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Nov 1988

Volume 84, Issue S1, pp. S2-S224

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back to top Session R. Underwater Acoustics II: Time Domain Methods for Underwater Acoustics
Invited Papers
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Pulse modeling in ocean acoustics: Brute‐force Fourier synthesis versus time‐domain techniques (A)

Finn B. Jensen

J. Acoust. Soc. Am. Volume 84, Issue S1, pp. S49-S50 (1988); (2 pages)

Online Publication Date: 13 Aug 2005

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There are fundamentally two different approaches to the pulse modeling problem. The first is to generate pulse results by Fourier synthesis of time‐harmonic solutions. This approach requires little programming effort and builds on the existing set of cw codes (normal modes, FFP, PE), which have been developed and continuously improved over the past decade or two. The second approach is to solve the problem directly in the time domain, which requires the development of an entirely new set of propagation codes. A similar effort would only pay off if there are significant computational advantages to solving the problem in the time domain. The issue of computational efficiency is addressed by solving characteristic short‐ and long‐range propagation problems in shallow and deep water, employing both Fourier‐synthesized cw codes (FFP and PE) and time‐domain codes recently developed by M. B. Porter (TDFFP) and M.D. Collins (TDPE).
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Time‐domain elastodynamic scattering problems (A)

J. D. Achenbach, S. Hituse, and Ch. Zhang

J. Acoust. Soc. Am. Volume 84, Issue S1, pp. S50-S50 (1988); (1 page)

Online Publication Date: 13 Aug 2005

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The interaction of an ultrasonic pulse with an inhomogeneity in an elastic solid is generally analyzed by the use of the FFT over time in combination with a numerical method for the scattering problem in the frequency domain. For pulses with a high‐frequency content this approach tends to be computationally intensive. In this talk the possibilities of a direct analytical time‐domain approach are explored, and then there is a discussion of numerical techniques. Results are presented for a single crack (slit and penny‐shaped) and for macrocrack‐microcrack configurations. Some of these results have been obtained by the finite difference method. The main emphasis in this paper is, however, on the development of a time‐domain boundary integral equation method. By the use of appropriate representation integrals, a system of boundary integral equations has been obtained, which has subsequently been cast in a form that is amenable to a solution by the boundary element method in conjunction with a time‐stepping technique. Particular attention has been devoted to dynamic overshoots of the stress intensity factors. Elastodynamic stress intensity factors have been computed as functions of time, and they have been compared with results of other authors.
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Acoustic radiation from an impulsive point source in a continuously layered fluid—An analysis based on the Cagniard method (A)

Adrianus T. de Hoop

J. Acoust. Soc. Am. Volume 84, Issue S1, pp. S50-S50 (1988); (1 page)

Online Publication Date: 13 Aug 2005

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Acoustic radiation from an impulsive point source in a continuously layered fluid with depth‐varying parameters is investigated theoretically with the aid of the modified Cagniard method, that starts with a one‐sided Laplace transformation with respect to time and a Fourier transformation with respect to the horizontal space coordinates. Using appropriate one‐sided Green's functions, the system of transform‐domain differential equations in the depth coordinate is rewritten as a system of integral equations that, for not too rapidly varying fluid properties, can be solved by iteration. The modified Cagniard method leads to space‐time expressions for the relevant iterates. To show the generality of the method, the fluid is assumed to show anisotropy in its volume density of mass. The continuously refracted waves emitted by the source and the singly, continuously, reflected wave in an isotropic fluid are discussed in detail. With this method, no difficulties arise with “turning rays” as is the case in the frequency‐domain analysis of the problem. [Work done as a Visiting Scientist at Schlumberger‐Doll Research, Old Quarry Road, Ridgefield, CT 06877‐4108.]
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Linear and nonlinear acoustics in the time domain: Long‐range pulse propagation (A)

B. Edward McDonald

J. Acoust. Soc. Am. Volume 84, Issue S1, pp. S50-S51 (1988); (2 pages)

Online Publication Date: 13 Aug 2005

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During recent years the nonlinear progressive wave equation (NPE) model has been developed as a nonlinear time domain counterpart of the linear frequency domain parabolic equation (PE) model [B. E. McDonald and W. A. Kuperman, J. Acoust. Soc. Am. 81, 1406–1417 (1987)]. It was motivated by investigation of nonlinear wave evolution, so that time domain formulation was natural. With nonlinearity absent, the NPE gives an efficient algorithm for linear broadband propagation in the time domain. (No Fourier transforms between frequency and time domains are involved.) Recent simulation results from the NPE model (given in a color movie) illustrate linear and nonlinear pulse propagation through a deep ocean convergence zone. Differences in physics between broadband linear and nonlinear propagation will be pointed out and discussed. Linear results reveal transients whose time scale as a function of range is “remembered” from the source. In corresponding nonlinear results, steepening and shock formation cause the source's time scale to be gradually “forgotten.” For the parameters of the example given, nonlinear spreading behind the shock increases the transients' time scale by roughly a factor of 3 in the farfield.
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On synthetic aperture sonar (A)

Masaaki Shishido

J. Acoust. Soc. Am. Volume 84, Issue S1, pp. S51-S51 (1988); (1 page)

Online Publication Date: 13 Aug 2005

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Synthetic aperture technology is used in airborne radar or on satellites like SEASAT to obtain high‐resolution pictures of the Earth's surface. On the other hand, in the field of underwater acoustics, the effectiveness of synthetic aperture side‐looking sonar has long been predicted. However, this has not come to practical use, mainly because of the influence of the trembling motion of the sonar platforms. First, the principle of synthetic aperture sonar and the similarity between CDP stacking of seismic exploration and synthetic aperture processing are discussed. Then, the influence of platform trembling on the synthetic aperture beamforming is quantitatively studied, and the degradation of the picture is evaluated with computer simulation to show the allowable range for the trembling motion amplitude and period against the used signal frequency.
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Reduction of bit‐error rates by adaptive equalization for a 500‐kbit/s underwater acoustic communication system (A)

Shinji Yauchi and Akio Kaya

J. Acoust. Soc. Am. Volume 84, Issue S1, pp. S51-S51 (1988); (1 page)

Online Publication Date: 13 Aug 2005

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For the video transmission from untethered subsea robots, an acoustic communication system using the 16‐ary quadrature amplitude modulation (16QAM) method is being developed to perform at a capacity of 500 kbit/s at a maximum transmission range of 60 m. To improve the quality of the transmitted information, an adaptive equalization technique will be introduced to this system. In this study, an adaptive equalizer based on a baseband decision‐directed equalization method is realized as a computer program. The optimal parameters of the equalizer such as the number of taps and step sizes are determined by computer simulations. In order to estimate the performance of the acoustic communication system with an adaptive equalizer, random code data modulated by 16QAM are transmitted to a receiver located 10–60 m from the source through a surface channel, and stored in a digital memory bank for the off‐line processing of an adaptive equalizer. Results show that the bit‐error rates in the output of the receiver are about 10−4 at a range of 60 m because of the channel distortion caused by multipath interference, the attenuation characteristics of the channel, etc. However, the bit‐error rates in the output of the adaptive equalizer are reduced to less than 10−7 in the 10‐ to‐60‐m range. [Conducted as part of the R&D Program of the Large‐Scale Project “Advanced Robot Technology” by the Agency of Industrial Science and Technology, Ministry of International Trade and Industry.]
Contributed Papers
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Wave field factorization for broadband acoustic signals (A)

John J. McCoy

J. Acoust. Soc. Am. Volume 84, Issue S1, pp. S51-S51 (1988); (1 page)

Online Publication Date: 13 Aug 2005

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A framework has been demonstrated for factoring the Helmholtz equation, governing for narrow‐band acoustic signals, into a pair of one‐way equations [L. Fishman and J. J. McCoy, J. Math. Phys. 25, 285–296 (1984)]. This factoring requires a range‐independent propagation environment. The factored Helmholtz equation has been demonstrated to provide a marching algorithm [L. Fishman and J. J. McCoy, Geophys. J. R. Astron. Soc. 80, 439–461 (1985)], which is a generalization of the split‐step algorithm, the latter being frequently used for marching the solution of the ordinary parabolic wave equation. The extension of these results to broadband acoustic signals is considered. Two factorizations are considered and shown to apply to different initial/boundary value problems. The first factorization is based on a Fourier synthesis of that obtained for narrow‐band signals. This applies for a forcing problem as a broadband time series acting across a source range plane. The second factorization obtains for the time coordinate of the wave equation. This applies for an infinite spatial domain problem for specified initial time data.
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The finite difference method for time domain solutions to range‐dependent bottom‐interaction problems (A)

Ralph A. Stephen

J. Acoust. Soc. Am. Volume 84, Issue S1, pp. S51-S52 (1988); (2 pages)

Online Publication Date: 13 Aug 2005

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An explicit second‐order finite difference scheme has been used to solve the elastic wave equation in the time domain. Solutions are presented for the perfect wedge, the lossless penetrable wedge, and the plane parallel waveguide, which have been proposed as benchmarks by the Acoustical Society of America. Good agreement with reference solutions is obtained if the media is discretized at 20 grid points per wavelength. The principle disadvantage of the technique is long computational times that are between 10 and 20 h on a minicomputer without an array processor. The method has the advantage of providing phase information and, when run for a pulse source, of providing insight into the evolution of the wave field and energy partitioning. Arbitrarily more complex models including velocity gradients, strong lateral heterogeneities, and random media can be solved with no additional computational effort. The method has also been formulated to include shear wave effects. [Work supported by ONR.]
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Time domain finite difference modeling of acoustic wave scattering from an elastic cylinder (A)

Martin E. Dougherty and Ralph A. Stephen

J. Acoust. Soc. Am. Volume 84, Issue S1, pp. S52-S52 (1988); (1 page)

Online Publication Date: 13 Aug 2005

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A 2‐D finite difference formulation of the elastic wave equation has been used to investigate seismo/acoustic scattering from laterally heterogeneous oceanic crust. In an effort to validate the use of this code to handle such problems, the same formulation has been used to solve the canonical problem of scattering of an acoustic wave from an infinite elastic circular cylinder. Analytical theory predicts that an acoustic wave will be scattered only into certain distinct azimuths after interaction with a cylinder of given elastic parameters. These scattering angles and amplitudes are very sensitive to both the frequency of the source and the diameter of the cylinder. The finite difference results of scattering of both a relatively broadband plane wave pulse and a series of monochromatic cw plane waves at different frequencies are presented. In general, the scattering pattern produced by the pulse source does not agree well with the analytical solution for the pulse center frequency. This is due to the relatively broad frequency band of the pulse. However, scattering patterns and amplitudes produced by the monochromatic cw plane wave sources do agree very well with the expected analytical solutions.
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Inversion of wave field data by simulated annealing (A)

Atanu Basu and L. Neil Frazer

J. Acoust. Soc. Am. Volume 84, Issue S1, pp. S52-S52 (1988); (1 page)

Online Publication Date: 13 Aug 2005

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Simulated annealing is a new Monte‐Carlo optimization method that (if properly used) does not get stuck in local minima of the objective function. This feature is attractive for the inversion of wave field data where the lack of low‐frequency energy makes cycle skipping a problem. To gain experience with the method, it was applied to a simple problem: determining a sound‐speed profile c(z) from recordings of two shots at unequal distances from a vertical array. For a nearly stratified ocean this problem is equivalent to a single shot, recorded on two vertical arrays. A profile c(z), propagating data from the near array to the far array, is assumed and then the propagated data are compared with the actual data at the second array. If the propagated and actual data agree then c(z) is a good profile. If the sound‐speed profile has, say, 15 parameters with, say, 10 possible values for each parameter then the number of possible profiles is 1015. In tests with synthetic data, simulated annealing gave a nearly correct profile with a few hours of iteration (on a desk‐side workstation). Experiments are currently going on with different annealing schedules. Results so far suggest that critical temperature (Tcr) is difficult to determine, and so annealing strategies which do not require a prior estimate of Tcr are more efficient than those which do. [Work supported by ONR.]
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Numerical experiments with time‐domain localization (A)

Peter I. Pecholcs and L. Neil Frazer

J. Acoust. Soc. Am. Volume 84, Issue S1, pp. S52-S52 (1988); (1 page)

Online Publication Date: 13 Aug 2005

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Time‐domain localization is of interest because: (a) ambiguity surfaces constructed using frequency‐domain methods have large sidelobes unless many frequencies are used; (b) time‐domain Green's functions can be rapidly constructed using ray theory; and (c) in theory, time‐domain methods can be used to directly determine the velocity, as well as the position, of the source. Here some natural time‐domain algorithms are applied to a homogeneous waveguide with a soft top and hard bottom. Clay's matched filter approach, and a technique known in the oil industry as reverse time migration, are attractive because neither requires a knowledge of the source waveform. If the source waveform is available (even though its time origin is not) then one can localize using a Bartlett, or a maximum likelihood, formula directly in the time domain. A concurrent search is needed to determine the best time origin for the source waveform. If the source waveform is available, then one can localize in velocity space by use of a ray theoretical Green's function in which the source waveforms of different rays are compressed or expanded according to the component of velocity parallel to each ray at a candidate source location. [Work supported by ONR.]
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The time‐domain parabolic wave equation and its path integral representation (A)

Dalcio K. Dacol

J. Acoust. Soc. Am. Volume 84, Issue S1, pp. S52-S52 (1988); (1 page)

Online Publication Date: 13 Aug 2005

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A path integral representation for the solution of a time‐domain parabolic wave equation (TDPE) was developed. It shows promise for describing propagation of sound pulses in the ocean when boundary interactions can be neglected. The TDPE is a linearized version of McDonald and Kuperman's nonlinear progressive wave equation [B. E. McDonald and W. A. Kuperman, J. Acoust. Soc. Am. 81, 1406 (1987)]. Using the techniques developed by these authors one can derive the TDPE from the acoustic wave equation thus showing that the TDPE's solution is an approximate solution to the acoustic wave equation [M.D. Collins, J. Acoust. Soc. Am. Suppl. 82, S122 (1987)]. The TDPE has the mathematical structure of a time‐dependent Schrödinger equation and a phase space path integral representation for its solution can be constructed by well‐known methods. Applications to be discussed include propagation in a sound channel and in randomly fluctuating media. [Work supported by U.S. Naval Research Laboratory.]
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Numerical modeling of acoustic emission from propagating cracks in an Arctic ice cover (A)

Henrik Schmidt and Jae Soo Kim

J. Acoust. Soc. Am. Volume 84, Issue S1, pp. S52-S53 (1988); (2 pages)

Online Publication Date: 13 Aug 2005

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An earlier developed numerical model for three‐dimensional propagation in horizontally stratified fluid/elastic media [H. Schmidt and J. Glattetre, J. Acoust. Soc. Am. 78, 2105–2114 (1985)] has been modified to incorporate seismic moment representations for compact cracks of tensile, dip‐slip, and strike‐slip types. The applied global matrix approach first yields the depth‐dependent Green's function simultaneously in all layers for an arbitrary number of individual source depths. The frequency domain solution for a three‐dimensionally propagating crack is then determined by wavenumber integration over a spatial grid of superpositions of individual source contributions multiplied by the proper phase terms. Finally, the time domain solution over the spatial grid is obtained by simple Fourier synthesis. The present Fourier transform approach has the advantage that many crack propagation scenarios can be treated with only a single computer intensive solution of the wave equation. Once the depth‐dependent Green's function has been determined for the relevant crack type and depths, the field can be evaluated very efficiently by superposition for any crack propagation direction and speed. The developed model has been applied to theoretical analysis of the sound field produced in an Arctic environment by ice cracking, demonstrating the effect of cracking mechanisms, propagation speed as well as environmental parameters in general. [Work supported by ONR.]
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Simulated autocorrelations of a broadband signal in an ocean with a layered bottom (A)

Gordon R. Ebbeson

J. Acoust. Soc. Am. Volume 84, Issue S1, pp. S53-S53 (1988); (1 page)

Online Publication Date: 13 Aug 2005

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It is well documented that the correlations between the multipath arrivals from a broadband acoustic source in a deep ocean can be greatly affected by the bottom sediment. As an aid to explaining these effects, the seismogram version of the SAFARI model was extended to simulate the autocorrelation of the received signal. As with the original model, the bottom environment is input in the form of a geoacoustic bottom model. However, the inputs to the extended model also include the source level, realistic ambient noise and sea state conditions, noise due to distant shipping, and the self‐noise levels of the receiving array. Simulations were carried out using the environment of the Tufts Abyssal Plain of the Northeastern Pacific. The geoacoustic bottom model for this area was developed at DREP [N. R. Chapman, J. Acoust. Soc. Am. 73, 1601–1607 (1983)] and has been validated by a detailed analysis of propagation loss measurements. It was found from these simulations that reflections from both the water‐sediment and sediment basement interfaces result in a time‐spreading of the correlogram peaks as well as a reduction in the overall correlation magnitude.
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The effects of time delay quantization on underwater ultrasonic imaging techniques (A)

A. H. Goode, J. M. Reeves, and S. O. Harrold

J. Acoust. Soc. Am. Volume 84, Issue S1, pp. S53-S53 (1988); (1 page)

Online Publication Date: 13 Aug 2005

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This paper describes different pulse echo imaging techniques based on time delay focused arrays for both transmission and reception. The effects on system performance of time delay quantization are examined using a versatile pulse echo imaging test facility and a corresponding computer simulation. The system currently used has B and C scan capability over a 40° sector. It is designed around 32‐element linear‐phased arrays, operating at 2 MHz, for both transmission and reception of short bursts of ultrasonic energy. The techniques described fall into two categories, high resolution and low resolution. The high‐resolution techniques calculate the sum of the corresponding instantaneous samples of each of the 32 individually received signals, therefore allowing phase cancellation/reinforcement to occur. The low‐resolution technique simply utilizes the total energy in the received signal. A brief description of the test facility is included together with the methods for using these types of imaging techniques. The sensitivity effects due to the time delay quantization are discussed for various levels of quantization, and three‐dimensional sensitivity contour plots depicting system performance are included.
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An application of the broken mirror approximation to modeling bistatic reverberation in the ocean (A)

Henry Weinberg

J. Acoust. Soc. Am. Volume 84, Issue S1, pp. S53-S53 (1988); (1 page)

Online Publication Date: 13 Aug 2005

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The Navy Interim Surface Ship Model (NISSM II), a monostatic reverberation model, was applied to data measured by the Canadian Defence Research Establishment Pacific (DREP). NISSM II could not explain the behavior of certain discrete arrivals. The source of the discrepancy was eventually attributed to the bistatic nature of the experiment. In 1986, the Generic Bistatic Reverberation Model was developed and applied to the data without much success. Other modelers were already aware that direct transmitter‐receiver arrivals, the counterpart of vertical fathometer returns in the monostatic case, could be significant in bistatic reverberation measurements. When these direct arrivals were added, it became obvious that the source of discrepancy between the model and the data had been isolated, but not resolved. The implementation of a “broken mirror” model provided the missing link for explaining the DREP data. This paper highlights the results of the bistatic investigation.
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