Range-dependent Waveguide Research Articles

Matched field range and depth resolution in range-dependent waveguides

Estimates of range and depth resolution are required in order to determine computational grid spacings for matched field processing (MFP). In this paper it is shown how previous results for range-independent waveguides can be extended to account for range dependence by using standard adiabatic formulations. Significant differences in MFP resolution are observed for up-slope versus down-slope propagation due to changes in the path-integrated attenuation loss. MFP resolution is set by multipath interference lengths, so resolution estimates also relate to expected spatial scales for transmission loss fading.

Ray-based description of normal mode amplitudes in a range-dependent waveguide

An analogue of the geometrical optics for description of the modal structure of a wave field in a range-dependent waveguide is considered. In the scope of this approach the mode amplitude is expressed through solutions of the ray equations. This analytical description accounts for mode coupling and remains valid in a nonadiabatic environment. It has been used to investigate the applicability condition of the adiabatic approximation. An applicability criterion is formulated as a restriction on variations of the action variable of the ray.

An Estimate of the Bottom Compressional Wave Speed Profile in the Northeastern South China Sea Using “Sources of Opportunity”

The inversion of a broad-band "source of opportunity" signal for bottom geoacoustic parameters in the northeastern South China Sea (SCS) is presented, which supplements the towed source and chirp sonar bottom inversions that were performed as part of the Asian Seas International Acoustics Experiment (ASIAEX). This source of opportunity was most likely a "dynamite fishing" signal, which has sufficient low-frequency content (5-500 Hz) to make it complimentary to the somewhat higher frequency J-15-3 towed source (50-260 Hz) signals and the much higher frequency (1-10 kHz) chirp signals. This low frequency content will penetrate deeper into the bottom, thus extending the other inverse results. Localization of the source is discussed, using both a horizontal array for azimuthal steering and the "water wave" part of the pulse arrival for distance estimation. A linear broad-band inverse is performed, and three new variants of the broad-band inverse, based on: 1) the Airy phase; 2) the cutoff frequency; and 3) a range-dependent medium are presented. A multilayer model of the bottom compressional wave speed is obtained, and error estimates for this model are shown, both for the range-independent approximation to the waveguide and for the range-dependent waveguide. Directions for future research are discussed.

Variations of mode amplitudes in a range-dependent waveguide

An analogue of the geometrical optics for description of the modal structure of a wave field in a range-dependent waveguide is considered. In the scope of this approach the mode amplitude is expressed through solutions of the ray equations. This analytical description accounts for mode coupling and remains valid in a nonadiabatic environment. It has been used to investigate the applicability condition of the adiabatic approximation. An applicability criterion is formulated as a restriction on variations of the action variable of the ray.

COUPLED-MODE PREDICTION OF BACKSCATTER

The application of coupled-mode theory to ocean acoustic propagation and scattering requires that ideal boundary conditions be applied at the surface and within the seabed. The depth of the lower boundary imposes limits on the ability of coupled-mode models to treat propagation and scattering at high grazing angles. Selecting this depth to predict the contributions of the continuous spectrum in a range-independent two-layered waveguide is not practical, and other methods must be introduced to apply coupled-mode theory in the near field of a source. An example of up-slope propagation in a range-dependent waveguide in which backscatter is governed by ray steepening and reversal is also treated. With a careful choice of the depth at which the lower boundary condition is applied, an estimate of the backscattered field is obtained.

Effects of refraction on the prediction of bistatic reverberation in range dependent shallow water waveguides

The BiStaR bistatic reverberation model has been benchmarked against analytic formulas for bistatic reverberation in isovelocity range dependent waveguides. Studies conducted using BiStaR to evaluate the effects of introducing refraction into the benchmark scenarios indicate that downward refraction can have a tremendous effect on the time-angle evolution of mono- and bistatic reverberation, especially in shoaling directions. Here recent advances in analytic formulas for propagation and reverberation in refractive range dependent waveguides are exercised to evaluate analytically the predicted changes in RL caused by the different propagation characteristics. The analytic results are compared with the numerical results and conclusions are drawn regarding the propagation regimes and mechanisms that cause the strong deviations from the isovelocity predictions. [Work supported by ONR and SACLANTCEN.]

Geoacoustic inversion using a rotated coordinate system and simulated annealing

An efficient method for geoacoustic inversions in a range-dependent ocean waveguide is implemented and tested with synthetic data. This method combines a simulated annealing search with an optimal coordinate rotation that increases the efficiency of navigating parameter landscapes for which parameter coupling is important. The coordinate rotation associated with the parameter couplings also provides information about which parameters are resolvable for a particular inversion frequency and array geometry. Using this information, results from several single-frequency inversions can be combined to obtain an estimate for the sediment parameters.

Benchmarking geoacoustic inversion methods for range-dependent waveguides

Inversion methods have been developed over the past decade to extract information about unknown ocean-bottom environments from acoustic field data. This paper summarizes results from the Office of Naval Research/Space and Naval Warfare Systems Command (SPAWAR) Geoacoustic Inversion Techniques Workshop, which was designed to benchmark present-day inversion methods. The format of the workshop was a blind test to estimate unknown geoacoustic profiles by inversion of synthetic acoustic field data. The fields were calculated using a high-angle parabolic approximation and verified using coupled normal modes for three range-dependent shallow-water test cases: a monotonic slope; a shelf break; and a fault intrusion in the sediment. Geoacoustic profiles were generated to simulate sand, silt, and mud sediments in these environments. Several different approaches for inverting the acoustic field data were presented at the workshop: model-based matched-field methods; perturbation methods; methods using transmission loss data; and methods using horizontal array information. An effective inversion must provide both an estimate of the bottom parameters and a measure of the uncertainty of the estimated values. New methods were presented at the workshop to formalize the measure of uncertainty in the inversion. Comparisons between the different inversions are discussed in terms of a metric-based transmission loss calculated using the inverted profiles. The results demonstrate the effectiveness of present-day inversion techniques and indicate the limits of their capabilities for range-dependent waveguides.

Coupled-mode sound propagation in a range-dependent, moving fluid.

Full-field acoustic methods for current velocity inversion require accurate and efficient mathematical models of sound propagation in a range-dependent waveguide with flow. In this paper, an exact coupled-mode representation of the acoustic field is derived. To account for the physics of the problem, normal modes in a corresponding range-independent waveguide are chosen as the local basis. In the absence of currents, mode shape functions form a complete orthogonal basis. This property is heavily used in coupled-mode theories of sound propagation in motionless fluid. Unlike in the motionless case, however, vertical dependencies of acoustic pressure in individual normal modes are not orthogonal in the presence of currents. To overcome this difficulty, linearized equations of hydrodynamics are rewritten in terms of a state vector. Its five components are expressed in terms of acoustic pressure and particle displacement due to the wave. Orthogonality of the state vectors corresponding to individual normal modes is established. Coupled differential equations are derived for range-dependent mode amplitudes, leading to a remarkably simple result. The mode-coupling equations have the same form as those known for the motionless case, but of course the values of the mode-coupling coefficients differ as long as the range dependence of the flow velocity contributes to mode coupling in addition to the range dependence of sound speed and fluid density. The mode-coupling formulation is verified against known coupled-mode equations for certain limiting cases and an exact analytic solution of a benchmark problem.

Nonadiabatic travel time and time series synthesis in range dependent waveguides

A WKB approximation for the range dependent modal group slownesses and dispersions in a range dependent waveguide is derived. The resulting slownesses can be used to synthesize time series in a narrow band or over broader bandwidths by adding narrow band results together coherently. The slownesses themselves are also highly useful intermediate products which help give insight into the speeds with which the modes of a range dependent waveguide propagate. The range dependent modal group slownesses are compared to their adiabatic approximations and conclusions are drawn regarding the relative accuracy of these two approximations for time series synthesis.

The ray approach for analyzing the modal structure of the sound field in a range-dependent waveguide

Simple ray-approximation formulas are obtained for the mode amplitudes in a waveguide with range-dependent parameters. The idea of the proposed approach is based on the mode expansion of the complex field amplitude determined using the geometrical-optics approximation. A specific example of calculating mode amplitudes is analyzed for a deep-water sound channel with a sound speed profile nonadiabatically varying with distance. The results of the calculation are compared with the numerical solution obtained for the same problem by the parabolic equation method.

Evaluation of the smoothed interference pattern under conditions of ray chaos.

A ray-based approach has been considered for evaluation of the coarse-grained Wigner function. From the viewpoint of wave propagation theory this function represents the local spectrum of the wave field smoothed over some spatial and angular scales. A very simple formula has been considered which expresses the smoothed Wigner function through parameters of ray trajectories. Although the formula is ray-based, it nevertheless has no singularities at caustics and its numerical implementation does not require looking for eigenrays. These advantages are especially important under conditions of ray chaos when fast growing numbers of eigenrays and caustics are the important factors spoiling applicability of standard semiclassical approaches already at short ranges. Similar factors restrict applicability of some semiclassical predictions in quantum mechanics at times exceeding the so-called "logarithm break time." Numerical calculations have been carried out for a particular model of range-dependent waveguide where ray trajectories exhibit chaotic motion. These calculations have confirmed our conjecture that by choosing large enough smoothing scales, i.e., by sacrificing small details of the interference pattern, one can substantially enhance the validity region of ray theory. (c) 2000 American Institute of Physics.

Wave chaos in terms of normal modes

Wave propagation in a range-dependent waveguide can be considered as a classical physics problem similar to the quantum chaos problem situations. This analogy becomes especially strong when one uses the parabolic equation approximation. By projecting the wave field taken in the quasiclassical approximation onto eigenfunctions of the unperturbed boundary value problem, analytical description has been obtained for normal mode amplitudes in terms of geometrical optics relations. This approach provides a convenient way to study how chaotic behavior of ray trajectories reveals itself in a range dependence of mode amplitudes, and, hence, in the solution of the wave equation. An analog to nonlinear ray-medium resonance for normal modes has been investigated in details and the impact of this phenomenon on modal structure is discussed. It is argued that overlapping of different mode-medium resonances causes a complicated range dependence of mode amplitude in almost the same manner as the overlapping of ray-medium resonances leads to ray chaos.

Wave propagation in range-dependent poro-acoustic waveguides

The parabolic equation method is extended to handle range-dependent poro-acoustic waveguides. A poro-acoustic medium is the limiting case of a poro-elastic medium in which the shear wave speed vanishes. Recent experiments indicate that this is a relevant limit [Chotiros, “Biot model of sound propagation in water-saturated sand,” J. Acoust. Soc. Am. 97, 199–214 (1995)]. Energy-conserving and single-scattering techniques are developed for handling vertical interfaces. The single-scattering solution is extended to problems involving fluid layers above poro-acoustic sediments. Improved rational function approximations are developed by rotating the branch cut [Milinazzo et al., “Rational square-root approximations for parabolic equation algorithms,” J. Acoust. Soc. Am. 101, 760–766 (1997)].

A three-dimensional analysis of sound propagation in facetted geometries

An analytical technique is presented for computation of the three-dimensional sound field due to an harmonic, point source in a range-dependent waveguide formed with two or more plane facets. The waveguide is assumed to be homogeneous with ideal (perfectly reflecting) boundaries. The theory is based on a development of the method of source images. The idea of a source image is abstracted into a set of reflections (a generating sequence) and a criterion for determining whether an image contributes to the sound field (a visibility criterion). These generalizations allow a solution to be built up without reference to a specific plane geometry. The sound field in a parallel-sided duct terminated by a wedge is calculated as an example of the technique.

Solutions of coupled-mode equations with a large dimension in underwater acoustics

A method is presented for the solution of coupled-mode equations for sound propagation in a range-dependent waveguide. By following a new approach recently introduced in nuclear theory, the coupled-mode equations are modified and then solved using the Lanczos method. Calculations are made for isovelocity waveguides with rigid bell-shaped bathymetries having large slopes. Convergence properties and computer CPU times are examined as a function of the dimension of the coupled-mode equations and the nature of the coupling. The efficiency of the approach is shown to increase as the dimension of the coupled-mode equations increases.

Causality and conservation of energy : their implications for prediction of receiver performance

The paper is concerned with the analysis of receiver performance in range-dependent waveguides. The problem is shown to be amenable to a simple theoretical treatment. The necessary analytical technique is based on the application of the principle of causality and the low of conservation of energy. The focus of the analysis is on prediction of limiting capabilities of an optimum detector of quasi-deterministic signals in irregular multi-mode channels. Explicit analytical formulae are derived for the probability of detection, the far-field directivity function and the Cramer-Rao bound for mean-root-square errors in estimates of signal parameters. The theory presented reveals clear physical limits on capabilities of signal processing technique in non-uniform oceanic environment

Scalar measures of modal amplitude distributions in range-dependent waveguides

In a shallow water waveguide with a depth-dependent sound velocity profile, the short-range modal amplitude distribution depends strongly upon the sound-speed profile at the source. At sufficiently high frequency, a source in the high-velocity portion of the water column excites primarily the higher-order modes while a source in the lower-velocity portion of the water column couples more strongly with the lower-order modes. Scalar measures, such as the correlation, cross-entropy and information divergence are used in this paper to differentiate between different modal amplitude distributions by projecting the cross-spectral density matrix (CSDM) onto the eigenvectors of a baseline CSDM. Environmental features which cause mode coupling (e.g., bottom slope) diminish the effectiveness of these measures. The robustness of these scalar measures in the presence of the mode coupling is examined. [Work sponsored by Office of Naval Research, Code 4530.]

An energy-conserving parabolic equation for elastic media

The accuracy of the parabolic equation (PE) method is improved for range-dependent elastic media. The energy-conserving elastic PE is a generalization of the energy-conserving acoustic PE. A range-dependent waveguide is approximated by a sequence of range-independent regions. A linear approximation is derived for the nonlinear condition corresponding to conservation of compressional energy flux at the vertical interfaces between range-independent regions. The rotated elastic PE is applied to generate reference solutions for demonstrating accuracy. The energy-conserving elastic PE is applied to solve problems involving the propagation of an interface wave along a sloping ocean bottom and a problem involving mode cutoff and coupling into shear wave beams in the ocean bottom. The latter problem is analogous to a cutoff problem that was first solved with the acoustic PE [F. B. Jensen and W. A. Kuperman, J. Acoust. Soc. Am. 67, 1564–1566 (1980)].

Low-frequency Arctic reverberation. II: Modeling of long-range reverberation and comparison with data

In the Arctic ocean, very low-frequency (10–50 Hz) reverberation returns from the ice and bottom both contribute to the total received reverberation and are not easily distinguishable in long-range reverberation data, except where there is a dominant bottom or ice feature. In this paper, a normal-mode model of scattering from surface and bottom protuberances is applied to model long-range reverberation data collected during the CEAREX 89 experiment in the Norwegian/Greenland Seas. Modeled reverberation spectrum levels at 23 Hz are compared with data to investigate the relative contributions of the ice and bottom to the measured reverberation. The normal-mode model of boundary scattering is based on a generalization of recent work of Ingenito [F. Ingenito, J. Acoust. Soc. Am. 82, 2051–2059 (1987)] treating scattering from a rigid sphere in a stratified waveguide. Adiabatic normal mode theory is used to model the propagation to and back from the scatterer in a range-dependent waveguide. Using the small-ka approximation for the scattering functions, where k is the wave number and a is the dimension of the boundary protuberance, the normal-mode calculations of the long-range reverberation levels are found to agree rather well with the CEAREX data for four different measurements involving different bottom bathymetries and source depths. For a source at 91-m depth in the 3000-m-deep basin, it is found that the reverberation level for a receiver at 60 m is dominated by scattering from the ice except for reverberation associated with certain identifiable bottom features. For the same environment but a deeper (244-m) source, reverberation levels from the ice and bottom are more comparable. For a strongly range-dependent environment, returns from bottom features are clearly identifiable in the data.