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Geoacoustic inversion is a very important issue in underwater acoustics, and the inversion method based on bottom reflection loss is a valid technique to invert bottom parameters. This paper describes a Bayesian method for estimating bottom parameters in the deep ocean based on inversion of reflection loss versus angle data which were obtained from an experiment conducted in South China Sea in 2013. The experimental data show that bottom loss depends on frequency. The Bayesian method can be applied in nonlinear inversion problems, and it provides useful indication about the quality of the inversion and parameter sensitivities. The bottom is modeled as a two-layer model, and each layer has constant parameters. The inverted parameters of sediment show a clay feature which is consistent with the core data. Furthermore, the inversion results are used to calculate transmission losses (TLs) along the experiment track which agree well with the direct measurements. Although the inversion results are limited to reveal exact structures of bottom, they are still useful for forecasting propagation losses in this area. [ABSTRACT FROM AUTHOR]

The interference characteristics of cross-correlated broadband fields received by a single hydrophone deployed near the bottom at two different ranges are analyzed in this paper. The ray theory is used to derive the interference pattern, which is a combination of two kinds of interference phenomena. One kind of interference period contains the information of radial source velocity, and the other one is related to source depth. The source motion parameters, including the range and time of closet point of approach (CPA), constant source velocity and source depth, can be estimated by computing the Fourier transform of cross-correlated broadband fields when the existence of a CPA is apparent in the data. If the CPA is not evident, only the radial source velocity and the discrimination of surface versus submerged source can be provided. Note that the proposed method is a broadband technique. Experimental results confirm this single hydrophone estimation method of radial source velocity and source depth. [ABSTRACT FROM AUTHOR]

A method for denoising underwater acoustic signals used in applications of acoustical oceanography is presented. The method has been introduced for imaging denoising and has been modified to be applied with acoustic signals. The method keeps the energy significant part of the raw signal and reduces the effects of noise by comparing overlapping signal windows and keeping components which resemble true signal energy. It is shown by means of characteristic experiments in connection with a statistical signal characterization scheme based on wavelet transform, that using the statistical features of the wavelet sub-band coefficients of the denoised signal, tomography or geoacoustic inversions lead to a reliable estimation of the parameters of a marine environment. [ABSTRACT FROM AUTHOR]

The parabolic equation approximation method is applied to build the model of the vertical spatial correlation and vertical directivity characteristics of ocean ambient noise under varying environment. The random noise sources which have the same intensity are represented by uncorrelated monopoles distributed uniformly over an infinite plane located a certain depth below the sea surface. The spatial properties of noise field are analyzed under the varying ocean environments which are the slope, seamount and varying sound speed profiles. According to the results of simulation, the varying environment changes the propagating paths of noise, so the spatial properties (correlation and directionality) of the noise field change. When the remote noise intensity increases, the noise intensity in low grazing angle and the vertical correlations of nose field become stronger. At last, the experiment's results support the results of simulation. [ABSTRACT FROM AUTHOR]

In ocean waveguides, the ocean bottom is usually approximated as a half-space. Thus, there exist no reflection waves at the half-space bottom and condition of radiation at infinity should be satisfied. In numerical solutions like parabolic equation methods, the depth domain has to be truncated, which can generate reflection waves from the truncated ocean bottom. To reduce the effect of reflection waves and to simulate an unbounded ocean bottom accurately, an artificial absorbing layer (ABL) was used. As was demonstrated, an ABL meets well the demand of accuracy in sound field calculation. However, both the sea-bottom layer and the artificial absorbing layer are needed to be set quite thick by using an ABL technique. Fortunately, a PML with several wavelengths can keep similar calculation accuracy with an ABL with dozens of wavelengths. In this paper, perfectly matched layer (PML) techniques for three parabolic equation (PE) models RAM, RAMS and a three-dimensional PE model in underwater acoustics are presented. A key technique of PML 'complex coordinate stretching' is used to truncate unbounded domains and to simulate infinity radiation conditions instead of the ABL in those models. The numerical results illustrate that the PML technique is of higher efficiency than the ABL technique at truncating the infinity domain with minimal spurious reflections in PE models. [ABSTRACT FROM AUTHOR]

An introduction is presented in which the editor discusses various reports within the issue on topics including estimation of the sound speed gradient in the seabed, numerical model for the vertical noise directivity and removal of noise from the acoustic data.

We present a numerical implementation of an alternative formulation of the geometrical, or ray, acoustics, where wavefronts rather than rays are the primary objects. Rays are recovered as a by-product of wavefront tracing. The alternative formulation of the geometrical acoustics is motivated, first, by the observation that wavefronts are often more stable than rays at long-range sound propagation, and, second, by a need for computationally efficient modeling of high-frequency acoustic fields in three-dimensionally inhomogeneous, moving or motionless fluids. Wavefronts are found as a finite-difference solution to a system of partial differential equations, which is equivalent to the eikonal equation and is a direct implementation of the intuitive Huygens' wavefront construction. The finite-difference algorithm is an extension of the approach originally developed in the framework of an open source Madagascar project. Benchmark problems, which admit exact, analytic solutions of the eikonal equation, are formulated and utilized to verify the finite-difference wavefront tracing algorithm. Huygens' wavefront tracing (HWT) is applied to modeling sound propagation in three-dimensionally inhomogeneous ocean and atmosphere. [ABSTRACT FROM AUTHOR]

To investigate statistical problem of moderate to low-frequency sound scattering on the two-dimensional (2D) random inhomogeneities of a shallow sea with horizontal boundaries (bottom and surface) and loss local-mode approach has been utilized. An explicit-form solution by quadrature for modal amplitudes as a function of distance is represented. In adiabatic approximation asymptotical estimations have been performed, which demonstrate how medium weak fluctuations influence the local eigenvalues and statistical characteristics of a field. It is shown that general effects previously established while studying the random layered problem keep the force. Spatial scales of statistical influence and laws of dependences are determined. Also it follows from the analysis of the explicit-form solution for modal amplitudes that in this shallow-sea model with horizontal boundaries and in the absence of regular variations of sound speed the coupling of modes is insignificant. General statistical effects are described well within the framework of adiabatic approximation. [ABSTRACT FROM AUTHOR]

Solution of wide-band underwater acoustic problems with the classical Normal Mode method in the frequency domain needs to solve the problem repeating for every frequency component of the wide-band source signal. In this paper, a direct and causal analytical Time Domain Normal Mode Method is presented for arbitrary time-dependent acoustic sources for a single layered isovelocity waveguide. An incomplete separation of variables technique is used to solve the inhomogeneous wave equation, directly in the time domain. Therefore, it becomes possible to calculate the time domain acoustic pressure in a single run. [ABSTRACT FROM AUTHOR]

An efficient and accurate numerical frequency domain formulation is proposed to investigate the 2D acoustic wave propagation within a shallow water region with a rigid bottom and a free surface. The proposed configuration combines different regions that have either a sloping or a flat rigid bottom. The numerical approach used here is based on the method of fundamental solutions (MFS). In this model only the vertical interface between different regions is discretized, as the model incorporates Green's functions that take into account the free water surface and the presence of either a horizontal or sloping rigid bottom. [ABSTRACT FROM AUTHOR]

Ocean acoustic wave propagation can be predicted by applying numerical methods to solve representative wave equations computationally. For this purpose, numerical methods have been introduced; a latest introduction was the Predictor-Corrector Method. An important question arises: Whether or not these numerical methods can produce satisfactory required accurate results? This may cause an accuracy concerned by the users. This paper introduces a new Predict-Correct Procedure to examine whether or not the result meets the accuracy requirement. If not, the procedure can improve the result until it becomes satisfactorily accurate. Discussions will be given on the mathematical and computational developments of the Predictor-Corrector Method as well as the Predict-Correct Procedure. Following that is a discussion on how the Predict-Correct Procedure works. An important part of this paper is devoted to show how this new procedure can achieve the goal of obtaining the required accurate prediction results. [ABSTRACT FROM AUTHOR]

We extend the Huygens wavefront tracing algorithm, which is a part of an open source Madagascar project, to sound propagation in inhomogeneous, moving media and apply it to a series of benchmark tasks. One set of tasks admits exact analytic solutions and serves the purpose of validation of the new algorithm. Another set of calculations demonstrates applicability of the algorithm to the studies of wavefront dynamics and stability in ocean and atmospheric acoustics. The method is based on a system of differential equations equivalent to the eikonal equation, but formulated in the ray coordinate system. In this paper, we present a first-order, two-dimensional discretization scheme that is interpreted very simply in terms of the Huygens' principle. The method has proved to be a convenient alternative to conventional ray tracing. [ABSTRACT FROM AUTHOR]

Internal tides can cause density and sound speed fluctuations in the ocean, and the thickness of the mixing layer can fluctuate in short periods of time. This phenomenon affects underwater sound propagation and induces transmission loss variations. In the sea area northeast of Taiwan, regular internal tide activity is observed. The topography and sediment there are also complex, which makes the effect on transmission loss by internal tides even more complicated. This paper studies how transmission loss variation is affected by internal tides in the sea area northeast of Taiwan. The hydrographic fields with influence from the internal tides are provided by an experiment survey on the 4th of September, 2008 and a 3-D tide model. The transmission loss comparison between different thicknesses of the mixing layer in the internal tide fields is shown. Furthermore, the correlation coefficient is calculated and shows that layer depth and transmission loss have a medium to high negative correlation in the upper water column during the summer spring-tide period, and a low to medium negative correlation during the summer neap-tide period. [ABSTRACT FROM AUTHOR]

A three-dimensional (3D) ocean environment is assimilated with measured ocean data in the ASIAEX SCS (Asian Seas International Acoustics EXperiment, South China Sea) experiment. The experiment site is characterized as an active internal wave propagation region along the Northwestern shelf break of the South China Sea. Three-dimensional acoustics effects in the area are studied using FOR3DW, a wide-angle version of the parabolic equation code FOR3D (a Finite difference solution, an Ordinary differential equation, and Rational function approximations for solving 3D problems), and MOS3DPEF (MOdal Spectrum analysis based on 3D PE Field). The TL comparison between Nx2D and 3D calculations are shown to demonstrate the 3D effects. Variations in topography of the shelf break and in the water column due to the internal waves cause the 3D effects in the acoustic field. The intercomparison of the importance of bottom steering 3D effects and nonlinear internal wave refraction 3D effects is therefore proposed to realize which possesses the major part of the 3D effects. Also, 3D modal analysis results show that the nonlinear internal wave front causes severe horizontal refraction for higher modes. [ABSTRACT FROM AUTHOR]

The acoustic propagation problem is modeled via the parabolic approximation. The physical domain consists of the water column with a horizontal water–bottom interface and the bottom region consists of N-strata with horizontal interfaces. The computational domain is restricted to the water column, while the stratified bottom region is modeled by a nonlocal boundary condition applied along the water–bottom interface, and having the form of a Neumann to Dirichlet map (NtD). The discrete analog of the NtD has been implemented in a finite difference scheme for the general wide angle PE model, and successfully tested for several benchmark problems. The stratification of the media can be either physical, e.g. sediment formulation in the bottom, or artificial/computational, e.g. forced by sparse distribution of environmental data measurements in the water column. It should be emphasized that the sound speed may vary from layer to layer, but is constant within each layer. The proposed NtD map can be used in geoacoustic inversion via the optimal control adjoint method. [ABSTRACT FROM AUTHOR]

Rough surface scattering theory is applied to the problem of estimating gravity-capillary wavenumber spectra from measurements of sea surface backscatter at high acoustic frequencies. Ensemble averaged scattering cross sections predicted by small-slope expansions are evaluated to examine the inversion of acoustic data assuming Bragg scatter. The ratio of the full fourth-order small-slope and Bragg predictions is found to exhibit a minimum value of ~ 2dB at moderate angles of incidence. At such angles, the corrections to perturbation theory depend weakly on acoustic frequency and environmental conditions. This latter finding indicates that only a modest effort is required to monitor sea surface conditions to estimate the correction. Corrections to Bragg predictions increase rapidly with increasing incidence angle and at high angles, the fourth-order contributions of the small-slope and extended small-slope expansions differ. This finding casts some doubt on the applicability of small-slope approximations to predict scattering at high-incidence angles. [ABSTRACT FROM AUTHOR]

We compare the results of a coupled mode method with those of a finite element method and also of COUPLE on two test problems of sound propagation and scattering in cylindrically symmetric, underwater, multilayered acoustic waveguides with range-dependent interface topographies. We observe, in general, very good agreement between the results of the three codes. In some cases in which the frequency of the harmonic point source is such that an eigenvalue of the local vertical problem remains small in magnitude and changes sign several times in the vicinity of the interface nonhomogeneity, the discrepancies between the results of the three codes increase, but remain small in absolute terms. [ABSTRACT FROM AUTHOR]

Numerical solutions are given for a parabolic approximation to the acoustic wave equation at 75 Hz in two and three spatial dimensions to determine if azimuthal coupling of the field significantly affects horizontal coherence. Coupling is a small effect at 4000 km in the presence of internal gravity waves. This implies that accurate solutions are possible using computations from uncoupled vertical slices through the field. The shape of horizontal coherence is inconsistent with shapes given by two theories. Estimates of horizontal coherence at 4000 km and 25, 50, and 75 Hz are 10, 2, and 1 km respectively. [ABSTRACT FROM AUTHOR]

The azimuthal limitation of the Parabolic Equation (PE) approximation in solving the three-dimensional (3D) wave equation in cylindrical coordinate has been studied in this paper. Typically, 3D problems are dealt with an N × 2D approximation, which treats a 3D field as a fan-like composition of many 2D vertical slices (r - z plane in cylindrical coordinate) ignoring the θ-coupling terms. To deal with problems possessing 3D effects, the θ-coupling terms have to be considered in PE approximation. Nevertheless, the azimuthal limitation in the 3D PE approximation is not defined as well as the vertical angle limitation. Hence, the theoretical derivation estimating the azimuthal limitation is put forth in this work. Numerical results of a modified benchmark problem are also presented to validate the arguments and the wide angle version of the 3D PE model, FOR3D. [ABSTRACT FROM AUTHOR]

Parabolic equations written in terms of energy flux are inherently immune to the problem of energy conservation at vertical interfaces. Mikhin [J. Comp. Acoust. 9 (2001) 183–203] achieved exact reciprocity and energy conservation in a finite-difference PE model following this approach. However, his model used the implicit Crank–Nicolson scheme in range that requires a small range step for accurate solution. The present paper generalizes the exponential propagator of Collins [J. Acoust. Soc. Am. 93 (1993) 1736–1742] to solve the energy-flux PE. The obtained solution remains strictly reciprocal and energy conserving, while allowing large range steps. The numerical efficiency is improved by one or two orders of magnitude. A technique is proposed to calculate the acoustic pressure within the large steps, so the solution combines fast advance in range with dense range sampling. Numerical examples are provided. [ABSTRACT FROM AUTHOR]

Efficient, high-order accurate methods for the numerical solution of the standard (narrow-angle) parabolic equation for underwater sound propagation are developed. Explicit and implicit numerical schemes, which are second- or higher-order accurate in time-like marching and fourth-order accurate in the space-like direction are presented. The explicit schemes have severe stability limitations and some of the proposed high-order accurate implicit methods were found conditionally stable. The efficiency and accuracy of various numerical methods are evaluated for Cartesian-type meshes. The standard parabolic equation is transformed to body fitted curvilinear coordinates. An unconditionally stable, implicit finite-difference scheme is used for numerical solutions in complex domains with deformed meshes. Simple boundary conditions are used and the accuracy of the numerical solutions is evaluated by comparing with an exact solution. Numerical solutions in complex domains obtained with a finite element method show excellent agreement with results obtained with the proposed finite difference methods. [ABSTRACT FROM AUTHOR]

Continuous innovations in adaptive matched-field processing (MFP) algorithms have presented significant increases in computational complexity and resource requirements that make development and use of advanced parallel processing techniques imperative. In real-time sonar systems operating in severe underwater environments, there is a high likelihood of some part of systems exhibiting defective behavior, resulting in loss of critical network, processor, and sensor elements, and degradation in beam power pattern. Such real-time sonar systems require high reliability to overcome these challenging problems. In this paper, efficient fault-tolerant parallel algorithms based on coarse-grained domain decomposition methods are developed in order to meet real-time and reliability requirements on distributed array systems in the presence of processor and sensor element failures. The performance of the fault-tolerant parallel algorithms is experimentally analyzed in terms of beamforming performance, computation time, speedup, and parallel efficiency on a distributed testbed. The performance results demonstrate that these fault-tolerant parallel algorithms can provide real-time, scalable, lightweight, and fault-tolerant implementations for adaptive MFP algorithms on distributed array systems. [ABSTRACT FROM AUTHOR]

This work describes some of the ongoing activities in the framework of the EU-sponsored project SITAR aimed at developing acoustic methods for imaging of waste barrels/containers of small dimension buried in unconsolidated sea sediments. In particular, the work relies on acoustic sub-bottom scattering measurement techniques, with adaptive geometrical configuration of the transmitting/receiving system. The approach ultimately leads to a full 3D measurement of the acoustic scattered field, including bottom and sub-bottom effects, plus the scattering due to buried objects in the scene. The 3D dense acoustic image is then processed in order to automatically extract relevant object(s) features, as size, 3D orientation, impedance contrast; this is obtained through a sequence of processing steps including filtering, enhancement, restoration and image segmentation. Preliminary results obtained with simulative data are presented: data are obtained by modeling the surfaces of both seabed and object(s) as a dense, random grid of discrete scatterers, following the Rayleigh reflection coefficient, and integrating the response of the scatterers. The effects due to absorption and refraction moving from water to sediments are also considered. Sediment volume inhomogeneities are modeled by a random distribution of small asymmetric scattering volumes, characterized by their 3D dimensions, density, and reflection coefficient. A volume growing segmentation approach has been applied, showing efficient segmentation capabilities, and robustness to uncertainty. [ABSTRACT FROM AUTHOR]

Modes and wavenumbers are the principal ingredients that characterize the pressure field in an oceanic waveguide. However, wavenumber and mode inversions are well-known to be a difficult task in underwater acoustics. Moreover, this double inversion has never been performed simultaneously from the same configuration of emitters and receivers. We present a new approach to this problem in a shallow water environment between two vertical arrays of sources and receivers. Starting from a classical modal decomposition of the pressure field, our algorithm focuses on a specific treatment of phase and amplitude variables. The key idea is to run a three-stage optimization by working separately on the phase and amplitude of the acoustic field. The high number of variables of the problem is turned into an advantage by using an adjoint code generated by an Automatic Differentiation software. Numerical results in the presence of noise show that modes and wavenumbers are estimated with a high accuracy. [ABSTRACT FROM AUTHOR]

A multidomain pseudospectral time-domain (PSTD) method is developed for acoustic wave equations in lossy media. The method is based on the spectral derivative operator approximated by Chebyshev Lagrange polynomials. In this multidomain scheme, the computational domain is decomposed into a set of subdomains conformal to the problem geometry. Each curved subdomain is then mapped onto a cube in the curvilinear coordinates so that a tensor-product Chebyshev grid can be utilized without the staircasing error. An unsplit-field, well-posed PML is developed as the absorbing boundary condition. The algorithm is validated by analytical solutions. The numerical solutions show that this algorithm is efficient for simulating acoustic wave phenomena in the presence of complex objects in inhomogeneous media. To our knowledge, the multidomain PSTD method for acoustics is a new development in three dimensions, although in two dimensions the method can be made equivalent to the two-dimensional method in electromagnetics. [ABSTRACT FROM AUTHOR]

Effects of horizontal refraction on underwater sound propagation in deep and shallow water are considered within geometrical acoustics and adiabatic normal modes approximations. Several distinct formulations of the adiabatic approximation have been proposed in the literature on modal propagation. These formulations differ in the predicted values of mode amplitudes and, hence, in their reciprocity and energy-conserving properties. The formulations are compared with respect to their accuracy and domain of validity, assuming small and smooth variation of mode propagation constants characteristic of underwater acoustic waveguides. Perturbation theory for horizontal (modal) rays is used in the analysis. An approximate expression for the adiabatic mode amplitude in 3-D problems is derived which requires environmental information only along the source-receiver radial and which has greater accuracy than previous formulations. It is shown that the uncoupled azimuth approximation, also known as the N × 2-D approximation, overestimates travel times of ray arrivals as well as phases of adiabatic normal modes in a horizontally-inhomogeneous ocean. The travel time and phase biases rapidly increase with the value of cross-range environmental gradients and propagation range. Simple and explicit expressions for leading-order corrections to the travel time and the phase are found in terms of path-averaged cross-range environmental gradients. Implications on applicability of the uncoupled azimuth approximation for sound propagation modeling in a horizontally-inhomogeneous ocean are discussed. A perfect-wedge model of the coastal ocean is chosen to illustrate the importance of the travel-time and phase biases due to horizontal refraction. [ABSTRACT FROM AUTHOR]

Typical applications of matched-field localization use low frequency signals received on large aperture vertical-arrays. However, small aperture arrays are much more practical for real-world systems and must be considered. Additionally, any practical localization algorithm must also be robust to environmental mismatch. In this paper, we present the broadband L[sub ∞]-norm estimator for robust matched-field localization of mid-frequency signals (e.g., 800-4000 Hz) received on very short aperture vertical-arrays. Realistic simulation results are presented using broadband signals in the band of 1000-3000 Hz received on a 3 m vertical array which demonstrate the substantial performance gains in using the L[sub ∞]-norm estimator over the asymptotically-optimal maximum a posteriori estimator and the conventional Bartlett processor. Experimental data results in an uncertain shallowwater environment using a 2.13 m vertical array in the band of 3000-4000 Hz are also presented. [ABSTRACT FROM AUTHOR]

In this paper, a method for solving the unknown object problem is presented for a two-dimensional object buried in a fluid seabed lying over a rigid basement. The algorithm makes use of a regularized Born approximation. Several examples are provided which demonstrate the utility of the algorithm. [ABSTRACT FROM AUTHOR]

An exact expression for the reflection coefficient is obtained with the Thomson-Haskell technique for the geoacoustical model of an ocean bottom consisting of an elastic homogeneous sediment layer overlying an elastic half-space. Characteristic equations for explicit determination of the position of each individual resonance contribution to the reflection coefficient are derived. Analytical expressions for the angular and frequency resonance positions are found. The resonance expression for the reflection coefficient is written in the form of a sum of resonance terms. Comparison between resonance theory and exact calculations for the elastic layer covering the elastic half-space is presented. The results of resonance formalism show excellent agreement with exact theory in all the cases. [ABSTRACT FROM AUTHOR]

A three-dimensional, two-way parabolic equation model developed for solving three-dimensional backscattering problems in previous work is applied incorporating a focus-marching procedure to study the image reconstructions for underwater targets. Intensive numerical simulations are performed in this paper. Targets in the water are formed by objects with simple shapes. The "experimental data" of the return signals from targets are simulated by the backscattered sound calculated at a short distance from the source. These simulated return signals are processed by reversing their phases, and numerically propagated back to the place of the targets. It is due to the conjugating process that the target image may be reconstructed with less deformation at a distance near the target surface. This realistic study demonstrates an encouraging technique that may be utilized for studying underwater target imaging in many sonar applications. [ABSTRACT FROM AUTHOR]

The ambient noise model CANARY calculates noise coherence and array noise response by treating the noise sources as surface distributions rather than points. This assumption leads to simplification of the propagation, even in range-dependent environments, and by allowing variations in the source density one can represent distant storms or groups of ships. Included is a description of the numerical algorithms used to calculate coherence. Some recently developed analytical solutions for uniform source distributions and uniformly sloping seabed are used as test cases for CANARY. Some additional examples demonstrate CANARY's performance in more realistic environments and conditions including wind and shipping sources, and comparisons are made with the noise model RANDI. [ABSTRACT FROM AUTHOR]

Due to the complexity of the seafloor as an acoustical system, it is very important to validate wave propagation models and test inversion methods first in the laboratory. A known sediment is placed in a water-filled tank, in such a way that a smooth water-sediment interface is obtained with minimal air bubbles retained in the sediment. Two broadband piston transducers are used to carry out reflection experiments at oblique incidence. The placement of the emitter and receiver is symmetrical with respect to a vertical plane perpendicular to the sediment surface. The aim of this work is to find physical parameters of the sediment from the reflected signals. A general viscoelastic model that considers losses due to absorption and dispersion along the propagation of the wave through the sediments is proposed. A rational transfer function is used to model the viscoelastic modulus of the bulk sediments and a comparison with constant Q viscoelastic modelling is performed. The estimation of the model parameters is elaborated using a Maximum Likelihood Estimator in the frequency domain. [ABSTRACT FROM AUTHOR]

The horizontal refraction method (HRM) of transverse current acoustics monitoring in the Fram Strait environment is modeled numerically. The current profile was constructed on the basis of experimental data on the West Spitsbergen Current (WSC) structure and the complex environment of the region presented by the sound speed profiles, which were derived from the experiments. The HRM is based on the measurements of the deflection of the horizontal modal rays due to the gradient of the refraction index produced by the transverse current. The signals received by the antennas in a receiving plane perpendicular to the propagation axis have a modal phase difference in proportion to the average transverse velocity, which is due to the different orientation of the acoustical path of the current. The interesting result is that even in a strong mode coupling environment the numerically obtained phase difference is quite close to its value as calculated by adiabatic approximation. The physical reason behind this is most likely that the mode coupling impact can be canceled at the sound signal propagation along the two very close paths. [ABSTRACT FROM AUTHOR]

To assess the adiabaticity of sound propagation in the ocean is very important for acoustic field calculating (forward problem) and tomographic retrieving(inverse problem). Most of the criterion in the literature is too restrictive, specially for the nongradual ocean structures. A new criterion of adiabaticity is suggested in this paper. It works for nongradual ocean structures such as front and internal solitary waves in shallow-water. [ABSTRACT FROM AUTHOR]

The problem of reflection/transmission of plane waves in homogeneous isotropic dissipative media is investigated. In dissipative media, the elastic moduli, seismic velocities and slowness vectors are complex-valued and frequency-dependent. Results of extensive computations of R/T coefficients for plane waves incident at a plane interface are presented and discussed. In all cases, the "reference R/T coefficients" are considered, computed for a fixed frequency equal to the reference frequency f[sub r], for which the elastic moduli are specified. The influence of angle of incidence i and attenuation angle gamma; of the incident wave on the coefficients is studied in detail. In general, the differences between the moduli of the R/T coefficients for dissipative and nondissipative models are usually small for realistic Q's and γ's. These differences are more distinct in critical and post-critical regions for the reflection coefficients, particularly for small Q's, large contrast of Q's across the interface, and for large ≈'s (say, γ > 50°). The differences between the phases of R/T coefcients for dissipative and nondissipative media may be larger. For some γ's, the signs of the phases for dissipative and nondissipative media may be roughly opposite, even for very high Q's. [ABSTRACT FROM AUTHOR]

The role of 3-D effects has long been debated in the ocean acoustics community. Typically, 3-D problems are handled in an approximation that uses a fan of bearing lines to build up a 3-D image of the acoustic field with many 2-D slices. This is the so-called N by 2-D approach and it is probably safe to say it is adequate for simple calculations of the SONAR range-of-the-day. On the other hand, acoustic models are now finding an important role in matched-field processing (MFP) where they are integrated with the signal processing to correct for the channel effects. These applications demand much more from the models but, somewhat surprisingly, recent broadband experiments have revealed that the models are up to the task. The main features of the echo patterns are well-predicted by such models and can be reliably exploited, at least in areas where the ocean bottom is fairly flat. The challenge now is to push MFP to more realistic scenarios with complicated topography and potential 3-D effects. One phase of the December 1997 Key West LWAD (Littoral Warfare Advance Development) experiment was designed to address exactly this issue. We use this Key West scenario as a backdrop to discuss modeling approaches combining beams and modes and the impact of the resulting 3-D variation on MFP for towed arrays. [ABSTRACT FROM AUTHOR]

We consider the problem of the reconstruction of the shape of an obstacle from some knowledge of the scattered waves generated from the interaction of the obstacle with known incident waves. More precisely we study this inverse scattering problem considering acoustic waves or electromagnetic waves. In both cases the waves are assumed harmonic in time. The obstacle is assumed cylindrically symmetric and some special incident waves are considered. This allows us to formulate the two scattering problems, i.e. the acoustic scattering problem and the electromagnetic scattering problem, as a boundary value problem for the scalar Helmholtz equation in two independent variables. The numerical algorithms proposed are based on the Herglotz Function Method, which has been introduced by Colton and Monk. We report the results obtained with these algorithms in the reconstruction of simple obstacles with Lipschitz boundary using experimental electromagnetic scattering data, that is the Ipswich Data and in the reconstruction of "multiscale obstacles" using synthetic acoustic scattering data. [ABSTRACT FROM AUTHOR]

The most recent 2-D split-step Padé parabolic-equation model was modified to include narro-wangle azimuthal coupling. This model was developed and applied to the Santa Barbara channel to assess the effect of 3-D propagation on the performance of a matched-field processor. These results, plus those from the Shallow Water Acoustic Modeling (SWAM) workshop's 3-D wedge and the Gaussian canyon cases, will demonstrate the importance of azimuthal coupling to sound propagation in littoral regions and its effect on the performance of a matched-field processor. Special emphasis is given to model limitations and suitable selection of model parameters that could be automated to achieve accurate predictions during production runs. [ABSTRACT FROM AUTHOR]

Three numerical acoustic models, a coupled normal-mode model (C-SNAP), an adiabatic normalmode model (PROSIM), and a parabolic equation model (RAM), are applied to test cases defined for the SWAM'99 workshop. The test cases consist of three shallow water (flat bottom) scenarios with range-dependent sound-speed profiles imitating internal wave fields and a shelf-break case, with range-dependent sound-speed profiles and bathymetry. The bottom properties in all the cases are range-independent and modeled as a homogeneous fluid half-space. The results from the modeling are presented as transmission loss for selected acoustic frequencies and source-receiver geometries, and as received time series. The results are compared in order to evaluate the effect of applying different propagation models to the same range-dependent underwater environment. It should be emphasized that the propagation analysis is not an attempt to benchmark the selected propagation models, but to demonstrate the performance of practical, range-dependent models based on different approximations in particular underwater scenarios. [ABSTRACT FROM AUTHOR]

Identifies the major features of underwater sound propagation over a realistic three-dimensional bathymetry of an escarpment in California. Speed and attenuation of compressional wave; Use of lawn mower pattern for measurements; Transmission loss at constant depth over concrete bottom.

The Shallow Water Acoustic Modeling (SWAM'99) Workshop was organized to examine the ability of various acoustic propagation models to accurately predict sound transmission in a variety of shallow water environments designed with realistic perturbations. In order to quantify this, tests of reciprocity, convergence, and stability must be considered. This paper presents the results of an established parabolic equation model based on the split-step Fourier algorithm. The test cases examined in this paper include a simple isospeed water column over a fiat bottom with geoacoustic parameter variations, a randomly sloping bottom with geoacoustic parameter variations, and a canonical shallow water profile perturbed by internal waves over a fiat, homogeneous bottom. Source configurations were generally held constant but numerous single frequency and broadband runs -were performed. Model testing is emphasized with specific criteria for accurate solutions being specified. Random perturbations are added to one test case to examine the influence of environmental uncertainty on the details of the propagation. The results indicate that point-wise accurate solutions to the acoustic field in shallow water cannot be achieved beyond a few kilometers. This is partly due to the inaccuracies of the split-step Fourier algorithm employed in these shallow water scenarios and the treatment of the bottom interface boundary conditions, but also due to the inherent variability caused by uncertain environmental specification. Thus, more general features of the acoustic field should be emphasized at longer ranges. [ABSTRACT FROM AUTHOR]

The Shallow Water Acoustic Workshop (SWAM) test cases stress low frequency propagation in shallow water environments dominated by energy refracted through the bottom. Ray based models are not normally considered applicable for such problems. The implementation and accuracy of the range dependent, Gaussian Ray Bundle eigenray model is examined for a subset of these test cases. [ABSTRACT FROM AUTHOR]

The energy conservation law and the flow reversal theorem are valid for underwater acoustic fields. In media at rest the theorem transforms into well-known reciprocity principle. The presented parabolic equation (PE) model strictly preserves these important physical properties in the numerical solution. The new PE is obtained from the one-way wave equation by Godin[sup 12] via Padé approximation of the square root operator and generalized to the case of moving media. The PE is range-dependent and explicitly includes range derivatives of the medium parameters. Implicit finite difference scheme solves the PE written in terms of energy flux. Such formalism inherently provides simple and exact energy-conserving boundary condition at vertical interfaces. The finite-difference operators, the discreet boundary conditions, and the self-starter are derived by discretization of the differential PE. Discreet energy conservation and flow reversal theorem are rigorously proved as mathematical properties of the finite-difference scheme and confirmed by numerical modeling. Numerical solution is shown to be reciprocal with accuracy of 10-12 decimal digits, which is the accuracy of round-off errors. Energy conservation and wide-angle capabilities of the model are illustrated by comparison with two-way normal mode solutions including the ASA benchmark wedge. [ABSTRACT FROM AUTHOR]

A range-dependent problem of shallow water acoustics is modeled by a liquid -wedge over fast-speed elastic substratum, and the solution is derived based on the method of generalized rays, where the total acoustic field is decomposed into a sum of partial waves, comprising the wave emitted from the point source and the multi-reflected waves. The contribution of each partial wave at a given time is represented by a single integral. The diffracted waves arising from scattering at the apex of the wedge are neglected in this otherwise exact solution. The pressure records are evaluated at the downslope receiver when the pressure pulse applied at a point situated within the -wedge has impulsive or harmonic time history. It was found that the arrival of the source pulse is preceded by the group of head wave arrivals, and this early portion of the record (the ground wave) includes considerable pressure build-ups. For a Heaviside source-pulse, we have found that the pressure records of the partial waves exhibit a singular behavior such as the logarithmic singularity at the arrival time of the totally reflected spherical wave. This singular behavior was not found for less sharp input, that is, a triangular source-pulse. We have also found that for a causal harmonic input of lower frequency the ground wave stands out very clearly, whereas for that of higher frequency it is almost suppressed, and for both frequencies the response becomes more or less steady-state soon after the arrival of a few partial waves. [ABSTRACT FROM AUTHOR]

PECan is a Canadian N×2D/3D parabolic equation (PE) underwater sound propagation model that was developed for matched-field processing applications. It is based on standard square-root operator and/or propagator approximations that lead to an alternating direction solution of the 3-D problem. A 2-D split-step Padé approximation is employed for propagation in range. The 3-D azimuthal corrections are computed using either a split-step Fourier method or a Crank-Nicolson finite-difference approximation. It features a heterogeneous formulation of the differential operators on an offset vertical grid, energy conservation, a choice of initial field including self-starter, and both absorbing and nonlocal boundary conditions. Losses due to shear wave conversion in an elastic bottom are handled in the context of a complex density approximation. In this paper, PECan is described and validated against some standard benchmark solutions to underwater acoustics problems. Subsequently, PECan is applied to several single-frequency test cases that -were offered for numerical consideration at the SWAM'99 Shallow Water Acoustic Modeling workshop. [ABSTRACT FROM AUTHOR]

A recently introduced theoretical model of wave propagation in an unconsolidated, sandy marine sediment is discussed in this article. Essentially, the model consists of four analytical expressions, which specify four wave properties of the sediment, namely the speed and attenuation of the compressional and the shear wave. These expressions contain just three unknown constants, which must be evaluated from data. A technique is described in which these constants are determined from measured values of the compressional wave speed, the shear wave speed, and the shear wave attenuation. This technique is applied to preliminary data from O.N.R.s SAX'99 recent experiment on a sandy sediment in the Gulf of Mexico. From the fully specified equations, the fourth wave property, the attenuation of the compressional wave, is computed and found to lie within 0.5 dB/m of the measured value. Based on this limited evidence, it appears that the wave properties of an unconsolidated sediment are highly correlated and predictable. According to the theory, the causal connections between the wave properties originate in the sliding of one micro-asperity against another on the surfaces of contact between contiguous grains in the medium. [ABSTRACT FROM AUTHOR]

A two-way coupled mode approach based on an integral equation formalism is applied to sound propagation through internal wave fields defined at the 1999 Shallow Water Acoustics Modeling Workshop. Solutions of the coupled equations are obtained using a powerful approach originally introduced in nuclear theory and also used to solve simple nonseparable problems in underwater acoustics. The basic integral equations are slightly modified to permit a Lanczos expansion to form a solution. The solution of the original set of integral equations is then easily recovered from the solution of the modified equations. Two important aspects of the integral equation method are revealed. First, the Lanczos expansion converges faster than a Born expansion of the original integral equations. Second, even when the Born expansion diverges due to strong mode coupling, the Lanczos expansion converges. It is shown that the internal wave problems examined are essentially one-way propagation problems because one observes good agreement between the coupled mode solutions and those provided by an energy-conserving parabolic equation algorithm. In the Workshop examples, at both 25 and 250 Hz, significantly greater coupling between modes occurs in the linear internal wave field case than the nonlinear soliton case. [ABSTRACT FROM AUTHOR]

The SWAM'99 (Shallow Water Acoustic Modeling, 1999) workshop on the topic of benchmarking shallow water range-dependent propagation modeling was held in Monterey CA in September 1999.[sup a] No specific benchmarks -were generated. Rather, each participant offered his (her) Transmission Loss curves for comparison with other results. This overview article will: discuss the six (6) test cases; discuss each individual's contribution to this benchmarking effort (see the associated articles in this Special issue for full details); conclude with suggestions for future efforts. [ABSTRACT FROM AUTHOR]

The numerical problems of SWAM'99 workshop are quite challenging for any method of sound field calculation. This report presents a detailed description of the enhanced ray theory approach briefly outlined in Ref. 2. It contains a new method of phase and amplitude computation along the ray, a new method of calculation of eigenrays, and a new method of analytic approximation of sound-speed and density. An application of these methods is presented. [ABSTRACT FROM AUTHOR]

In this paper we closely examine the performance of several propagation models, i.e., KRAKEN (coupled and adiabatic) and PE (energy-conserving), applied to a number of the SWAM'99 rangedependent shallow water test cases (FLAT, DOWN, and UP). We begin by considering rangeindependent behavior (including the ORCA model) in: the CAL case of Workshop'97 (Vancouver, '97),[sup 9] the first segment of FLATa, and the Benchmark Wedge test case³ but with a flat bottom of 200 m depth. We next examine the proper Benchmark Wedge behavior for the sloping bottom for our PE (conserving and nonconserving) and for our normal mode model (KRAKEN, adiabatic and coupled). These preliminary tests confirm that the models are behaving properly under known conditions and that the input parameters have been appropriately set. Thus, when we study the models' behavior on the new SWAM'99 cases we will have some confidence that they are being applied properly. It is nontrivial to run these models even when one is familiar with them. The SWAM'99 test cases which are examined here are run only to 10 km range (five-step segments) and at a single frequency of 25 Hz. No elasticity is considered. We find that all the models generally agree, but there are quantitive differences. Since there are no proper benchmark solutions for these SWAM'99 test cases, it is difficult to determine to what extent any of them are in error. However, for the purposes of Matched Field Processing, particularly the tomographic geoacoustic inversion using adibatic normal modes (KRAKEN), it is likely that the simple adiabatic normal mode KRAKEN model is sufficiently accurate under most circumstances, i.e., unless there is a loss or gain of a critical mode. [ABSTRACT FROM AUTHOR]