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Oct 1984

Volume 76, Issue S1, pp. S1-S95

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back to top Session Q. Underwater Acoustics III: Computation Intensive Ocean Acoustics II
Invited Papers
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Computation intensive propagation modeling using the PESOGEN system (A)

F. D. Tappert

J. Acoust. Soc. Am. Volume 76, Issue S1, pp. S37-S37 (1984); (1 page)

Online Publication Date: 12 Aug 2005

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The development of a special‐purpose microcomputer system (called PESOGEN = parabolic equation solution generator) that performs high‐speed PE model computations using the split‐step Fourier algorithm was reported previously [L. Nghiem‐Phu, S. C. Daubin, and F. Tappert, J. Acoust. Soc. Am. Suppl. 1 75, S26 (1984)]. Applications of PESOGEN to three‐variable modeling are reported here. (1) Full‐wave computations of pulse propagation, signal waveforms, and cross‐correlation functions require p(r,z,t), a function of three variables. PESOGEN computes p(r,z,ω) in the frequency domain for many values of ω sequentially, and then obtains p(r,z,t) in the time domain by numerical Fourier transforms [L. Nghiem‐Phu and F. Tappert, J. Acoust. Soc. Am. Suppl. 1 68, S51 (1980)]. Examples of pulse transmission to long range in deep and shallow range‐dependent oceans are presented, with emphasis on numerical accuracy (tested by time‐domain reciprocity) and PESOGEN throughout times (typically less than 1 h). (2) Full‐wave computations of responses of directional receivers to line‐radiation sources require p(x,y,z), a function of three variables. Using specified farfield beam patterns, PESOGEN computes p(x,ϕ,z] for many values of the azimuthal angle ϕ sequentially, and then obtains TL′ = TL − ASG, where ASG is the array signal gain [F. Tappert and L. Nghiem‐Phy, J. Acoust. Soc. Am. Suppl. 1 75, S63 (1984)]. Examples of directional receiver response to long range sources in three dimensions are presented, with emphasis on full‐wave effects in the beam deviation loss and PESOGEN throughput times. Conceptual designs of large special‐purpose computer systems for three‐variable propagation modeling using multiple PESOGEN units in parallel with single‐instruction multiple‐data architectures are also presented.
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A progressive time domain wave equation for nonlinear acoustic (A)

B. Edward McDonald and W. A. Kuperman

J. Acoust. Soc. Am. Volume 76, Issue S1, pp. S38-S38 (1984); (1 page)

Online Publication Date: 12 Aug 2005

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A nonlinear time domain counterpart of the linear frequency domain parabolic wave equation (PE) has been derived for investigation of pulse propagation in a refracting medium, including caustics. Assuming nearly unidirectional propagation, equations of hydrodynamics yield a quadratic correction term for the linear second‐order wave equation. Perturbation analysis about unidirectional wave propagation yields a first‐order nonlinear progressive wave equation (NPE) cast in a wave following frame. This equation explicitly separates terms for the physical processes of refraction, nonlinear steepening, radial spreading, and diffraction. Self‐refraction is manifest through a continuous interaction between steepening and diffraction terms. When the wave is taken to be linear and monochromatic, the NPE reduces to the familiar PE, within appropriate assumptions. A new numerical algorithm of the flux correction type has been constructed for integration of the NPE. Successful applications to date include: (1) development of initially smooth pulses into aging N wave shocks, (2) wideband linear pulse propagation in a slab, and (3) the evolution of a nonlinear N wave incident on a caustic. [Work supported by ONR].
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The application of stepwise coupled modes to an ocean waveguide with periodic bottom roughness (A)

Richard B. Evans and Kenneth E. Gilbert

J. Acoust. Soc. Am. Volume 76, Issue S1, pp. S38-S38 (1984); (1 page)

Online Publication Date: 12 Aug 2005

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The method of stepwise coupled modes can be used to compute the solution (including backscatter) of the elliptic wave equation for acoustic propagation in a cylindrically symmetric range‐dependent ocean. We review the method and extend it to apply to periodic depth variations of the water‐sediment interface. The extension, which is based on an eigenvalue decomposition of the generalized propagator matrix for one period, allows efficient computation of the acoustic field in a ocean waveguide of infinite horizontal extent. Numerical examples are given which compare propagation loss in a rough‐bottom waveguide to that in a waveguide with a smooth bottom. It is shown that propagation loss is significantly grater for the rough waveguide. The increased loss is attributed to scattering of energy out of the waveguide. [Work supported by NORDA.]
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Evaluation of propagation for two underwater acoustic ducts (A)

M. A. Pedersen, D. F. Gordon, and D. Edwards

J. Acoust. Soc. Am. Volume 76, Issue S1, pp. S38-S38 (1984); (1 page)

Online Publication Date: 12 Aug 2005

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Perturbations in mode eigenvalues, associated with interactions between two ducts, were first investigated by the authors in 1969. The investigation of this interaction is extended to the frequency dependence of the coupling between ducts. A numerical measure of this coupling has been developed and used to determine optimum frequencies of propagation between a source located within one duct and a receiver located within the other duct. These optima occur near frequencies where the phase velocity difference between two adjacent modes forms a minimum. The coupling is strongly frequency dependent. For an example from the North Atlantic, one optimum frequency was found at 53.23 Hz. Propagation loss versus range plots show about 10 dB less loss at 53.23 Hz as compared to 64 Hz, where the mode phase velocities are well separated. Contour plots of propagation loss in the range‐receiver depth plane have been generated for a source in the upper duct. At 53.23 Hz these plots exhibit a range periodic transfer of energy back and forth between ducts, with this range period determined by the frequency and the phase velocity difference between the critical adjacent modes. [Work supported by ONR code 4250A.]
Contributed Papers
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Sound propagation in range‐degendent double ducts (A)

Homer P. Bucker and Philip W. Schey

J. Acoust. Soc. Am. Volume 76, Issue S1, pp. S38-S38 (1984); (1 page)

Online Publication Date: 12 Aug 2005

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In a companion paper, M. A. Pedersen et al. (Abstract Q4) discuss sound propagation in range‐independent double ducts. Here we examine the effects of range dependence on the interchange of energy between adjacent acoustic ducts associated with a pair of resonant normal modes. The basic interchange mechanism is reviewed and the interchange distance (i.e., distance required to transfer acoustic energy from one duct to the other) is related to profile parameters. Calculations for a partial field (two modes) and a complete field (all modes) will be shown. Comparisons are then made between the exact solution (normal modes) and the approximate solution (parabolic equation) which will be used for range‐dependent calculations. Propagation loss curves and sound intensity contours will be given for two realistic cases of range dependence. It is shown that moderate range dependence does not destroy the fundamental resonance transfer of energy between ducts, but it does cause significant variation of the interchange range. [Work supported by ONR code 425AC.]
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Nonlinear effects in long range underwater propagation (A)

Frederick D. Cotaras, Christopher L. Morfey, and David T. Blackstock

J. Acoust. Soc. Am. Volume 76, Issue S1, pp. S39-S39 (1984); (1 page)

Online Publication Date: 12 Aug 2005

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An ongoing project to investigate the importance of nonlinear effects in long range underwater propagation is described. The project consists of three tasks: (1) to generalize weak shock theory to include effects of relaxation in the ocean, (2) to determine the effects of the stratified medium on propagation of finite‐amplitude waves, and (3) to investigate the nonlinear effects close to a caustic. Results, in the form of time waveforms and their power spectral densities, are presented for task 1, task 2, and simplified merger of tasks 1 and 2. In particular the propagation of an explosion pulse along a single ray tube is computed. Emphasis is placed on the differences between the results obtained using nonlinear theory and linear theory. The role of the reduced range variable math = s0 ln(Gs/so), wherein s is the path length, s0 is the reference range, and G is a number indicating the effects of the stratification on nonlinearity, is discussed. [Work supported by ONR.]
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The uniform WKB approach extension to multiple channels and bottom propagation (A)

R. F. Henrick, J. R. Brannan, and G. P. Forney

J. Acoust. Soc. Am. Volume 76, Issue S1, pp. S39-S39 (1984); (1 page)

Online Publication Date: 12 Aug 2005

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The treatment of more complex acoustic signals that have significant bandwidth of limited time duration requires significantly more effort to model ocean propagation. Consideration of such signals requires accurate inclusion of ocean properties such as diffraction and bottom interaction that may show significant variation across the signal bandwidth. Inclusion of such full wave effects typically implies significant computational requirements. A joint analytical/numerical approach using uniform asymptotics was previously demonstrated [R. F. Henrick, J. R. Brannan, D. B. Warner, and G. P. Forney, J. Acoust. Soc. Am. 74, 1464—1473 (1983)] to yield significant reduction in computer run time compared to brute force numerical techniques. This initial application was, however, limited to single channels and did not accurately include bottom interacting energy. Recent extensions include both multiple channel leakage and a realistic geoacoustic bottom. Examples are presented illustrating both the necessity of including the bandwidth of the signal and the accuracy of the approach. It is shown that judicious use of analytical techniques and analysis can be used in conjunction with numerical techniques to reduce the computational load by one to two orders of magnitude.
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Numerical considerations in ray tracing and ray expansions of the acoustics wavefield (A)

Michael G. Brown

J. Acoust. Soc. Am. Volume 76, Issue S1, pp. S39-S39 (1984); (1 page)

Online Publication Date: 12 Aug 2005

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In separable geometries (range‐independent sound speed profile, flat bottom) the reduced wave equation may be solved using the WKB technique. The resulting integral expression is a plane wave or ray expansion the acoustic wavefield. In nonseparable geometries the Maslov technique provides an expression of the same form. Use of the stationary phase technique reduces these integral expressions to standard ray theory. We focus our attention on numerical considerations associated with: (1) computing the geometric ray information which appears in these integral wavefield expressions; and (2) evaluating the integrals. Many commonly occurring problems associated with (1) (ray tracing) may be avoided by appropriately parametrizing the model and rewriting the travel time in terms of the phase integral, τ (sometimes referred to as the delay or intercept time). Problems associated with (2) are particularly troublesome when caustics are present. These may be avoided entirely by transforming to the time domain. [Work supported by ONR.]
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Underwater acoustic signal simulating in range‐dependent environments using Maslov asymptotic theory (A)

Elizabeth A. Kendall

J. Acoust. Soc. Am. Volume 76, Issue S1, pp. S39-S39 (1984); (1 page)

Online Publication Date: 12 Aug 2005

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Asymptotic ray theory can be used to simulate acoustic waves in range‐dependent oceans, but singularities often occur at points of great interest. Transform methods, such as the WKBJ solution used by M.G. Brown [Ph.D. thesis, University of California, San Diego, CA (1982)], describe waves at the singular points, but they are restricted to laterally homogeneous media. Maslov asymptotic theory combines asymptotic ray theory and transform methods to provide a uniform result applicable in range‐dependent environments, and the technique was used by C. H. Chapman and R. Drummond [Bull. Seismol. Soc. Am. 72 (6), S217–S317 (December 1982)] to compute synthetic body‐wave seismograms. This paper describes a. computer simulation of underwater acoustic signals in range‐dependent oceans that is based upon Maslov asymptotic theory. The theory and computer implementation will be summarized, and examples will be discussed. Preliminary results on range‐dependent signal inversions for underwater acoustic tornography will also be presented.
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A new look at acoustic refraction by mesoscale ocean features with Hamiltonian ray tracing (A)

T. M. Georges, R. M. Jones, and J. P. Riley

J. Acoust. Soc. Am. Volume 76, Issue S1, pp. S39-S39 (1984); (1 page)

Online Publication Date: 12 Aug 2005

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Tomographers use networks of acoustic paths to map mesoscale ocean structure. To know where to deploy sensors and how to interpret their measurements, one must understand how the sound channel and mesoscale features refract sound in three dimensions, and how such refraction affects acoustic measurables. In particular, one would like to know how ray refraction affects acoustic measurables. In particular, one would like to know how ray refraction affects the perturbation assumptions underlying linear inversion techniques. We use a Hamiltonian ray‐tracing program called HARPO to compute the refraction by continuous three‐dimensional ocean models and display the results in a way that adds insight about refractive effects. By numerically integrating Hamilton's equations through continuous ocean models, we avoid the discontinuities characteristic of models that break the medium into triangular patches. We begin with simple range‐independent models of the sound channel, progress through range‐dependent models and finally add a realistic model of a mesoscale eddy, including its currents. Two diagrams that have not been widely used before—plots of range versus launch angle and range versus travel time for all ray‐loop numbers—are useful ways to display the arrival‐time and ray‐focusing perturbations caused by changes in ocean structure.
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