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May 1990

Volume 87, Issue S1, pp. S1-S164

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back to top Session ZZ. Underwater Acoustics IX: Propagation and Tomography
Contributed Papers
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An exact solution of the (Helmholtz) Weyl composition equation in underwater acoustics (A)

Louis Fishman

J. Acoust. Soc. Am. Volume 87, Issue S1, pp. S130-S130 (1990); (1 page)

Online Publication Date: 13 Aug 2005

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Phase space and path integral methods have been applied to both mathematical and computational direct and inverse wave propagation modeling at the level of the scalar one‐way Helmholtz equation. These methods are particularly appropriate for extended, strongly inhomogenenous, multidimensional channeling environments. Operator symbols play a pivotal role in the analytical constructions and numerical algorithms. The construction of the operator symbol requires the exact (or approximate) solution of the (Helmholtz) Weyl composition equation in the Weyl pseudodifferential operator calculus. The exact symbol for the profile K2(q)  =  K02 + A tanhρq + B sech2 ρq is constructed and briefly analyzed. This family of profiles is particularly appropriate for ocean seismo‐acoustic modeling, as it includes (1) both symmetric and asymmetric wells with trapped modes and (2) sharp gradient features. Two limiting cases are the delta and discontinuity profiles. The results are used to illustrate several points pertinent to wide‐angle propagation modeling and the refractive index profile reconstruction problem. [Work supported by NSF, AFOSR, and ONR.]
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A three‐dimensional time‐domain paraxial approximation for underwater acoustic wave propagation (A)

B. J. Orchard, W. L. Siegmann, and M. J. Jacobson

J. Acoust. Soc. Am. Volume 87, Issue S1, pp. S130-S130 (1990); (1 page)

Online Publication Date: 13 Aug 2005

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One‐way narrow‐ and wide‐angle three‐dimensional time‐domain paraxial approximations to the wave equation are developed to model acoustic propagation. The approximate equations are designed to be appropriate for ocean applications including pulse propagation with dissipative volume attenuation and variable density. First, pseudodifferential equations for acoustic pressure are obtained from a thermodynamic model, which incorporates attenuation due to the presence of multiple acoustically absorbing chemical species. Comparisons are made to corresponding results obtained from the phenomenological model of Stokes. Padé approximants and the method of multiple scales are then used to generate partial differential equations with paraxial characteristics. Appropriate boundary, initial, and interface conditions are described for the model equations. Analytical expressions for pulse‐type solutions to a special case of the narrow‐angle equation are obtained which demonstrate some of model's properties and restrictions. Stability of the narrow‐angle approximation is demonstrated by means of an energy integral. [Work supported by ONR.]
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An investigation of sound ray dynamics in a range‐dependent model of the ocean volume using an area preserving mapping (A)

Michael G. Brown, Frederick D. Tappert, and Gustavo J. Goni

J. Acoust. Soc. Am. Volume 87, Issue S1, pp. S130-S130 (1990); (1 page)

Online Publication Date: 13 Aug 2005

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An area preserving mapping that describes sound ray propagation in a simple range‐dependent ocean sound channel is derived and studied. The unbounded ocean model has a bilinear sound‐speed profile in which the vertical sound‐speed gradient above the sound channel axis varies sinusoidally in range. It is assumed that the scale of the range‐dependent perturbation is small compared to a typical upper loop length of a ray. The explicit mapping that results gives successive iterates of range and upgoing ray angle at the sound channel axis, (rn, θn) → (rn+1,,θn+ 1). The degree of stochasticity of the mapping is governed by a single dimensionless parameter ε—the strength of the range‐dependent perturbation. Iterates of the mapping indicate that only a small fraction of all ray trajectories are chaotic, i.e., exhibit extreme sensitivity to initial conditions, for perturbations comparable in strength to those produced by internal waves in the ocean. The chaotic nature of these rays is confirmed by the calculation of positive Lyapunov exponents.
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Stable and accurate interface conditions for wide‐angle parabolic wave equations (A)

Arne Sundström

J. Acoust. Soc. Am. Volume 87, Issue S1, pp. S130-S130 (1990); (1 page)

Online Publication Date: 13 Aug 2005

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The proper formulation of mathematical and numerical conditions at a fluid/elastic interface is studied for the standard and higher‐order parabolic wave equations. For wide‐range integrations in shallow oceans, the amplitude and phase error of the bottom reflection coefficient and the error growth of the scheme must be as small as possible. Schemes with minimal local error and error growth are given, both for the usual parabolic wave equation, the higher‐order variants based on Padé approximations, and the shallow‐water variants suggested by Collins [J. Acoust. Soc. Am. 86, 1097–1102 (1989)].
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LSVOCN: A pulse‐propagation model for a linear, space‐variant ocean (A)

Lawrence J. Ziomek

J. Acoust. Soc. Am. Volume 87, Issue S1, pp. S130-S131 (1990); (2 pages)

Online Publication Date: 13 Aug 2005

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A full‐wave, pulse‐propagation model for three‐dimensional wave propagation in a Pekeris waveguide based on linear systems theory is presented. The randomly rough ocean surface and bottom are accounted for via coherent (average) reflection coefficients. Attenuation due to absorption in all three fluid media is included. Transmit and receive planar arrays with beam steering can be simulated and, as a result, vertical arrays and a single, omnidirectional point source are automatically included. A built‐in signal generator can simulate arbitrary amplitude and angle‐modulated carriers. Outputs from this model include plots of the magnitude and phase of the ocean surface and bottom reflection coefficients, the complex acoustic field across the receive array. Because of its highly modular structure, the model can also be used to generate pulse‐propagation solutions using any time‐harmonic solution such as normal mode theory or the parabolic equation method. Preliminary computer simulation results are presented. [Work supported by ONR, Code 11250A, and the Naval Postgraduate school.]
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Marching and spatial‐spectral filtering of localized phase‐space representations of wave fields in layered media (A)

B. Z. Steinberg and J. J. McCoy

J. Acoust. Soc. Am. Volume 87, Issue S1, pp. S131-S131 (1990); (1 page)

Online Publication Date: 13 Aug 2005

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Spatial and spectral (directional) information of the wave data are of equal importance in the analysis and synthesis of wave phenomena. Their simultaneous collaboration in a phase‐space format may be achieved by incorporating windowing techniques into (conventional) spectral integrals. The result is a local‐spectral representation of the field that is concentrated inherently around physically meaningful regions in phase space. This representation is most naturally suited to perform simultaneous spatial and spectral processing of wave data and therefore may serve as a powerful tool in a variety of applications such as remote sensing, imaging, field reconstruction, and more. In this work a method to propagate the local spectra of wave fields through plane stratified media is developed and discussed. An adaptive marching algorithm that permits control of the localization process will be presented. The ability of the new scheme to perform simultaneous spatial and spectral data filtering of wave phenomena, and its resolving power in phase space, will be discussed and demonstrated by means of numerical examples.
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Secondary sound channel formation in the South Pacific Ocean between 40° and 50° South Latitude (A)

R. N. Denham, D. D. Browning, and R. J. Christian

J. Acoust. Soc. Am. Volume 87, Issue S1, pp. S131-S131 (1990); (1 page)

Online Publication Date: 13 Aug 2005

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A prominent feature of the thermal structure of the Southwest Pacific Ocean between latitudes 40° S and 50° S is an isothermal layer of subantarctic mode water. This layer occupies the water column between depths of 400 and 600 m and has a temperature of 7–8°C. In winter, this feature can give rise to a surface sound channel down to 600 m and in summer can result in a subsurface subantarctic duct with axis at 100–250 m above a SOFAR channel with axis at typically 1200 m. The acoustic characteristics of this profile are examined and typical results are given for various source and receiver configurations. [Work supported by DSE and NUSC.]
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Application of wave propagation models and simulated annealing to seismo‐acoustic inverse simulations (A)

Michael D. Collins, W. A. Kuperman, and Henrik Schmidt

J. Acoust. Soc. Am. Volume 87, Issue S1, pp. S131-S131 (1990); (1 page)

Online Publication Date: 13 Aug 2005

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Frequency‐domain seismo‐acoustic inverse models attempt to determine the ocean bottom parameters to the appropriate depth and resolution for the frequency involved. For realistic problems, the number of parameters to be estimated can be very large. For inverse models based on wave propagation models, the estimate for the bottom parameters corresponds to the parameter values for which the synthetic wave solution best agrees with the measured data. Since solving the frequency‐domain wave equation in underwater environments can require significant computation time, it is usually not practical to perform an exhaustive search for the best solution. Simulated annealing is an efficient method for solving large optimization problems. The application of this method to seismo‐acoustic inverse simulations will be discussed. In stratified environments, this approach is practical for determining the depth dependence of the parameters as well as the locations of interfaces. Simulated annealing is analogous to the formation of a perfect crystal by slowly cooling a pure liquid substance. To develop an efficient simulated annealing algorithm for the inverse problem, the appropriate analogy appears to be that of a mixture of liquids with different freezing points, where both the depth within the bottom and the parameter type determine the molecular species.
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Surface wave, wave group, and internal wave observations in the 1988 Monterey Bay Tomography Experiment (A)

James F. Lynch, Arthur E. Newhall, James H. Miller, Ching‐Sang Chiu, Robert C. Dees, Kevin P. Schaaff, and Sönke Paulsen

J. Acoust. Soc. Am. Volume 87, Issue S1, pp. S131-S131 (1990); (1 page)

Online Publication Date: 13 Aug 2005

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In December 1988, an experiment was conducted in Monterey Bay, California in order to verify earlier work [Miller et al., J. Acoust. Soc. Am. 86, 326–345 (1989)] that proposed using acoustic tomography to observe the surface wave frequency‐direction spectrum. This experiment also looked at the effects of internal waves upon the acoustic arrivals in a complicated coastal environment. In this presentation, the main concentrate will be on the acoustic determination of the surface wave spectrum. The basic issues addressed are the identification, stability, and resolution of the multipath arrivals. The directional resolution of the surface wave spectrum is examined. Detailed comparisons of the spectra generated by inversions of the acoustic field to “ground‐truth” measurements made by a nearby NDBC wave buoy are shown. The acoustic data also show the appearance of a strong spectral peak due to wave groups that is not observable by the NDBC buoy. At lower frequencies, spectral peaks are observed that are attributed to internal wave activity. An interesting possibility for the generation of the observed internal wave peaks is the nonlinear interaction of two noncolinear surface waves. This mechanism, as well as other possible mechanisms for the generation of the internal wave spectral peaks, will be discussed. [Work supported by ONR and the Naval Postgraduate School Research Council.]
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Acoustic tomographic measurement of oceanic advective heat flux (A)

R. Timothy Barock, Ching‐Sang Chiu, James H. Miller, R. Michael Clancy, and James F. Lynch

J. Acoust. Soc. Am. Volume 87, Issue S1, pp. S132-S132 (1990); (1 page)

Online Publication Date: 13 Aug 2005

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Acoustic tomography is assessed as a means of measuring the seasonal oceanic advective heat transport into the Barents Sea from the Norwegian Sea. The assessment is made by using seasonal climatological data to simulate the regional temperature and current fields in the computer. Inversion of the synthetic acoustic travel time data gives the reconstructed ocean fields from which the advective heat flux is estimated. Resolution and variance analyses of several array geometries are performed in an effort to determine an optimal configuration for a given number of moored transceivers. Furthermore, the acoustic technique is compared to conventional methods.
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Monitoring El Niño by using modal ocean acoustic tomography (A)

E. C. Shang and Y. Y. Wang

J. Acoust. Soc. Am. Volume 87, Issue S1, pp. S132-S132 (1990); (1 page)

Online Publication Date: 13 Aug 2005

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The El Niño‐Southern Oscillation (ENSO) phenomenon has been identified as the most powerful family of atmospheric and oceanic variations on a time scale of months to several years. To detect the El Niño onset and estimate its intensity as early as possible are a challenge for global climate forecasting and modeling. In this paper, the possibility of monitoring El Niño by using modal ocean acoustic tomography (MOAT) [Shang, J. Acoust. Soc. Am. 85, 1531́1537 (1989)] has been investigated. A simple acoustic model of El Niño based on the 1982–1983 event (Georges et al., 1988) has been used for numerical simulation. It has been found that acoustic modes 7–12 at 10 Hz can properly sample the effective El Niño profile (from the surface to a 250‐m depth). Both forward (modal travel time and kernel matrix synthesis) and backward (El Niño profile inversion) processes are carried out on a CYBER 205. The retrieved El Niño profile is very promising. [Work supported by NOAA and ONR.]
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Experimental studies of sound propagation using a scaled marine geoacoustic model (A)

Allen Hundley and Stewart A. L. Glegg

J. Acoust. Soc. Am. Volume 87, Issue S1, pp. S132-S132 (1990); (1 page)

Online Publication Date: 13 Aug 2005

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This paper will describe a sound propagation experiment with a scaled shallow‐water geoacoustic model. This two‐layer seafloor model has dimensions 1.2×2.5 m and is composed of an epoxy layer 5.8‐cm thick overlying a concrete basement. With a water depth of 15 cm, this model represents a shallow‐water marine environment where the surficiai sediment possesses enough rigidity to transmit shear waves. This experiment concentrates upon the pressure magnitude as a function of depth in the water column using a fixed cw source with frequencies between 8 and 30 kHz. These pressure‐depth shapes are compared with the effective depth theory of Chapman et al. [J. Acoust. Soc. Am. 85, 648–653 (1989)]. [Work supported by ONR.]
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Linear density‐reciprocal sound velocity relationships for two continental shelf surface sediment classes (A)

Juliette W. Ioup, Grayson H. Rayborn, and George E. Ioup

J. Acoust. Soc. Am. Volume 87, Issue S1, pp. S132-S132 (1990); (1 page)

Online Publication Date: 13 Aug 2005

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The density to reciprocal sound velocity dependence of two predominant classes of continental shelf surface sediments as measured by Hamilton [J. Acoust. Soc. Am. 68, 1313–1340 (1980)] can be described as a subclass of Nobes's cases [J. Acoust. Soc. Am. 86, 290–294 (1989) ] by the Wood equation [Wood, A Textbook of Sound (Macmillan, New York, 1941)] or by straight line fits to the Wood equation or the data [J. Acoust. Soc. Am. Suppl. 1 80, S113 (1986)]. The data classes can be characterized as sand‐silt and clay‐sand‐silt. Although the Wood equation is nonlinear in density versus reciprocal sound velocity, for the porosity domain of these sediments it is nearly linear, as are the measured data. Also a linear relation may be derived from the Wood equation by doing a Taylor series expansion about the midpoint velocity‐density value for each sediment type. These results can be used to choose model study parameters, to calculate sediment densities from shipboard measured sound speeds, or to estimate average grain densities and velocities from measured bulk sediment densities and sound speeds. [Work supported by the Naval Oceanic and Atmospheric Research Laboratory through the U.S. Navy‐ASEE Summer Faculty Research Program and through Grant No. N00014‐89‐J‐6002.]
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