Range-dependent Ocean Environments Research Articles

A Chebyshev–Tau spectral method for coupled modes of underwater sound propagation in range-dependent ocean environments

A coupled-mode model is a classic approach for solving range-dependent sound propagations and is often used to provide benchmark solutions in comparison with other numerical models because of its high accuracy. Existing coupled-mode programs have disadvantages such as high computational cost, weak adaptability to complex ocean environments, and numerical instability. In this paper, a new algorithm that uses an improved range normalization of a “stair-step” and global matrix approach to address range dependence in ocean environments is designed. This algorithm uses the Chebyshev–Tau spectral method to solve the eigenpairs in the range-independent segments. The Chebyshev–Tau spectral method can converge rapidly, and the rate of convergence depends on the smoothness of the sound speed and density profiles. The main steps of the algorithm are parallelized, so parallel computing technologies are also applied for further acceleration. Based on this algorithm, an efficient program is implemented, and numerical simulations verify that this algorithm is reliable, accurate, and capable. Compared with the existing coupled-mode programs, the newly developed program is more stable and efficient with comparable accuracy and can simulate waveguides in more complex and realistic ocean environments.

A novel algorithm to solve for an underwater line source sound field based on coupled modes and a spectral method

A high-precision numerical sound field is the basis of underwater target detection, positioning and communication. A line source in a plane is a common type of sound source in computational ocean acoustics. The exciting waveguide in a range-dependent ocean environment is often structurally complicated; however, traditional algorithms often assume that the waveguide has a simple seabed boundary and that the line source is located at a horizontal range of 0 m, although this ideal situation is rarely encountered in the actual ocean. In this paper, a novel algorithm is designed that can solve for the sound field excited by a line source at any position in a range-dependent ocean environment. The proposed algorithm uses the classic stepwise approximation approach to address the range dependence of the environment and uses the Chebyshev–Tau spectral method to solve for the horizontal wavenumbers and modes of approximately range-independent segments. Once the modal information of these flat segments has been obtained, a global matrix is constructed to solve for the coupling coefficients of all segments, and finally, the complete sound field is synthesized. Numerical experiments using a robust numerical program developed based on this algorithm verify the correctness and usability of our novel algorithm and software. Furthermore, a detailed analysis and test of the computational cost of this algorithm show that it is efficient.

A coupled mode model for omnidirectional three-dimensional underwater sound propagation.

A fully three-dimensional (3D) omnidirectional numerical coupled mode model of acoustic propagation is detailed. A combination of normal mode and finite element computational methods is applied to produce the numerical results. The technique is tested in a strongly range-dependent ocean environment modeled after the Hudson Canyon. Modeled sound from three source locations selected over different bathymetric depths is examined to determine capabilities and difficulties associated with varying numbers of propagating vertical modes across the horizontal domain, and variable amounts of mode coupling. Model results are compared to those from a unidirectional Cartesian 3D parabolic equation simulation, and from adiabatic (uncoupled) simulations to illustrate the capabilities of the techniques to study the influences of coupling, strong refraction, and reflection.

An immersed interface method for the solution of the standard parabolic equation in range-dependent ocean environments.

A numerical approach for the treatment of irregular ocean bottoms within the framework of the standard parabolic equation is proposed. The present technique is based on the immersed interface method originally developed by LeVeque and Li [(1994). SIAM J. Numer. Anal. 31(4), 1019-1044]. The method conserves energy to high order accuracy and naturally handles generic range-dependent bathymetries, without requiring any additional specific numerical procedure. An illustration of its capabilities is provided by solving the well-known wedge problem.

An immersed interface method for the solution of the wide-angle parabolic equation in range-dependent ocean environments

An immersed interface method for the solution of the wide-angle parabolic equation in range-dependent ocean environments

An experimental benchmark for geoacoustic inversion methods

Over the past 25 years, many methods have been developed for estimating parameters of geoacoustic models of the ocean bottom from acoustic field data. The methods involved model-based comparisons between experimental data and calculated fields or field quantities. Benchmarking workshops based on simulated field data confirmed the ability of the methods for inverting geoacoustic model parameters for range-independent and range-dependent ocean environments. Although there are many published examples of geoacoustic inversions in various different ocean environments, the methods have not been tested in an experimental benchmark. This paper describes the design of an experimental benchmark for geoacoustic inversion methods, and presents an analysis of the performance of the methods with experimental data. The benchmark involves application of different inversion methods to data spanning a frequency band from 50to 2500 Hz that were obtained at a single well-surveyed ocean bottom site. The performance metric involves comparisons of: estimated geoacoustic profiles against the ground truth information of the site; modal wavenumbers for the inverted models; and transmission loss calculations based on the estimated models against measured data. The analysis shows that the methods are capable of estimating realistic geoacoustic profiles, with sound speed the most reliable estimated model parameter.

Development of Range-Dependent Ray Model for Sonar Simulator

소나 시뮬레이터에 적용되는 음파 전달 알고리즘은 빠른 계산 성능이 요구되며, 한국 해양 환경의 특성을 고려하여 거리와 깊이 방향의 환경 의존성을 구현할 수 있어야 한다. 이러한 요구사항을 충족하는 음파 전달 알고리즘은 음선 모델이며, 본 논문에서는 거리 종속 해양환경의 음선 알고리즘을 개발하였다. 본 알고리즘에서는 사각 격자법과 층법으로 음선을 추적하여 음속 구조의 깊이 방향 의존성을 고려하였으며, 거리 방향은 split-step 개념을 적용하여 음속구조의 거리 방향 의존성을 구현하였다. 고유음선은 음선 묶음의 보간법을 통해 계산되었으며, 가우시안 보간 함수가 적용되었다. 소나의 시계열 수신 신호는 음원 신호와 고유 음선 주파수 해의 푸리에 변환을 이용하여 모의되었다. 최종적으로 제안된 음파 알고리즘을 검증하기 위해 Pekeris 도파관, 쐐기, 심해의 환경에서 전달손실 결과를 BELLHOP, SNUPE, KRAKEN, OASES 등 검증된 모델의 결과와 비교하였으며, 결과적으로 만족스런 결론을 얻을 수 있었다. Sound propagation algorithm for a sonar simulator is required to run in real-time and should be able to model the range and depth dependence of the Korean ocean environments. Ray model satisfies these requirements and we developed an algorithm for range-dependent ocean environments. In this algorithm, we considered depth-dependence of sound speed through rays based on a rectangular cell method and layer method. Range-dependence of sound speed was implemented based on a split-step method in the range direction. Eigen-ray is calculated through an interpolation of ray bundles and Gaussian interpolation function was used. The received time signal of sonar was simulated by Fourier transform of eigen-ray solution in the frequency domain. Finally, for the verification of proposed algorithm, we compared the results of transmission loss with other validated models such as BELLHOP, SNUPE, KRAKEN and OASES, for the Pekeris waveguide, wedge, and deep ocean environments. As a result, we obtained satisfactory agreements among them.

Elastic parabolic equation solutions for underwater acoustic problems using seismic sources

Several problems of current interest involve elastic bottom range-dependent ocean environments with buried or earthquake-type sources, specifically oceanic T-wave propagation studies and interface wave related analyses. Additionally, observed deep shadow-zone arrivals are not predicted by ray theoretic methods, and attempts to model them with fluid-bottom parabolic equation solutions suggest that it may be necessary to account for elastic bottom interactions. In order to study energy conversion between elastic and acoustic waves, current elastic parabolic equation solutions must be modified to allow for seismic starting fields for underwater acoustic propagation environments. Two types of elastic self-starter are presented. An explosive-type source is implemented using a compressional self-starter and the resulting acoustic field is consistent with benchmark solutions. A shear wave self-starter is implemented and shown to generate transmission loss levels consistent with the explosive source. Source fields can be combined to generate starting fields for source types such as explosions, earthquakes, or pile driving. Examples demonstrate the use of source fields for shallow sources or deep ocean-bottom earthquake sources, where down slope conversion, a known T-wave generation mechanism, is modeled. Self-starters are interpreted in the context of the seismic moment tensor.

Scattering from extended targets in range-dependent fluctuating ocean-waveguides with clutter from theory and experiments

Bistatic, long-range measurements of acoustic scattered returns from vertically extended, air-filled tubular targets were made during three distinct field experiments in fluctuating continental shelf waveguides. It is shown that Sonar Equation estimates of mean target-scattered intensity lead to large errors, differing by an order of magnitude from both the measurements and waveguide scattering theory. The use of the Ingenito scattering model is also shown to lead to significant errors in estimating mean target-scattered intensity in the field experiments because they were conducted in range-dependent ocean environments with large variations in sound speed structure over the depth of the targets, scenarios that violate basic assumptions of the Ingenito model. Green's theorem based full-field modeling that describes scattering from vertically extended tubular targets in range-dependent ocean waveguides by taking into account nonuniform sound speed structure over the target's depth extent is shown to accurately describe the statistics of the targets' scattered field in all three field experiments. Returns from the man-made targets are also shown to have a very different spectral dependence from the natural target-like clutter of the dominant fish schools observed, suggesting that judicious multi-frequency sensing may often provide a useful means of distinguishing fish from man-made targets.

Scattering from extended targets in a range-dependent fluctuating ocean waveguide from theory and experiments where the sonar equation is invalid.

Bi-static, long-range measurements of acoustic scattered returns from vertically extended, air-filled cylindrical targets were made during three separate ONR-sponsored field experiments in fluctuating continental shelf environments. We show that the sonar equation estimates of mean scattered intensity from these targets lead to large errors, differing by an order of magnitude from both our measurements and waveguide scattering theory. This is because the sonar equation approximation is not applicable to targets large compared to the acoustic wavelength in an ocean waveguide. We find that use of the Ingenito scattering model also leads to significant errors in estimating mean target scattered intensity in our field experiments because they were conducted in range-dependent ocean environments with large variations in sound speed structure over the depth of the targets, scenarios that violate the basic assumptions of the Ingenito model. Here we describe scattering from extended cylindrical targets in a range-dependent fluctuating ocean waveguide using a Green’s theorem based full-field model that takes into account nonuniform sound speed structure over the target’s depth extent. We show that this model accurately describes the statistics of the acoustic field scattered by the targets in all three field experiments.

MEASUREMENT AND SIMULATION FOR WIND NOISES IN THE OCEAN ENVIRONMENTS WITH NONLINEAR INTERNAL WAVES

This study obtains wind noise variations by experimental data and simulated results to describe meteorological and oceanic effects. The ambient noise data were measured by a vertical line array in the 2001 ASIAEX South China Sea experiment. An acoustic propagation model is used in noise modeling for calculating the sound pressure of noises at receiving sites, including the effects of ocean environmental changes, bottom interactions, and noise fluctuations at different depths. Both range-independent and range-dependent sound speed profiles are generated with in-situ water temperature data. Results show fluctuating noise levels with variations in ocean environments. But the fluctuations are small such that only weak correlation exists in the acoustic noise data and ocean data. Results also indicate that using range-independent sound speed profiles can simulate noise field in range-dependent ocean environments with nonlinear internal waves for shallow regions with flat bottoms.

Rytov approximation of tomographic receptions in weakly range-dependent ocean environments

An approximation method based on the Born and Rytov approximation is presented for the wave-theoretic prediction of acoustic arrival patterns associated with long-range pulse propagation in weakly range-dependent ocean environments. The environment is considered as a perturbation of a range-independent background state, and normal-mode theory is used, for the representation of the background Green’s function. Using the Born and Rytov approximations, the perturbed Green’s function corresponding to the range-dependent environment is expressed for each frequency within the source bandwidth in terms of the background Green’s function and the medium (sound-speed) perturbation. The actual arrival pattern in the time domain is then computed through the inverse Fourier transform. Using the normal-mode representation, closed-form expressions for the first and second Born and Rytov approximations are derived, generalizing previous range-independent results, and indicating that the effect of range dependence on the acoustic field in the case of adiabatic perturbations is of second order. To cope with the multimodal nature of ocean acoustic propagation, a variation of the standard Rytov method is applied, proposed by Keller, according to which each modal component must be treated independently. A number of numerical examples demonstrate an advantage of the Rytov approximation (over the Born approximation) for time-domain calculations.

Study on Range-Dependent Evolution of the Mode Eigenvalue by Using the Wigner Distribution Function

In an attempt to obtain the eigenvalues of local modes in a range-dependent ocean environment, the Wigner distribution function (WDF) is exploited in the range-wavenumber domain, instead of in the time-frequency domain, in analogy with time-dependent signal processing. In the first place, it is confirmed that the WDF can extract the exact eigenvalues for the acoustic field simulated in a horizontally stratified environment. Then, the WDF is applied to a range-dependent field simulated using the parabolic equation model. Consequently, the WDF peaks are recognized to evolve laterally in the same manner as local modes; however, some of the small peaks are difficult to identify due to the affection of false images generated in the WDF. As a result of applying a technique to enhance the amplitude of those peaks, their identification can be improved.

Geoacoustic inversion in range-dependent ocean environments using a plane wave reflection coefficient approach

A new, efficient, versatile ray-based model is presented that performs geoacoustic inversions in range-dependent ocean waveguides faster than alternative forward models for which the computation time becomes extremely long, especially for broadband inversions. The water propagation is approximately separated from the seabed interaction using predetermined bathymetry and a possibly range-dependent water sound speed profile. The geometrical optics approximation is used to calculate eigenrays between sources and receivers, including bottom reflecting paths. Modeled broadband pressure fields are obtained by computing the plane wave reflection coefficient at specific angles and frequencies and by then linking this result with the bottom reflected eigenrays. Each perturbation of the seabed requires a recalculation of the plane wave reflection coefficient, but not a recalculation of the eigenrays, resulting in a highly efficient method. Range-independent problems are treated as a limiting case of the approach. The method is first described and then demonstrated with a few simple range-independent theoretical models. The versatility of addressing range-dependence in the bottom seabed is demonstrated with a simulated data set. Finally, the new model is applied to inversion from a measured data set, taken with impulsive sources, for both range-independent and range-dependent continental shelf environments.

Numerical study of geoacoustic inversion in range-dependent ocean environments

Simulated acoustic data for two-dimensional waveguides were used to estimate the properties of a sea bed over which the depth of the water column varies with range. The simulated data were produced by a parabolic equation method. No approximate knowledge of the local sea-bed representation or parameter bounds was given prior to the inversions. In addition, little approximate information was given on the nature of the range dependence of the sea bed. The inversion methodology used a simulated annealing approach and a variation of the algorithm that generated the original acoustic data. For the purpose of consistency, a second method was employed, which used the same simulated annealing approach but with a range-dependent ray approach in which the sea-bed interaction is described by a complex plane wave reflection coefficient. Various combinations of frequencies and source-receiver positions commonly used in real acoustic measurements at sea were selected for the inversions. The goal of the inversion was to efficiently achieve a coarse description of the environment by several inversions; short-range data at low frequencies were employed for the purpose of efficiency. In the later stages of the inversion process, data from longer ranges and higher frequencies were included to provide additional details of the sea bed. Sea-bed parameters were assumed to vary linearly with range between geoacoustic profiles defined at specific ranges. Inversion results obtained prior to the reporting of the actual solutions are presented.

Study of a novel range-dependent propagation effect with application to the axial injection of signals from the Kaneohe source.

A novel range-dependent propagation effect occurs when a source is placed on the seafloor in shallow water with a downward refracting sound speed profile, and sound waves propagate down a slope into deep water. Under these conditions, small grazing-angle sound waves slide along the bottom downward and outward from the source until they reach the depth of the sound channel axis in deep water, where they are detached from the sloping bottom and continue to propagate outward near the sound channel axis. This "mudslide" effect is one of a few robust and predictable acoustic propagation effects that occur in range-dependent ocean environments. As a consequence of this effect, a bottom mounted source in shallow water can inject a significant amount of acoustic energy into the axis of the deep ocean sound channel that can then propagate to very long ranges. Numerical simulations with a full-wave range-dependent acoustic model show that the Kaneohe experiment had the appropriate source, bathymetry, and sound speed profiles that allows this effect to operate efficiently. This supports the interpretation that some of the near-axial acoustic signals, received near the coast of California from the bottom mounted source located in shallow water in Kaneohe Bay, Oahu, Hawaii, were injected into the sound channel of the deep Pacific Ocean by this mechanism. Numerical simulations suggest that the mudslide effect is robust.

Fast coupled-mode approximation for broad-band pulse propagation in a range-dependent ocean

An approximation method is proposed for the prediction of broad-band acoustic signals propagating in range-dependent ocean environments. The method is based on the one-way coupled-mode approach and uses second-order frequency expansions of eigenvalues, eigenfunctions, and coupling coefficients about the central frequency of the source. Exploiting analytic expressions for the frequency derivatives of eigenvalues and eigenfunctions, their frequency behavior over the source bandwidth is described from the solution of the vertical eigenvalue problem at the central (reference) frequency. The expansion obtained for the coupling coefficients enables their approximate evaluation at frequencies other than central in terms of reference quantities and, thus, bypasses the need for evaluative eigenfunctions in the intermediate range segments for these frequencies. The method is applied to a 600-km range-dependent section from the Thetis-2 tomography experiment in the western Mediterranean sea. A sufficient degree of accuracy is obtained, particularly for the low- and intermediate-order modes, corresponding to the intermediate and late part of the arrival pattern in the time domain. The approximation is faster by two orders of magnitude than the exact broad-band coupled-mode calculation.

On the use of matched-field processing and hybrid algorithms for vertical slice tomography

Matched-field processing and a hybrid scheme for vertical slice tomography are studied in characteristic cases of range-independent and range-dependent ocean environments using simulated data obtained at discrete points in the sound field along a vertical line, representing a vertical array of hydrophones. The matched-field processing is associated with a Genetic Algorithm, while the basic characteristic of the hybrid scheme is the application of matched-field processing for the definition of a reference environment to be subsequently used in connection with a modal-phase inversion scheme. In all cases studied, the sound-speed profiles are reconstructed with the use of empirical orthogonal functions. It is shown that the reconstruction of either the single sound-speed profile characterizing the range-independent environment, or the set of profiles characterizing an eddy in the range-dependent environment is achieved with good accuracy, despite the fact that a very wide search space has been considered. The apparent nonuniqueness in the solution of the inverse problem for the range-dependent case is remedied by applying physical constraints in the structure of the sea eddy and averaging over the admissible solutions obtained by the matched-field inversion scheme.

Rapid calculations of acoustic propagation loss in range dependent oceans

Calculation of transmission loss in range-dependent ocean environments usually involves CPU-intensive models that offer little insight into the problem. The authors present a new approach based on hybrid ray and mode concepts. A set of incoherent intensity formulas is given for different acoustic components of the propagation. The key points are the conservation of energy flux and the exploitation of the ray invariant to model weak range dependence. Predictions from these formulas are compared with benchmark solutions to demonstrate both their accuracy and the insight provided by the individual components.

Spectral super-element approach to range-dependent ocean acoustic modeling

The spectral super-element approach uses a hybridization of finite elements, boundary integrals, and wave-number integration to solve the Helmholtz equation in a range-dependent ocean environment. The range-dependent ocean is divided into range-independent sectors or super-elements. Wave-number integral representations can be derived for an influence matrix representing the relation between displacement and pressure expansions on the vertical boundaries. The integration kernels are determined very efficiently by the direct global matrix method in combination with a numerical quadrature scheme. The unknown expansion coefficients are then found by matching the boundary conditions of continuous displacement and stress between the sectors, with the acoustic field following by evaluating the wave-number integrals within each sector, e.g. using the FFP technique. Two different boundary matching schemes are applied. One solves the global coupling problem incorporating all multiple scattering. A second, more efficient approach applies a single-scatter approximation at each vertical sector boundary, allowing for a marching solution. Numerical solutions to a series of canonical benchmark problems are given and compared to solutions obtained by other numerical approaches such as parabolic equations and coupled modes.