Underwater Waveguide Research Articles

Dual-functional pentamode metamaterial with water-like and topological transmission properties

In this paper, a water-like pentamode metamaterial (PM) with a single metallic material is designed and the topological edge-state transmission properties of elastic waves in the PM are thoroughly investigated. Numerical results indicate that by introducing structural perturbation into PM, the Dirac point degeneracy at K-point can be opened and topological band inversion can be generated. Topological edge states are also obtained by organizing PM structural units, which are robust to defects such as bending and cavities. In addition, it also has the mimics water in acoustic properties over a wide frequency range, i.e. it exhibits transparency when surrounded by water. Therefore, it will have both good transmission efficiency and acoustic stealth performance when used as an underwater waveguide. The dual-functional PM proposed in this study provides theoretical guidance for designing underwater stealth acoustic waveguides.

Subarray-based joint source localization in shallow water waveguide via subspace intersection

By the use of an underwater bottom-mounted Horizontal Linear Array (HLA), the two-dimensional joint localization technique and its accuracy are analyzed in this article. The proposed method takes advantage of arrival angles measured by a dual-subarray system consisting of a large-aperture HLA. Then, for the system, expressions for source position estimate and error variation are derived. Analysis of the Geometrical Dilution of Precision, which is a measure of localization error defined in Eq. (4), reveals that the localization error is mainly related to the source bearing, subarray interval and their measurement errors. In order to investigate the impact of the underwater waveguide, numerical simulations were carried out based on the normal mode theory. By using the distribution of acoustic intensity and structure of modal arrival, it is proved that the localization accuracy increases as the grazing angle and the subarray interval increase. However, when the measurement errors of source bearing and subarray interval increase, the localization accuracy will decrease. In addition, the obtained bearing estimation result provides an evident characteristic of beam spreading. When sources are near the end-fire direction of the dual-subarray system, significant bearing estimation error occurs, the negative effect of which is then presented. By applying the Subspace Intersection method, unbiased bearing estimation has been achieved, with relatively reduced computational complexity. Most of all, the improved localization performance is validated by experimental data collected in the South China Sea.

Simultaneous integration of acoustic and environmental data in a graph-based framework for underwater waveguide analysis

Accurate assessment of underwater acoustic propagation relies heavily on understanding variability in the waveguide. Typically, prevailing methods in the field use environmental data exclusively to evaluate water column fluctuations. This study breaks new ground by integrating a graph-based approach, merging insight from acoustics and environmental data to comprehensively analyze ocean fluctuations. The proposed framework leverages data obtained during the Shallow Water ‘06 Experiment (SW06) from a densely measured region in the experimental area. The data used in this work include acoustic broadband signals below 1 kHz from a 48-element L- shape array and environmental measurements from 59 thermistors across 16 mooring arrays, affected by the passing of internal waves. The spatial relationship in the data, facilitated by sensor locations, is harnessed through a graph built upon underlying features from the datasets, providing a nuanced understanding of environmental variability in the water column. The proposed framework is not confined to theoretical constructs; it is substantiated through rigorous model evaluation on the measured data. This validation process robustly demonstrates the generalization power of the proposed architecture, affirming its effectiveness in a highly fluctuating water column and showcasing its potential for advancing underwater acoustic research. [Work supported by ONR Ocean Acoustics program.]

Sound radiation from a cylindrical shell in an underwater waveguide

Sound radiation from cylindrical structures immersed in an underwater acoustic waveguide, that is, a fluid layer with an upper free surface and lower rigid floor, is a challenging engineering problem to analyze due to the complex interaction of the radiation from the excited structure and its subsequent propagation within an acoustic waveguide. To contribute to the understanding of this phenomenon, an analytical model is presented. The model involves an infinitely-long three-dimensional cylindrical shell that is point-excited and submerged in a perfect underwater waveguide, where the reflections off the free surface and rigid floor have no absorption. The equations of motion of the shell are given by thin shell theory with heavy fluid loading. The image-source method is applied directly to the acoustic boundary conditions to account for the vibroacoustic coupling of the shell and waveguide. Together, these techniques combine into an analytical framework that can evaluate both the vibration of the shell and its acoustic radiation. Results include the far-field radiated sound pressure with observations of the relative and combined effect of the waveguide boundaries.

Predicting the acoustic response of a cylindrical shell immersed in an underwater waveguide using a substructuring technique

Sound radiation from structures in an underwater waveguide presents a challenging underwater acoustics problem typically resolved with numerical methods. This can be computationally inefficient and limited to low-frequency analysis. Hybrid approaches improve on these limitations by combining numerical methods with analytical solutions. This study utilises a substructuring technique called the condensed transfer function approach (CTF) and a decoupling technique called the reverse condensed transfer function approach (rCTF). The hybrid CTF-rCTF approach builds systems by coupling and decoupling simpler subsystems. Each subsystem is represented at the junction interfaces, described by condensed transfer functions (CTFs) that can be analytically or numerically determined. These CTFs are decomposed into orthonormal condensation functions (CFs), for example, gate or exponential functions. To demonstrate the potential of CTF-rCTF, the acoustic response of an infinitely long cylindrical shell under line-distributed load and immersed in an underwater waveguide composed of an upper free surface and lower rigid floor is predicted. This system is built from an underwater waveguide decoupled with a fluid volume and coupled with an excited shell that takes place of the decoupled fluid. Acoustic pressures received in the fluid domain are predicted and verified against an analytical solution. It is particularly shown that using exponential functions as the CFs improves the prediction quality compared to gate functions.

Acoustic radiation from a baffled finite shell in an underwater waveguide

Analytical modelling of vibroacoustic systems can help us to understand the physical phenomena involved in more complex problems, and it provides a benchmark solution and reference upon which more complex systems can be built. In the present work, the system of interest consists of a finite elastic cylindrical shell inserted in infinitely rigid cylindrical baffles and immersed in an underwater acoustic waveguide. The latter consists of a finite fluid layer bounded by an upper free surface and a lower rigid floor. In such a fluid domain, the acoustic waves radiated from the excited shell will exhibit reflections off the boundaries. This phenomenon is modelled by the image-source theory and embedded in the fluid loading term, which intervenes in the shell equations. Investigations into the influence on the finiteness of the elastic shell, types of supports (i.e., simply supported, clamped, free, and combinations of these), and depth of the waveguide on the shell’s acoustic radiation are presented.

Active intensity vortex and stagnation point singularities in a shallow underwater waveguide.

Vector acoustic properties of a narrowband acoustic field are observed as a function of range from a source towed in waters of depth 77 m on the New England Mud Patch. At the source frequency (43 Hz), the waveguide supported three trapped modes, with mode 2 weakly excited owing to the towed source depth. The receiving sensor was positioned 1.45 m above the seafloor with a sampling range aperture of 2500 m. The vector acoustics observations enabled study of vortex regions that encompass two singular points for active acoustic intensity: the vortex point, which is co-located with a dislocation, and stagnation point. Interpretative modeling, based on the normal modes and using a geoacoustic model consistent with those emerging from studies conducted at this location, is in agreement with these measurements. Model-data comparisons were based on the first-order variables of acoustic pressure and velocity along with inverse Hankel transforms, which yield normalized horizontal wavenumber spectra, and second-order variables in the form of horizontal and vertical intensity as well as non-dimensional intensity-based ratios. These measures provide a degree of observational confirmation of some vortex region properties. Both observations and modeling point to a gradual deepening of such regions with increasing range owing to sediment attenuation.

Inversion in an uncertain ocean using Gaussian processes.

Gaussian processes (GPs) can capture correlation of the acoustic field at different depths in the ocean. This feature is exploited in this work for pre-processing acoustic data before these are employed for source localization and environmental inversion using matched field inversion (MFI) in an underwater waveguide. Via the application of GPs, the data are denoised and interpolated, generating densely populated acoustic fields at virtual arrays, which are then used as data in MFI. Replicas are also computed at the virtual receivers at which field predictions are made. The correlations among field measurements at distinct spatial points are manifested through the selection of kernel functions. These rely on hyperparameters, that are estimated through a maximum likelihood process for optimal denoising and interpolation. The approach, employing Gaussian and Matérn kernels, is tested on synthetic and real data with both an exhaustive search and genetic algorithms and is found to be superior to conventional beamformer MFI. It is also shown that the Matérn kernel, providing more degrees of freedom because of an increased number of hyperparameters, is preferable over the frequently used Gaussian kernel.

Forced vibroacoustic response of a cylindrical shell in an underwater acoustic waveguide

An analytical approach is proposed to analyze vibroacoustics of an infinitely long thin cylindrical shell under line-distributed harmonic excitation immersed in an underwater waveguide formed by a free surface and a rigid floor. Equations of motion of the thin shell are modeled using Flügge’s shell theory, the fluid–structure coupling is implemented with the image source method to account for the infinite reflections of acoustic waves off the waveguide boundaries and Graf’s addition theorem is used to reconcile the coordinate systems of the image sources in the analytical expressions. The vibroacoustic response from the proposed analytical model is verified by numerical results obtained from a finite element model, showing excellent agreement. The analytical approach provides a computationally efficient tool for parametric investigation into the relative effects of the proximity of the free surface and/or rigid floor on the vibroacoustic behavior of the shell.

Low-Frequency Sound Propagation in an Underwater Waveguide with a Giant Gassy Pockmark

Bottom formations known as pockmarks basically arise due to extensive gas emission. Active pockmarks are characterized by exceptionally high gas saturation and substantially reduced sound speed. The latter circumstance leads to strong attenuation of sound waves contacting with a pockmark. In the present paper, we study low-frequency sound propagation in a 10-km long waveguide crossing a giant pockmark. A new method of acoustic waveguide scanning based on measurement of the wavefield propagator is represented. This method allows one to explore attenuation anomalies associated with the presence of the gas-saturated bottom region. In particular, one can find out which beams fall into a pockmark area and therefore experience strong losses. Identifying such beams, as well as beams which avoid pockmark-assisted losses, one can estimate probable locations of the pockmark segment in the waveguide, provided information about the background medium is sufficient.

Surficial sediment sound speed estimation from wide-angle multipath arrivals.

Multipath acoustic arrivals on fixed receivers from a moving source in an underwater waveguide include wide-angle bottom reflections that are affected by sediment properties. Hence, one can use them as input data for seabed geoacoustic parameter estimation. In this study, the effects of seabed properties on such measurements are theoretically analyzed. The result shows that one can utilize time delays and source distances at the critical angle points of multipath arrivals to determine the sediment sound speed. The effect of sediment attenuation is also discussed, and the proposed method is demonstrated with experimental data.

Graduate programs in physical, engineering, and underwater acoustics at the Naval Postgraduate School

The Departments of Physics and of Electrical and Computer Engineering at the Naval Postgraduate School offer graduate programs in acoustics leading to MS and PhD degrees in applied physics and engineering acoustics. Engineering acoustics degrees can be completed in either traditional or distance learning modes. The departments also offer stand-alone academic certificate programs in fundamentals of engineering acoustics, underwater acoustics, and sonar system applications, with a set of three certificates leading to a MS degree in engineering acoustics. MS and PhD programs are interdisciplinary, with courses and laboratory work drawn principally from the fields of physics and electrical engineering. Subjects covered include waves and oscillations; fundamentals of physical and structural acoustics; the generation, propagation, and reception of sound in the ocean; civilian and military applications of sonar systems; and acoustic signal processing. Topics of recent theses and dissertations include development and field testing of novel sensors for atmospheric and ocean acoustics, modeling and measurements of ambient noise and sound propagation in the ocean, sound scattering in underwater waveguides, acoustic vector sensors and vector field properties, acoustic communications, noise interferometry, time reversal in acoustics, geo-acoustic inversion, acoustic remote sensing of the ocean, and acoustics of autonomous underwater and aerial vehicles.

Range-Dependent Inversion for Seabed Parameters Using Vector Acoustic Measurements of Underwater Ship Noise

The Intensity Vector Autonomous Recorder (IVAR) measures acoustic particle velocity and pressure simultaneously. IVAR was deployed on the seabed during the 2017 Seabed Characterization Experiment (SBCEX) with the primary objective to study sound propagation within underwater waveguides for which the seabed consists of fine-grained, muddy sediments. In this study, a Bayesian framework is applied to underwater noise recorded by IVAR from a cargo ship traversing the central region of the SBCEX2017 area for the purpose of inversion to characterize sediment properties. The vector acoustic data are in the form of a bounded, nondimensional form known as circularity, a quantity that is independent of the ship noise-source spectrum and that can be interpreted as the normalized curl of active intensity. The inversion model space for the seabed consists of a low-compressional speed layer and underlying basement half-space, with each having compressional and shear components. The interpretative model for producing a replica of the data is based on the plane wave reflection coefficient for a layered, elastic seabed in conjunction with the depth-dependent Green’s function that is integrated in the complex wave number plane to obtain pressure and particle velocity fields. The small change in water depth between the location of the ship source and IVAR is addressed using adiabatic mode theory. The inversion results exhibit slow variation over the 20-min observation period, representing approximately 5 km of travel by the ship source.

The fluid bottom approximation and its implications for sound attenuation in underwater waveguides

The fluid-bottom model makes forward and inverse problems more amenable to theoretical analysis and numerical simulations but has some well-known limitations. The accuracy and weaknesses of the fluid approximation are elucidated in this paper by quantifying the effects of weak shear rigidity on acoustic normal modes. Mathematically, appearance of finite shear rigidity and attendant slow shear waves is a singular perturbation of the fluid-bottom model, which standard perturbation theories fail to capture correctly. The problem is addressed here by combination of an asymptotic technique and an analysis of exact solutions for idealized seabed models and placed in the context of earlier studies of the effects of shear rigidity. Due to coupling between compressional and shear waves at the seafloor and within the seabed, shear rigidity affects phase and group speeds of normal modes. By transferring the energy from compressional to shear waves, wave coupling makes a significant contribution to sound attenuation from low up to mid-frequencies. It is found that the effects of shear rigidity on the acoustic field in water are magnified by seabed stratification and especially by density variations. Implications of the results for seabed parameterization in geoacoustic inversions will be discussed. [Work supported by ONR.]

Shear waves and sound attenuation in underwater waveguides.

In addition to dissipation of acoustic energy in the seabed, bottom-interacting normal modes are attenuated by radiation of shear waves into soft sediments, where shear speed is small compared to the sound speed in water. The shear-wave contribution and the dissipation have distinct frequency dependencies, and their relative magnitude affects the observed frequency dependence of mode attenuation. Previous studies suggested that the shear-wave contribution to the attenuation is proportional to the cube of the small ratio of the shear and sound speeds. Here, coupling of compressional and shear waves in layered soft sediments is analyzed. Besides the well-known, third-order contribution to the attenuation due to shear-wave generation at the water-sediment interface, a stronger, first-order, contribution is found to occur due to compressional-to-shear wave conversion at interfaces within the sediment. First-order effects of weak shear on mode travel times are also identified. Stratification of the sediment density and interference of shear waves reflected within the seabed control the frequency dependence of the shear-wave contribution to sound attenuation. With the shear-wave contribution being larger than previously estimated, its effect on the experimentally measured frequency dependence of the sound dissipation may need to be re-assessed.

Vector acoustic observations of underwater ship noise from the 2017 seabed characterization experiment

The Intensity Vector Autonomous Recorder (IVAR) measures acoustic particle velocity and pressure simultaneously. IVAR was deployed on the seabed at depth of 75 m during the 2017 Seabed Characterization Experiment (SBCEX) with objective to study sound propagation within underwater waveguides for which the seabed consists of fine-grained, muddy sediments. In this presentation, vector acoustic observations of ship generated noise recorded by IVAR from a cargo ship traversing the central region of the SBCEX are discussed. Pressure and particle velocity data as a function of frequency are converted into a bounded, non-dimensional form known as circularity, a quantity that is independent of the ship noise source spectrum and which can be interpreted as the normalized curl of active intensity. The frequency dependent pattern in circularity is sensitive to the sediment layering structure, and bathymetry. This pattern, as the vessel closes and opens in range, is inverted for sediment properties using a Bayesian framework, with inversion model space consisting of a low-compressional speed elastic layer, above an elastic half-space. Change in water depth between the location of the ship source and IVAR over the 20-min observation period is addressed using adiabatic mode theory. [Study supported by Office of Naval Research.]

Adaptive subspace detection based on two-step dimension reduction in the underwater waveguide

In the underwater waveguide, the conventional adaptive subspace detector (ASD), derived by using the generalized likelihood ratio test (GLRT) theory, suffers from a significant degradation in detection performance when the samplings of training data are deficient. This paper proposes a dimension-reduced approach to alleviate this problem. The dimension reduction includes two steps: firstly, the full array is divided into several subarrays; secondly, the test data and the training data at each subarray are transformed into the modal domain from the hydrophone domain. Then the modal-domain test data and training data at each subarray are processed to formulate the subarray statistic by using the GLRT theory. The final test statistic of the dimension-reduced ASD (DR-ASD) is obtained by summing all the subarray statistics. After the dimension reduction, the unknown parameters can be estimated more accurately so the DR-ASD achieves a better detection performance than the ASD. In order to achieve the optimal detection performance, the processing gain of the DR-ASD is deduced to choose a proper number of subarrays. Simulation experiments verify the improved detection performance of the DR-ASD compared with the ASD.

Target detection method using multipath information in an underwater waveguide environment

Interface scattering in the ocean environment consistently results in reverberation and multipath echo, thereby decreasing the detection probability of moving targets. In this work, a new detection method which fully uses underwater acoustic channel characteristics to realise high detection probability for moving targets is proposed. First, this method combines fractional Fourier transform and fractional convolution theory to build a delay time-Doppler shift matrix related to multipath echoes. Second, the insensitivity of linear modulated frequency signal and distribution of multipath echo analysis are utilised to detect the moving target in a severe environment. Simulation results show that the proposed method can obtain higher detection probability and more accurate parameter estimation than the traditional method. Experimental results also verify that the proposed method has favourable performance even in strong reverberation environment.

Sound propagation in inhomogeneous waveguides with sound-speed profiles using the multimodal admittance method

The multimodal admittance method and its improvement are presented to deal with various aspects in underwater acoustics, mostly for the sound propagation in inhomogeneous waveguides with sound-speed profiles, arbitrary-shaped liquid-like scatterers, and range-dependent environments. In all cases, the propagation problem governed by the Helmholtz equation is transformed into initial value problems of two coupled first-order evolution equations with respect to the modal components of field quantities (sound pressure and its derivative), by projecting the Helmholtz equation on a constructed orthogonal and complete local basis. The admittance matrix, which is the modal representation of Direchlet-to-Neumann operator, is introduced to compute the first-order evolution equations with no numerical instability caused by evanescent modes. The fourth-order Magnus scheme is used for the numerical integration of differential equations in the numerical implementation. The numerical experiments of sound field in underwater inhomogeneous waveguides generated by point sources are performed. Besides, the numerical results computed by simulation software COMSOL Multiphysics are given to validate the correction of the multimodal admittance method. It is shown that the multimodal admittance method is an efficient and stable numerical method to solve the wave propagation problem in inhomogeneous underwater waveguides with sound-speed profiles, liquid-like scatterers, and range-dependent environments. The extension of the method to more complicated waveguides such as horizontally stratified waveguides is available.

Matched Field Processing in Phase Space

The traditional method of matched field processing is based on comparing the complex amplitudes of the measured and calculated sound fields in an underwater waveguide. Because of the high sensitivity of the wave field to variations in environmental parameters, the use of this approach requires accurate knowledge of the ocean-acoustic environment. In this paper, it is shown that under conditions of uncertain environment, instead of comparing the depth dependencies of complex field amplitudes, it is advisable to compare their field amplitude distributions in the phase plane “grazing angle-depth.” Such distributions are calculated using the coherent state expansion borrowed from quantum mechanics. Due to the absence of multipath in the phase space, the amplitudes of the coherent states are less sensitive to variations in the environmental parameters than the total wave field. This makes it possible to construct the similarity coefficients of measured and calculated fields that almost “do not notice” the differences of the compared fields caused by weak sound-speed variations, and “react” only to differences caused by strong changes in the sound-speed field and/or source position.