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Nov 1987

Volume 82, Issue S1, pp. S1-S124

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back to top Session CC. Underwater Acoustics IV: Wedge Model Propagation
Contributed Papers
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Range‐dependent cut‐an frequencies in a three‐dimensional ocean environment (A)

Stewart A. L. Glegg and Jong R. Yoon

J. Acoust. Soc. Am. Volume 82, Issue S1, pp. S60-S61 (1987); (2 pages)

Online Publication Date: 13 Aug 2005

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Sound propagation in a three‐dimensional wedge‐shaped ocean environment demonstrates significant ray curvature in a direction parallel to the wedge apex. The theoretical prediction of this shows that these effects are more significant at low frequencies than at high frequencies; consequently, the three‐dimensional ocean acta as a range‐dependent acoustic filter. This paper describes an experimental and theoretical investigation of pulse propagation in a model scale three‐dimensional wedge‐shaped ocean. In the experimental setup the complete acoustic field could be measured for a given source position and the wedge angle could be changed. The results show good agreement with the idealized modal solution of Buckingham, and demonstrate how the pulse is distorted as a function of range. They also demonstrate how the cut‐on frequency for acoustic propagation increases as a function of range parallel to the shoreline.
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Scattering in basins or horizontally refracting modes: Which is it? (A)

C. H. Harrison

J. Acoust. Soc. Am. Volume 82, Issue S1, pp. S61-S61 (1987); (1 page)

Online Publication Date: 13 Aug 2005

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In a large basin there are at least two types of 3‐D ray paths from a source to a distant receiver via the sloping basin edge (other than the direct path). One is the simple scattered ray at the seabed, and the other is the multiple reflected ray that steepens in shallow water but finally turns in the horizontal plane towards deep water (otherwise interpreted as a horizontally refracting vertical mode contribution [C. H. Harrison, J. Acoust. Soc. Am. 65, 56–61 (1979)]). If the total change in heading of the latter ray is 2θ, its elevation angle will never exceed θ [C. H. Harrison, J. Acoust. Soc. Am. 62, 1382–1388 (1977)], and the path may exist despite reflection losses in realistic environments. Therefore, if the top and bottom surfaces are perfectly smooth, there will be no scattering and there will certainly be multiple reflection. Conversely, if the surfaces are rough, the multiple reflection will be inhibited but there will definitely be a scattered return. Since there is scope for misinterpretation of experimental results, this paper proposes some experiments to distinguish the two paths.
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Diffraction of sound by hard strips and truncated wedges (A)

Ivan Tolstoy

J. Acoust. Soc. Am. Volume 82, Issue S1, pp. S61-S61 (1987); (1 page)

Online Publication Date: 13 Aug 2005

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Starting from rigorous diffraction solutions for single, hard, semi‐infinite wedges, it has long been possible to construct approximate solutions for more complex angular surfaces [A.D. Pierce, J. Acoust. Soc. Am. 55, 941–955 (1974)]. Demonstrated here is an exact procedure that formulates the multiple scatter between vertices of an angular body via the standard self‐consistent algorithm. This allows one to obtain the correct diffracted field of each vertex. Summing these together with the relevant incident and image fields leads to an exact solution for the full sound field. This is done here for the case of a plane harmonic incident sound field for (1) a truncated wedge and (2) a hard strip of width l. Numerical results for the latter model are shown to compare satisfactorily for all kl with experimental data [H. Medwin et al., J. Acoust. Soc. Am. 72, 1005–1013 (1982)]. This theoretical procedure yields, in the plane wave case, a formal estimate of the error incurred in the “double diffraction” approximation (i.e., the procedure that neglects all but the first two terms of the multiple scatter series). This error decreases like elkl/kl for increasing kl. It is then possible to confirm theoretically the observation of Medwin et al. who showed that, for the geometry of their strip experiment, this approximation is actually very good for kl≳ 3 and quite adequate in the region 1 < kl < 3, using the Biot‐Tolstoy rigorous impulsive point source solution for the perfect wedge [M. A. Biot and I. Tolstoy, J. Acoust. Soc. Am. 29, 381–391 (1957)] for their double‐diffraction solution. [Work supported by ONR.]
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An accurate numerical solution to ASA Benchmark Problem I using the finite element method (A)

Joseph E. Murphy and Stanley A. Chin‐Bing

J. Acoust. Soc. Am. Volume 82, Issue S1, pp. S61-S61 (1987); (1 page)

Online Publication Date: 13 Aug 2005

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A Special Session on Numerical Solutions of Two Benchmark Problems was presented at the 113th Meeting of the Acoustical Society of America in Indianapolis, Indiana, 11‐15 May 1987. The underwater acoustics community was invited to present solutions to these problems and compare them against a numerically “exact” solution obtained from the R. B. Evans' coupled mode model [F. B. Jensen, J. Acoust. Soc. Am. Suppl. 1 81, S40 (1987)]. Our finite element ocean acoustic propagation model [J. E. Murphy and S. A. Chin‐Bing, J. Acoust. Soc. Am. Suppl. 1 81, S9 (1987)] to Problem I is applied here. (Problem I dealt with shallow water upslope propagation in a wedge‐shaped channel.) This finite element model gives a full‐wave solution for range‐dependent acoustic propagation with accuracy that rivals coupled mode models. The model's capability will be demonstrated by presenting a numerical solution to Problem I that compares favorably to the Evans' coupled mode model solution. [Work supported by ONR/NORDA.]
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Sound interaction with a sloping, upward‐refracting ocean bottom (A)

Hassan B. Ali, Juan I. Arvelo, Anton Nagl, and Herbert Überall

J. Acoust. Soc. Am. Volume 82, Issue S1, pp. S61-S61 (1987); (1 page)

Online Publication Date: 13 Aug 2005

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Results of a parobolic‐equation (PE) code are shown for the problem of sound interaction with an upsloping, upward‐refracting ocean bottom. They are compared with the results of a coupled‐mode code [J. F. Miller et al., J. Acoust. Soc. Am. 79, 562 (1968)] for a range‐dependent environment. This includes bottom penetration effects at mode cutoff and a study of how these are affected by the sound‐speed gradient and by the absorption in the sediment. The bottom penetration features are further illuminated by employing Gaussian sound pulses and studying their propagation, illustrating the effects of bottom penetration and reradiation back up into the water (as caused by the upward‐refracting bottom gradient), arriving ahead of the water‐borne pulse.
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Spherically symmetric acoustic propagation across a fluid/fluid boundary (A)

Michael J. Buckingham

J. Acoust. Soc. Am. Volume 82, Issue S1, pp. S61-S61 (1987); (1 page)

Online Publication Date: 13 Aug 2005

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The acoustic field produced by a point source at the center of a fluid sphere, which itself is immersed in a fluid medium, is of interest in connection with ambient noise in the Arctic Ocean. A solution for the field in the internal and external fluid domains is presented based on novel finite Hankel transforms. The method involves internal and external Hankel transformations of the Helmholtz equation, which introduce explicitly the boundary values of the field and its spatial derivative at the spherical interface between the two fluids. By combining the resultant equations with the boundary conditions (continuity of pressure and normal component of velocity) all the unknown constants are determined, and on performing the inverse Hankel transforms, the final expression for the field is obtained. The mathematical formalism of the finite Hankel transforms introduced here has the advantage of being able to handle complicated boundary conditions, whereas previous finite Hankel transform techniques are limited to problems involving Dirichlet, Neumann, or mixed (i.e., impedance) boundaries. [This work was supported by the Office of Naval Research, Contract No. N00014‐86‐K‐0325.]
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Sound transmission experiments from an impulsive source near rigid wedges (A)

Saimu Li and C. S. Clay

J. Acoust. Soc. Am. Volume 82, Issue S1, pp. S61-S62 (1987); (2 pages)

Online Publication Date: 13 Aug 2005

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Experimental sound transmissions in air from a spark source to a small microphone were made near rigid wedges. Two types of experiments were made. The first experiments were transmissions within an approximately 12° wedge and a 52° wedge. The Biot‐Tolstoy wedge solution [I. Tolstoy, Wave Propagation (McGraw‐Hill, New York, 1973)] was used to calculate the theoretical impulse response. The “free air” transmission from the spark source was convolved with the theoretical transmission. The transmissions within the wedge gave finite sets of multiple reflections or image arrivals and a diffraction arrival. The diffraction was sensitive to leaks at the wedge apex. Theory and experiment matched. The second set of experiments was made near a 270° wedge. Arrivals were the direct reflection and the diffraction. The image reflection when the specular “reflection point” was very near the wedge apex was of interest. Comparisons of data and theoretical signals using Biot‐Tolstoy theory were excellent. Theoretical diffraction signals calculated with Trorey's theory had poor matches [A. W. Trorey, Geophysics 35, 762–784 (1970)].
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Impulse response of density contrast wedge using normal coordinates (A)

D. Chu and C. S. Clay

J. Acoust. Soc. Am. Volume 82, Issue S1, pp. S62-S62 (1987); (1 page) | Cited 1 time

Online Publication Date: 13 Aug 2005

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The exact impulse response of a point source to a rigid wedge was derived by Biot and Tolstoy [I. Tolstoy, Wave Propagation (McGraw‐Hill, New York, 1973)]. The solution by the experiments has been verified. The wedge having free (pressure release) boundaries has the same form as the rigid boundary solution [W. A. Kinney et al., J. Acoust. Soc. Am. 73, 183–194 (1983)]. These solutions cannot be applied directly to many actual cases such as ocean floor, where the ratio of density of the base sediment to that of the water approaches neither infinite (rigid) nor zero (pressure release). The solution is the impulse response to an isovelocity (v1 = v2) and density contrast (ρ1≠ρ) wedge. It is an extension of the solution given by Biot and Tolstoy. The reflection part of the solution is an impulse series weighted by reflection coefficient with different order. The diffraction part is the summation of the diffractions due to the individual image sources. The amplitudes are a function of the reflection coefficient and the number of multiple reflections. [This work was partly supported by the People's Republic of China and the Office of Naval Research.]
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