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Apr 1991

Volume 89, Issue 4B, pp. 1851-2015

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back to top Session 2UW: Underwater Acoustics and Acoustical Oceanography: Inverse Methods
Invited Papers
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Inverse methods and detection and estimation theory (A)

Arthur B. Baggeroer

J. Acoust. Soc. Am. Volume 89, Issue 4B, pp. 1873-1873 (1991); (1 page)

Online Publication Date: 14 Aug 2005

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Inverse methods have long been used to determine models for geophysical processes. These methods are closely related to the topics of parameter estimation and system identification in the detection and estimation theory literature, yet results from this area are seldom exploited in inversions. System concepts such as controllability and observability are important in specifying an inverse operator; threshold concepts are needed when parameters are nonlinearly related to observables and/or perturbations are employed; yet they are seldom used. More important, there are many bounds upon the performance of parameter estimators that can be applied to inverse problems in geophysics. This presentation will discuss how methods in system theory and detection and estimation can be applied to geophysical inverse problems. [Work supported by ONR.]
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Determination of geoacoustic parameters of the ocean bottom—Data requirements (A)

Subramaniam D. Rajan

J. Acoust. Soc. Am. Volume 89, Issue 4B, pp. 1873-1873 (1991); (1 page)

Online Publication Date: 14 Aug 2005

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An important problem in ocean acoustics is the determination of the acoustic parameters of the ocean bottom sediment layers. A variety of inverse methods has been proposed in the literature for obtaining these quantities from measurements of the acoustic field in the water column using either narrow‐band sources. The ability of some of the perturbative methods to yield accurate estimates of the unknown parameters is investigated. For shallow water experiments, it is shown that a full wave method that uses the complex pressure field as data is nonlinear, the nonlinearity increasing with frequency and waveguide thickness. Methods that use modal eigenvalues as input data are only weakly nonlinear and can successfully yield estimates with acceptable resolution if the experiment is performed over a number of frequencies. In the case of deep water experiments, however, the experimental configuration can be so arranged as to make methods based on full wave inversion only weakly nonlinear.
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High‐resolution matched‐field inversion of ocean sediment parameters with simulated annealing (A)

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

J. Acoust. Soc. Am. Volume 89, Issue 4B, pp. 1874-1874 (1991); (1 page)

Online Publication Date: 14 Aug 2005

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High‐resolution inversion of ocean sediment parameters is possible with matched‐field processing. If the ocean bottom is complicated, matched‐field inversion requires an efficient nonlinear optimization method such as simulated annealing [Kuperman et al., J. Acoust. Soc. Am. 88, 1802 (1990)] to search the high‐dimensional parameter landscape, which can have many local minima. An efficient propagation model is also essential because the wave equation must be solved many times. Single‐frequency matched‐field inversion simulations have been performed using various types of source and receiver arrays, including an array of sources beamed toward the ocean bottom, for problems involving fluid sediments, elastic sediments, and range dependence. The acoustic and elastic parabolic wave equations are used to construct replica fields for range‐dependent inversion problems. For problems that can be regarded as range independent between the sources and receivers, large gains in efficiency can be achieved by working in wave number space using the synthetic aperture approach [G. V. Frisk and J. F. Lynch, J. Acoust. Soc. Am. 76, 205 (1984)] because the number of wave number samples required for inversion is much smaller than the number of wave number samples required to construct replica fields.
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An overview of the tomographic forwnrd/inverse problem (A)

Bruce D. Cornuelle and Bruce M. Howe

J. Acoust. Soc. Am. Volume 89, Issue 4B, pp. 1874-1874 (1991); (1 page)

Online Publication Date: 14 Aug 2005

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In ocean acoustic tomography, the travel time along a ray path is a weighted average of the propagation speed along the path. Because oceanographers generally have intuition about point measurements or simple averages, it has been necessary to transform travel time data into point values (maps) before communicating the results. The transformation can be done with a variety of methods, ranging from exhaustive Monte Carlo searches to Backus‐Gilbert constrained estimation. The transformation converts travel time data with more or less independent errors to point value estimates with correlated errors that may have complicated, nonlocal structure. Since the error bars usually presented with an ocean map do not include the correlations, they do not accurately reflect the information content of a tomographic dataset. In addition, it is no longer possible to distinguish between the data errors and sampling blind spots by examining the error bars (or even the error covariances). Communicating tomographic results thus requires more effort, and more plots. Resolution (or averaging) kernels show how the estimate at a point is a weighted average of the entire field (with the average becoming more local as the number of rays increases). Null space vectors show fields that may be added to the estimated map without changing the data significantly. Given that the goal of ocean observations is to test dynamical hypotheses, it is also reasonable to consider transforming hypotheses into constraints on the travel times, rather than transforming the travel times into constraints on physical space hypotheses. [Work supported by ONR and ONT.]
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On the use of ocean dynamics to improve acoustic tomography estimates (A)

Ching‐Sang Chiu and James H. Miller

J. Acoust. Soc. Am. Volume 89, Issue 4B, pp. 1874-1874 (1991); (1 page)

Online Publication Date: 14 Aug 2005

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The resolution of maps obtained from ocean acoustic tomography is largely determined by the trajectories of the acoustic multipaths connecting sources and receivers. Since the distribution of crossings of the multipaths is nonuniform, tomographic resolution generally varies in space. Thus, depending on the characteristics of the sound channel and the scales of the ocean variability, “pure acoustic maps” can be inaccurate in those locations where spatial resolution is poor. In order to improve the resolution of the maps, it is necessary to add independent information to the inverse problem. In a computer experiment, the improvement in the tomography maps resulting from the incorporation of ocean dynamics is assessed. Here, the integration of dynamical information into tomography is accomplished using a Kalman filter. For the assessment, the maps obtained by assimilating synthetic tomography data into a nonlinear, quasigeostrophic ocean model are compared with the “pure acoustic maps.” Moreover, the sensitivity of the Kalman filter output to the inexact specification of ocean dynamics is examined.
Contributed Papers
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Converting bottom loss measured from a rough layered sediment to the equivalent “flat bottom” loss (A)

Diana F. McCammon

J. Acoust. Soc. Am. Volume 89, Issue 4B, pp. 1875-1875 (1991); (1 page)

Online Publication Date: 14 Aug 2005

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In the BLUG parameter‐estimation technique, measured bottom loss is inverted to obtain a “best‐fit” set of ten geoacoustic parameters that characterize the sediment. This inversion process has been improved and automated with Monte Carlo methods; however, in spite of these advances, the inversion process can still give poor results, notably in rough thin sediment regions, because the inversion model assumes flat interfaces between water, sediment, and basement. The purpose of this paper is to describe a correction factor that can be applied to the measured data to convert it from rough surface loss to the equivalent loss if the interfaces had been smooth. With this correction, the data can be made to conform to the assumptions of the model, which should lead the inversion process to a better fitting set of parameters. Four examples of this application are shown; in two thin sediment cases, the correction gave improved model/data correlations and lower squared errors; in the two smoother thicker sediment cases, the correction did not significantly affect the result. [Work supported by NAVOCEANO.]
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Time domain inversion of two‐dimensional velocity fields using simulated annealing (A)

P. Gerstoft, J. M. Pedersen, and P. D. Vestergaard

J. Acoust. Soc. Am. Volume 89, Issue 4B, pp. 1875-1875 (1991); (1 page)

Online Publication Date: 14 Aug 2005

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Inversion of scattered sound fields caused by horizontal and lateral velocity variations can be done using an efficient Monte Carlo method called simulated annealing. The subsurface contains large velocity variations in both depth and range and thus, for inversion of transient signals, at least a two‐dimensional (2‐D) representation of the velocity field is required. This 2‐D description requires that the nonlinear inversion is carried out in a huge parameter space. Standard local optimization methods will be trapped in local minima and a search throughout is computationally prohibitive. Thus the simulated annealing method is used. The present implementation is here based on an ensemble approach whereby several copies are annealed simultaneously. By using several copies it is possible to obtain statistical information about the optimal cooling rate. In order to make the method converge in acceptable time, both optimization and the forward modeling method of the inversion have to be fast. Thus geometrically flexible but computationally exhaustive methods such as finite difference are not yet used. At present, the forward modeling is done by either the one‐dimensional convolution model or ray tracing. The 2‐D effect of the one‐dimensional convolution is obtained by geometrically requiring the structure to be stratified with a weak variation in range. For the ray tracing, the substructure shall also be stratified but here the wave propagation is in a real 2‐D environment.
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Linearization of the matched‐field processing approach to acoustic tomography (A)

A. Tolstoy

J. Acoust. Soc. Am. Volume 89, Issue 4B, pp. 1875-1875 (1991); (1 page)

Online Publication Date: 14 Aug 2005

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This paper continues the approach presented in Tolstoy et al. [J. Acoust. Soc. Am. 89, 1119–1127 (1991)] but offers a much improved inversion technique, i.e., a linearization of the problem, which reformats the computations in terms of simple nonsquare matrix inversion for an overdetermined system. This linearization results in sound‐speed accuracies that are an order of magnitude better than the earlier technique. In addition, calculations confirm that for simulations with white, Gaussian, uncorrelated noise, the linear/Bartlett processor results are identical to those of the minimum‐variance/Capon processor. Finally, optimal source‐receiver configurations have been determined by exhaustively computing the condition numbers for the associated matrices in the new linear formulation. Simulation results now show that three arrays located at optimal coordinates in a 250‐ by 250‐km ocean region with shot sources distributed around the perimeter can result in 3‐D sound‐speed profiles determined to accuracies better than 0.07 m/s and better than 0.03 m/s for four arrays located at optimal coordinates. Such results presently assume perfect knowledge of sound‐speed profiles at the arrays and around the region perimeter.
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Matched‐field processing (MFP) tomography for inverting the El Niño profile (A)

E. C. Shang and Y. Y. Wang

J. Acoust. Soc. Am. Volume 89, Issue 4B, pp. 1875-1875 (1991); (1 page)

Online Publication Date: 14 Aug 2005

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The matched‐field processing (MFP) method has been substantially applied for source localization studies in recent years. It has been demonstrated that the MFP is very sensitive to the mismatch of sound‐speed profile (SSP) with a high‐resolution MFP estimator. It turns out that the high‐resolution MFP is also a potential powerful tool for SSP inverting with a known source‐receiver system [A. Tolstoy and O. Diachok, J. Acoust. Soc. Am. Suppl. 1 88, S117 (1990)]. In this paper, the high‐resolution mode matching (HRMM) estimator [E. C. Shang, J. Acoust. Soc. Am. 86, 1960 (1989)] has been used for El Niño profile inverting. By matching a proper set of modal travel time perturbation, the El Niño profile can be efficiently inverted in a 2‐D parameter space based on a simple acoustic model of the 1982‐1983 El Niño event. [Work supported by ONR and NOAA.]
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Tomographic reconstruction of stratified fluid flow (A)

Daniel Rouseff, Kraig B. Winters, and Peter Kaczkowski

J. Acoust. Soc. Am. Volume 89, Issue 4B, pp. 1875-1875 (1991); (1 page)

Online Publication Date: 14 Aug 2005

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A new method for imaging a moving fluid using acoustic tomography is evaluated by numerical simulation. A cross section of the medium is probed by high‐frequency acoustic waves from several different directions. It can be shown that the resulting measured travel time data contain sufficient information to reconstruct both the spatially varying sound speed and the transverse component of the fluid vorticity [K. B. Winters and D. Rouseff, Inverse Problems 6, L33 (1990)]. The results are exact to within the validity of the straight‐ray geometric acoustics approximation. To evaluate a discrete version of the reconstruction algorithm, a three‐dimensional stably stratified mixing layer is simulated. The flow exhibits characteristic features in both density (sound speed) and vorticity. The dynamics of the fluid flow can be described as the instability of a vortex sheet. The acoustic travel time is calculated by integrating through the simulated flow fields. The synthetic data are then inverted to yield reconstructions of both the density and the vorticity of the evolving flow. [Work supported in part by the U.S. Navy under Contract No. N00039‐89‐C‐0001.]
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