity gradients of varying degrees of complexity are then given.
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Propagation‐loss fluctuations at long ranges from towed low‐frequency sound sources (A)

Ian A. Fraser and J. B. Franklin

J. Acoust. Soc. Am. Volume 62, Issue S1, pp. S20-S20 (1977); (1 page)

Online Publication Date: 11 Aug 2005

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The propagation of underwater sound at 30 and 115 Hz along an 1800‐km path has been studied using sound sources supplied by the U.S. Naval Research Laboratory and towed by their research ship HAYES. From consecutive 5‐min averages of narrow‐band spectra of the received signal, time series of propagation loss were formed for each frequency, and filtered to remove trends. Following statistical analysis, a three‐parameter phenomenological model involving the convolution of two gamma distributions afforded a good fit to the resulting probability distribution functions. Data recorded on the few occasions when the tow speed varied significantly suggest that the fluctuation rate is primarily governed by source tow speed rather than by instabilities in the medium. In addition, a monotonic decrease in the average fluctuation rate was observed with increasing range. Physical mechanisms to account for these results will be suggested.
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Underwater sound propagation in a range‐dependent environment (A)

G. L. Zarur, Anton Nagl, Jacob George, H. Überall, and A. J. Haug

J. Acoust. Soc. Am. Volume 62, Issue S1, pp. S20-S20 (1977); (1 page)

Online Publication Date: 11 Aug 2005

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For an ocean sound channel whose environmental parameters depend not only on depth, but in a gradual fashion also on range, the wave equation may be separated by the adiabatic range variation method of Pierce. For cases of less gradual range dependence, the range equations (and hence the modes) become coupled, and may be solved by diagonalization methods. This approach is used here to calculate underwater sound propagation in a channel with arbitrarily given range dependence, and also with arbitrary depth dependence of the sound velocity profiles, by employing Airy function solutions of segmentwise linearized problems. (For the coupling aspects, the simplification of segmentwise constant problems is made.) Our results are illustrated for a realistic deep water case with profiles from the Western North Atlantic, as well as a shallow water example from the Norwegian Sea, and are compared against the experimental transmission‐loss data, and the results of calculations using other methods for the same cases. [Supported in part by NRL Code 8120.]
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Numerical calculation of the intensity distribution in sound channels using coherence theory (A)

Alan M. Whitman and Mark J. Beran

J. Acoust. Soc. Am. Volume 62, Issue S1, pp. S20-S20 (1977); (1 page)

Online Publication Date: 11 Aug 2005

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We have demonstrated that coherence theory can be applied to the practical computation problem of the propagation of a beam in an infinite half‐space with stratified but arbitrarily varying speed of sound variations. The intensity distributions found in this manner are the same as those of an equivalent point source in regions removed from the caustics of the geometrical ray family, but the intensity formula is continuous everywhere in the field and may be used in the vicinity of caustics. The computer time and storage requirements are equivalent to those of a ray program. [Work supported by NSE.]
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Improved energy‐flux model for predicting range‐averaged propagation loss in deep water (A)

Ian A. Fraser

J. Acoust. Soc. Am. Volume 62, Issue S1, pp. S20-S20 (1977); (1 page)

Online Publication Date: 11 Aug 2005

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A pocket calculator program has been developed to predict propagation losses smoothed over range in situations where energy incident on the bottom can be considered lost, as in many deep water scenarios at long ranges. Input parameters are range, source frequency, sound‐speed profile gradients (assumed bilinear) and the sound speeds at source, receiver, channel axis, and bottom. To determine the effective channel depth, an extension of a familiar expression for propagation loss in a channel [D. E. Weston, J. Sound Vib. 18, 271–287 (1971)] averages over the rate at which ray paths intersect the receiver depth. The model also accommodates Lloyd mirror effects, some finite wavelength effects, and horizontal gradients of sound speed. Since individual ray paths are not considered, convergence zones and statistical fluctuations are not reproduced. Other limitations of the model, further simplifications, and cases in which it outperforms more familiar models will be presented.
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