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Oct 1984

Volume 76, Issue S1, pp. S1-S95

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back to top Session E. Underwater Acoustics I: Computation Intensive Ocean Acoustics I
Invited Papers
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The state‐of‐the‐art parabolic equation approximation as applied to underwater acoustic propagation with discussions on intensive computations (A)

Ding Lee

J. Acoust. Soc. Am. Volume 76, Issue S1, pp. S9-S9 (1984); (1 page)

Online Publication Date: 12 Aug 2005

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The Parabolic Equation (PE) has applications in many different scientific fields such as electromagnetics, optics theory, quantum mechanics, plasma physics, seismology, underwater acoustics, etc. This presentation centers on a discussion of the parabolic equation approximation as applied to underwater acoustic wave propagation—past, present, and future directions. A review will be given of past contributions. Recent developments are highlighted. Looking ahead we discuss what the parabolic equation method can do in order to stimulate future research and development, as well as applications. Intensive computations with respect to the parabolic equation implementation will also be discussed.
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The application of multi‐array processors to underwater acoustics (A)

Martin H. Schultz

J. Acoust. Soc. Am. Volume 76, Issue S1, pp. S10-S10 (1984); (1 page)

Online Publication Date: 12 Aug 2005

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Ocean acoustic problems are very complicated by nature and require large scale computations. Recent computer technology advances have produced very fast, inexpensive pipelined array processors. These processors allow the efficient, cost effective solution of complicated problems. This presentation begins with a demonstration of a two‐dimensional model ocean acoustic long range propagation problem and discusses its solution on both a conventional sequential computer and a pipelined array processor. The next step of the application of multi‐array processors is presented. A three‐dimensional model ocean acoustics problem is chosen as a sample problem for such multiprocessors. [Work supported by ONR.]
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Radiation and scattering from large axisymmetric structures in an infinite or semiinfinite fluid medium (A)

J. S. Patel

J. Acoust. Soc. Am. Volume 76, Issue S1, pp. S10-S10 (1984); (1 page)

Online Publication Date: 12 Aug 2005

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A complex axisymmetric structure immersed in an infinite or semiinfinite fluid medium, excited by a plane acoustic wave or by a spherical or cylindrical acoustic wave emanating from a source in the vicinity of the structure or by a mechanical force acting on the structure, scatters and/or radiates the acoustic waves in the fluid medium. At a lower frequency range of excitation, vibrations of the structure and the radiating acoustic pressure strongly couples, whereas at higher frequency of excitation the structure can be regarded as rigid. A program called FIST (Fluid Interacting with STructures) is developed to analyze these problems. Using the Helmholtz integral, one can write a linear relation between the particle velocity normal to a cavity surface and the corresponding acoustic pressure. For efficiency and economy of calculations and for the consistency of velocity distribution between the structural elements and the corresponding fluid elements in contact, the distribution of pressure and velocity on the cavity surface is described by a cubic polynominal. These fluid equations couple with the equations of motion of the structure. Combining the fluid and structural equations we get Mmath + Cmath + Kx  =  Finc + Fmech. (1) Since this is a steady‐state excitation problem, differential equation (1) reduces to a set of algebraic equations (− Mω2 + iωC + K)x  =  Finc + Fmech (2) Here matrix C is full and complex, K is real and banded, and M is real and diagonal. Further, the elements of K are several orders of magnitude larger than those of C. This ill conditioning causes a severe degradation in computational accuracy when one attempts to decompose the dynamic matrix. Two alternatives are available. (a) Iterate Eqs. (2) using the initial vector given by the solution of the in vacuo response of the structure. (b) Transform Eqs. (2) using in vacuo modes of the structure. We opted for the second approach and using that we have calculated the signature of a full scale marine structure. Construction of fluid and the modal matrices are computationally quite intensive. An original attempt to use a UNIVAC 1108 was dropped because it would have taken approximately 250 h of CPU time to calculate one bistatic plot. A UNIVAC 1110, although faster, took 50 h of CPU time to calculate one bistatic plot. Using a CRAY computer with its large core and speed of computations, it took only 20 min of CPU time to calculate a complete monostatic plot.
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A numerically efficient global matrix approach to the solution of the wave equation in stratified environments (A)

Henrik Schmidt

J. Acoust. Soc. Am. Volume 76, Issue S1, pp. S10-S10 (1984); (1 page)

Online Publication Date: 12 Aug 2005

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Solution of wave propagation problems in horizontally stratified environments arises in many fields, including underwater acoustics, seismology, and ultrasonics. When the environment is considered range‐independent the wave equation can be separated in depth and range by standard integral transform techniques. The depth‐dependent solution is then found by matching boundary conditions at horizontal interfaces, and the field as a function of range is found by evaluating the inverse integral transforms. Several numerical methods have been developed for this purpose, in underwater acoustics known as the fast‐field technique and in seismology as full wave field and reflectivity methods. These methods have generally been based on propagator matrix solutions for the multilayer Green's function. In contrast to these techniques, the use of a global matrix approach to solve the depth‐separated wave equation automatically yields the possibility of treating problems with several sources and receivers without requiring separate Green's function calculations. Unconditionally stable solutions are obtained in a computationally efficient fashion, leading to a code that is an order of magnitude faster than existing models. The generality and efficiency of this global matrix method makes it well suited to a wide class of propagation problems, as demonstrated by selected examples from underwater acoustics. Total wave fields in depth and range are calculated for both cw and pulsed sources.
Contributed Papers
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Reflection and transmission of narrow beams at a water/bottom interface (A)

Henrik Schmidt and Finn B. Jensen

J. Acoust. Soc. Am. Volume 76, Issue S1, pp. S10-S11 (1984); (2 pages)

Online Publication Date: 12 Aug 2005

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The reflection and transmission of narrow sound beams at the interface between two fluid media was studied experimentally by Muir et al. Sound Vib. 64, 539–551 (1979)] who found that narrow beams impinging on a sedimentary bottom at grazing angles below the critical angle will not be totally reflected as predicted by Snell's law. Here a numerical model yielding an exact solution to the wave equation in horizontally stratified environments is used to analyze the observed phenomenon. A beam of any realistic width is generated by introducing a vertical source array and properly phasing the single sources. It is shown that the deviation from Snell's law is due to the finite width of the angular spectrum of narrow beams, and the results given are in good qualitative agreement with the experimental results.
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A hybrid numerical/analytic technique for the computation of wave fields in stratified media based on the Hankel transform (A)

Douglas R. Mook, George V. Frisk, and Alan V. Oppenheim

J. Acoust. Soc. Am. Volume 76, Issue S1, pp. S11-S11 (1984); (1 page)

Online Publication Date: 12 Aug 2005

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A hybrid numerical/analytic technique for computing the field due to a monochromatic point source in a horizontally stratified medium was developed. This procedure is extremely accurate for all ranges. It is particularly appropriate when the field is composed of few dominant modes and a significant contribution from the continuous spectrum. This is the case for long‐range propagation in the deep ocean when the source and receiver are near the bottom and there is a low speed layer at the water‐bottom interface. The method is based upon a numerical evaluation of the Sommerfeld integral, which is in the form of a Hankel transform. Both computational speed and high accuracy are obtained by treating the singularities in the kernel of the Sommerfeld integral with a new technique that allows the singular portions to be handled analytically but which keeps the remaining portion of the integral well behaved numerically. The treatment of these singularities was motivated by a study of the effects of aliasing in the Hankel transform. Both speed and accuracy in the calculation of the Hankel transform are obtained by applying a new fast (N ∗ log N) Hankel transform algorithm that requires its input on a square root grid. This grid is more suitable for representation of the kernel of the Sommerfeld integral than more conventional linear grids. The algorithm has significant speed advantages over quadrature and adaptive integration techniques.
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A technique for generating synthetic acoustic fields in shallow water (A)

Michael S. Wengrovitz and George V. Frisk

J. Acoust. Soc. Am. Volume 76, Issue S1, pp. S11-S11 (1984); (1 page)

Online Publication Date: 12 Aug 2005

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A numerical scheme for generating both the trapped mode and continuum portions of acoustic fields for a horizontally stratified ocean and bottom is presented. The technique is based on the fact that the branch line integral corresponding to the continuum portion of the field can be performed by Hankel transforming a modified Green's function. The modified Green's function is obtained by removing the pole contributions from the actual Green's function. The continuum portion is then added to the trapped mode portion to form the total synthetic field. The technique has the advantage that it is fast, accurate, and can be used for a more general geoacoustic model than the Pekeris waveguide. Synthetic results for several examples are presented and discussed.
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Numerical implementation of intrinsic mode Green's functions for oceans with weakly sloping penetrable bottom (A)

E. Topuz, L. B. Felsen, and J. Yaniv

J. Acoust. Soc. Am. Volume 76, Issue S1, pp. S11-S11 (1984); (1 page)

Online Publication Date: 12 Aug 2005

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Two recently developed related spectral theories [A. Kamel and L. B. Felsen, J. Acoust. Soc. Am. 73, 1120–1130 (1983); J. M. Arnold and L. B. Felsen, J. Acoust. Soc. Am. 73, 1105–1119 (1983)] have provided potentially new options for calculating source‐excited sound fields in a weakly range‐dependent ocean environment. These theories have so far been applied to a homogeneous two‐dimensional ocean and bottom separated by a plane sloping interface. It has been recognized that their common building blocks are what have been referred to as “intrinsic modes” [J. M. Arnold and L. B. Felsen, J. Acoust. Soc. Am. (to appear)]. Intrinsic modes have spectral integral representations that reduce in a lowest order approximation to adiabatic modes, where these can be defined, but which remain uniformly valid in their integral form through the cutoff transition in upslope propagation. An efficient numerical algorithm has been developed for calculating the intrinsic mode Green's function in the ocean and in the bottom. In a sense, this algorithm may be regarded as a range‐dependent generalization of the range‐independent Fast Field Program (FFP), but with the important difference that angular wave spectra replace the conventional rectilinear spectral decomposition. Numerical results are compared with those from the parabolic equation [F. B. Jensen and W. Kuperman, J. Acoust. Soc. Am. 67, 1564–1566 (1980)] and the augmented adiabatic mode theory [A. Pierce, 3. Acoust. Soc. Am. 74, 1837–1847 (1983)]. Also discussed and compared are asymptotic approximations of the spectral integral, which do not require the patching of the augmented adiabatic model. [Work supported by ONR Ocean Acoustics.]
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Finite difference seismograms for laterally varying marine models (A)

R. A. Stephen

J. Acoust. Soc. Am. Volume 76, Issue S1, pp. S11-S11 (1984); (1 page)

Online Publication Date: 12 Aug 2005

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The method of finite differences is applied to the elastic wave equation to generate synthetic seismograms for laterally varying seafloor structures. The results are compared with borehole seismic data from the Gulf of California (Deep Sea Drilling Project Site 485) in which lines were shot over flat and rough topography. The significant new phenomenon observed in both the synthetic seismograms and the field data is the generation of a “double head wave” due to the interaction of the incident wavefront with the side of a hill and the flat sea floor adjacent to the hill. In these models the hills are on the order of a seismic wavelength in height and steep velocity gradients occur over distances comparable to wavelengths. Ray theoretical methods would not be suitable for studying such structures. True amplitude record sections are obtained by the finite difference method, which show for these models that the head wave generated at the flat sea floor adjacent to the hill is lower in amplitude than if the hill were not present and is lower in amplitude than the head wave generated at the hill. A second feature which is important for borehole receivers is the existence of the “direct wave root” in the upper basement. This energy occurs below the sharp interface when the direct wave impinges on the interface from above. There is no corresponding Snell's law ray path for this energy and the energy is evanescent with depth in the lower medium. The properties of both the double head wave and the direct wave root are clearly demonstrated in the finite difference “snapshot” displays.
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Shear high angle PE (shape): A PE‐type wave equation for seismic wave propagation (A)

Robert R. Greene

J. Acoust. Soc. Am. Volume 76, Issue S1, pp. S11-S11 (1984); (1 page)

Online Publication Date: 12 Aug 2005

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A model of acoustic propagation in solid media has been derived. It is a one‐way wave equation based on a high‐order Padé approximation to the square root function. The physical properties of the environment are modeled as thin stratified layers. A generalization of the equations to range‐dependent environments is easily implemented by allowing the material properties of the layers to vary in range. Furthermore, reflecting interfaces of variable depth can be approximated by using an equivalent reflector, consisting of two thin layers whose material properties vary in range.
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