Acoustic scattering from a solid aluminum cylinder in contact with a sand sediment: measurements, modeling, and interpretation

Validation and verification of three-dimensional finite element target scattering models and Green's functions

A configurable three-dimensional (3D) finite element framework is used for modeling acoustic scattering from various elastic targets on seabed and for the numerical determination of Green's functions used in far-field target scattering prediction. The 3D selection is chosen for possible inclusion of complex seafloor geometries, such as rough, rippled, cluttered, or variably layered seabeds, in which two-dimensional modeling approaches cannot capture the full acoustic interaction with the target and the seabed. Model results are verified and validated against analytic scattering theories and measured results from the 2013 Target and Reverberation Experiment (TREX) and the 2017 CLUTTEREX experiment.

Backscattering enhancements by partially exposed spheres due to reflected subsonic Rayleigh waves at air-water interfaces

Air-water interfaces can enable distinct target scattering mechanisms different from the mechanism under free field conditions. In this study, backscattering experiments are performed by lowering an acrylic or polymethylmethacrylate sphere through the air-water interface into the water and insonifying the sphere from below at grazing incidence. Pronounced backscattering enhancements associated with the subsonic Rayleigh wave propagation mechanism are observed before the specular reflection point of the sphere reaches the water. The results indicate that, for a partially exposed sphere, subsonic Rayleigh waves can pass through the air-water interface and circumnavigate the sphere multiple times. The phase velocities of Rayleigh waves are different when propagating above and below the air-water interface. Moreover, subsonic Rayleigh waves are partially reflected when passing through the air-water interface, generating wavefronts that propagate in the reverse direction.

Backscattering by a tilted intermediate thickness cylindrical metal empty shell in water

Backscattering by metal shells in water was investigated by Morse, Marston, and Kaduchak [J. Acoust Soc. Am. 103(2), 785-794 (1998)]. The evolution of the backscattering as a function of frequency and tilt angle, the "acoustic color," depended on the shell's thickness. The present study concerns scattering by a shell with an intermediate thickness-to-radius ratio (0.106). The results include: (a) meridional rays associated with a supersonic antisymmetric guided wave cause a prominent tilt-angle dependent enhancement at frequencies above the coincidence frequency; (b) a subsonic guided wave is also prominent over a range of frequencies and tilt angles; and (c) meridional ray contributions are evident in the time-frequency-angle domain.

Radiation forces on highly reflecting circular cylinders in two slanted plane waves: Specular-reflection contributions

Situations arise where it is desirable to understand and estimate the radiation force on large smooth highly reflecting objects in water illuminated by beams of ultrasound. The approach examined here is to extend a formulation experimentally confirmed by Herrey [J. Acoust. Soc. Am. 27, 891-896 (1955)] for tilted reflecting surfaces in fluids that are modeled as being inviscid. The formulation applies Brillouin's analysis of the Langevin-like radiation force on objects in open containers. The specular reflection contributions to the radiation force of two slanted plane waves incident on a rigid cylinder is approximated and compared with a full partial wave series (PWS) solution for an infinitely long cylinder in an inviscid fluid. The availability of the PWS solution gives support to approximations introduced in the geometric analysis, provided ka (the wave number-cylinder-radius product) is sufficiently large. The normalized force projection is plotted as a function of the wave slant angle relative to the symmetry axis. Deviations between the specular and PWS analysis for ka of 7.5 are diminished for ka of 15 and 25. A region of enhanced force associated with constructive interference narrows with increasing ka.

Physics-Based Modelling and Simulation of Multibeam Echosounder Perception for Autonomous Underwater Manipulation

One of the key distinguishing aspects of underwater manipulation tasks is the perception challenges of the ocean environment, including turbidity, backscatter, and lighting effects. Consequently, underwater perception often relies on sonar-based measurements to estimate the vehicle’s state and surroundings, either standalone or in concert with other sensing modalities, to support the perception necessary to plan and control manipulation tasks. Simulation of the multibeam echosounder, while not a substitute for in-water testing, is a critical capability for developing manipulation strategies in the complex and variable ocean environment. Although several approaches exist in the literature to simulate synthetic sonar images, the methods in the robotics community typically use image processing and video rendering software to comply with real-time execution requirements. In addition to a lack of physics-based interaction model between sound and the scene of interest, several basic properties are absent in these rendered sonar images–notably the coherent imaging system and coherent speckle that cause distortion of the object geometry in the sonar image. To address this deficiency, we present a physics-based multibeam echosounder simulation method to capture these fundamental aspects of sonar perception. A point-based scattering model is implemented to calculate the acoustic interaction between the target and the environment. This is a simplified representation of target scattering but can produce realistic coherent image speckle and the correct point spread function. The results demonstrate that this multibeam echosounder simulator generates qualitatively realistic images with high efficiency to provide the sonar image and the physical time series signal data. This synthetic sonar data is a key enabler for developing, testing, and evaluating autonomous underwater manipulation strategies that use sonar as a component of perception.

Specular reflection contributions to dynamic radiation forces on highly reflecting spheres (L)

Specular reflection contributions to dynamic radiation forces were recently mentioned for highly reflecting spheres to facilitate comparison with forces on cylinders [Marston, Daniel, Fortuner, Kirsteins, and Abawi, J. Acoust. Soc. Am. 149, 3042-3051 (2021)]. Both shapes of reflectors were taken to be illuminated by short-wavelength plane wave double-sideband suppressed-carrier ultrasound. Here, the geometric method of evaluating dynamic forces on spheres is illustrated along with an analysis of the phase of the modulated radiation force. Comparison with partial wave series solutions supports the relevance of the specular reflection analysis for insight into forces on highly reflecting objects in water.

Spatially variant autofocus for circular synthetic aperture sonar

Circular synthetic aperture sonar (CSAS) is a method for improving the resolution and target detection capabilities of a synthetic aperture sonar system. CSAS data are difficult to focus because of their large aperture sizes and elevation sensitivity. This difficulty has sometimes been addressed by using transponders or distributing isotropic scatterers in the field of view of the system; however, this comes at the cost of reduced practicality. As an alternative, map-drift based multipoint autofocus ("multilateration") was proposed by Cantalloube and Nahum [IEEE Trans. Geosci. Remote Sens. 49, 3730-37 (2011)] for autofocusing analogous circular synthetic aperture radar data. Multilateration also solves the problem of aberration spatial variance by providing a three-dimensional navigation correction. In circular synthetic aperture focusing problems, though, correcting aberrations is a joint navigation and elevation estimation problem, and the present work extends the multilateration approach to simultaneously solve both a navigation solution and coordinate corrections for the multilateration control patches. Additionally, methods for addressing the stability and behavior of the inverse problem are addressed, and an adaptive weighting scheme for reducing the influence of outliers is presented. The field results demonstrate near optimal point-spread functions on distributions of natural isotropic scatterers and robustness in regions with bathymetric variability.

Passive underwater acoustic identification tags using multi-layered shells

The development of pre-deployed underwater infrastructures to aid in autonomous underwater vehicle (AUV) navigation is of keen interest, with the increased use of AUVs for undersea operations. Previous literature has introduced a class of passive underwater acoustic markers, termed acoustic identification (AID) tags [Satish, Trivett, and Sabra, J. Acoust. Soc. Am. 147(6), EL517-EL522 (2020)], which are inexpensive to construct, simple to deploy, and reflect unique engineered acoustic signatures that can be detected by an AUV instrumented with high-frequency sonar systems. An AID tag is built of multi-layer shells with different acoustic properties and thicknesses to generate a unique acoustic signature, composed of the multiple reflections created by the layer interfaces, thus akin to an "acoustic barcode." AID tags can be used as geospatial markers to highlight checkpoints in AUV trajectories or mark areas of interest underwater. This article investigates the optimization of the AID tag's design using energy based metrics and evaluates the detectability of an AID tag in the presence of interfering signals, such as clutter using matched-filter based techniques. Furthermore, experimental results of AID tags interrogated by a standard high-frequency sonar are presented to provide proof of concept of AID tag detection in a reverberant water tank.

Specular-reflection contributions to static and dynamic radiation forces on circular cylinders

Interest in the response of highly reflecting objects in water to modulated acoustical radiation forces makes it appropriate to consider contributions to such forces from perfectly reflecting objects to provide insight into radiation forces. The acoustic illumination can have wavelengths much smaller than the object's size, and objects of interest may have complicated shapes. Here, the specular contribution to the oscillating radiation force on an infinite circular cylinder at normal incidence is considered for double-sideband-suppressed carrier-modulated acoustic illumination. The oscillatory magnitude of the specular force decreases monotonically with increasing modulation frequency, and the phase of the oscillating force depends on the relative phase of the sidebands. The phase dependence on the modulation frequency can be reduced with the appropriate selection of a sideband relative-phase parameter. That is a consequence of the significance of rays that are incident on the cylinder having small impact parameters that are nearly backscattered. For one choice of a relative sideband phase, a prior partial wave series (PWS) solution is available, which supports the specular analysis when the PWS is evaluated for a rigid cylinder. The importance of specular contributions for aluminum cylinders in water is noted. A specular analysis for an analogous spherical reflector is also summarized.

Sonar target representation using two-dimensional Gabor wavelet features

This paper introduces a feature extraction technique that identifies highly informative features from sonar magnitude spectra for automated target classification. The approach involves creating feature representations through convolution of a two-dimensional Gabor wavelet and acoustic color magnitudes to capture elastic waves. This feature representation contains extracted localized features in the form of Gabor stripes, which are representative of unique targets and are invariant of target aspect angle. Further processing removes non-informative features through a threshold-based culling. This paper presents an approach that begins connecting model-based domain knowledge with machine learning techniques to allow interpretation of the extracted features while simultaneously enabling robust target classification. The relative performance of three supervised machine learning classifiers, specifically a support vector machine, random forest, and feed-forward neural network are used to quantitatively demonstrate the representations' informationally rich extracted features. Classifiers are trained and tested with acoustic color spectrograms and features extracted using the algorithm, interpreted as stripes, from two public domain field datasets. An increase in classification performance is generally seen, with the largest being a 47% increase from the random forest tree trained on the 1-31 kHz PondEx10 data, suggesting relatively small datasets can achieve high classification accuracy if model-cognizant feature extraction is utilized.

Method of numerical Green's function determination for far-field scattering solutions from objects at a water-sediment interface

A method is presented for numerically determining Green's functions for the purpose of calculating the far-field scattering from objects resting on or buried within the seafloor. To obtain the far-field scattering, initial evaluation of the three-dimensional near-field solution is required, through finite element analysis or other means. The Green's function and its spatial derivatives are then numerically evaluated for input into the Helmholtz-Kirchhoff integral, yielding the far-field scattering solution. This numerical technique determines the Green's function directly and avoids requiring analytic forms of Green's functions, which may be difficult or time consuming to evaluate for complex environments. This paper demonstrates the effectiveness of applying the numerical Green's function determination technique in conjunction with near-field results from finite element models to determine the far-field scattering for various elastic targets in free-field and flat seafloor environments. The method may be generalizable to arbitrary targets at complicated interfaces, incorporating interface roughness, layering, and volume inhomogeneities.

Efficient, wide-band rigid-body and elastic scattering computations using transient equivalent sources

A previous paper by the author has shown that transient structural-acoustic problems can be solved using time stepping procedures with the structure and fluid modeled using finite elements and equivalent sources, respectively. Here, the analysis is extended to included scattering problems. Although scattering problems have been discussed extensively in the literature, the current formulation is unique because the acoustic coupling matrix is treated as sparse. Also, most of the previous analyses have assumed the problem is time harmonic, and there is an advantage to performing the computations in the time domain because only a limited number of time steps are required to obtain wideband frequency resolution. This is especially true if the main emphasis is on the mid- to high-frequencies since the ringing response is typically dominated by the lowest frequency modes. Several examples are solved to validate the computations and to document the computation times and solution accuracy.

Echo statistics associated with discrete scatterers: A tutorial on physics-based methods

When a beam emitted from an active monostatic sensor system sweeps across a volume, the echoes from scatterers present will fluctuate from ping to ping due to various interference phenomena and statistical processes. Observations of these fluctuations can be used, in combination with models, to infer properties of the scatterers such as numerical density. Modeling the fluctuations can also help predict system performance and associated uncertainties in expected echoes. This tutorial focuses on "physics-based statistics," which is a predictive form of modeling the fluctuations. The modeling is based principally on the physics of the scattering by individual scatterers, addition of echoes from randomized multiple scatterers, system effects involving the beampattern and signal type, and signal theory including matched filter processing. Some consideration is also given to environment-specific effects such as the presence of boundaries and heterogeneities in the medium. Although the modeling was inspired by applications of sonar in the field of underwater acoustics, the material is presented in a general form, and involving only scalar fields. Therefore, it is broadly applicable to other areas such as medical ultrasound, non-destructive acoustic testing, in-air acoustics, as well as radar and lasers.

Sparse estimation of backscattered echoes from underwater object using integrated dictionaries

The problem of time-delays estimation of backscattered echoes from underwater targets is presented using a sparse reconstruction framework employing an integrated dictionary. To achieve high resolution, the used dictionary is usually defined over a finely spaced grid over the region of interest. Such a procedure may result in problems of being computational cumbersome or suffering from basis mismatch. In addition, the shape of the backscattered echoes may differ significantly from the expected waveforms used to form the dictionary, causing further mismatch problems. To alleviate such problems, the use of an integrated dictionary framework is introduced. Unlike traditional dictionaries that are defined over a set of grid points, the elements in an integrated dictionary are formed by integrating the expected waveform over bands of the parameter space. The resulting dictionary may be used to find initial regions of the parameters of interest using a smaller dictionary than otherwise required, without suffering a loss of performance. The elements can also better match with the backscattered echoes, even if these differ from their expected shape. Simulated results of the backscattered echoes from a cylindrical shell, as well as results from experimental measurements, illustrate the performance of the proposed method.

Integrated calculation method of acoustic radiation and propagation for floating bodies in shallow water

Based on the three-dimensional sono-elasticity theory for ship structures, the Green's function is incorporated and an integrated calculation method of acoustic radiation and propagation for floating bodies in shallow water considering the sound velocity profile is proposed. The near-field and arbitrary far-field acoustic radiation problem can be efficiently calculated. A numerical example of a rigid sphere is given and the results are compared with the finite element method solution to validate the reliability and demonstrate improvements in efficiency. The method is applied to an elastic capsular shell, verifying the applicability of the method for any elastic floating bodies.

Geometry and topology of the space of sonar target echos

Successful synthetic aperture sonar target classification depends on the "shape" of the scatterers within a target signature. This article presents a workflow that computes a target-to-target distance from persistence diagrams, since the "shape" of a signature informs its persistence diagram in a structure-preserving way. The target-to-target distances derived from persistence diagrams compare favorably against those derived from spectral features and have the advantage of being substantially more compact. While spectral features produce clusters associated to each target type that are reasonably dense and well formed, the clusters are not well-separated from one another. In rather dramatic contrast, a distance derived from persistence diagrams results in highly separated clusters at the expense of some misclassification of outliers.

Rayleigh scattering of a cylindrical sound wave by an infinite cylinder

Rayleigh scattering, in which the wavelength is large compared to the scattering object, is usually studied assuming plane incident waves. However, full Green's functions are required in a number of problems, e.g., when a scatterer is located close to the ocean surface or the seafloor. This paper considers the Green's function of the two-dimensional problem that corresponds to scattering of a cylindrical wave by an infinite cylinder embedded in a homogeneous fluid. Soft, hard, and impedance cylinders are considered. Exact solutions of the problem involve infinite series of products of Bessel functions. Here, simple, closed-form asymptotic solutions are derived, which are valid for arbitrary source and receiver locations outside the cylinder as long as its diameter is small relative to the wavelength. The scattered wave is given by the sum of fields of three linear image sources. The viability of the image source method was anticipated from known solutions of classical electrostatic problems involving a conducting cylinder. The asymptotic acoustic Green's functions are employed to investigate reception of low-frequency sound by sensors mounted on cylindrical bodies.

Passive underwater acoustic markers using Bragg backscattering

This letter demonstrates the feasibility of a passive underwater acoustic marker technology (or "AcoustiCode") for use in underwater navigation. An AcoustiCode tag is a planar surface with machined periodic patterns capable of producing Bragg backscattering beampatterns with engineered spatial and frequency variations, thus having a unique three-dimensional acoustic signature over a selected frequency band. Hence, these AcoustiCodes enable three-dimensional navigation and information signaling in a totally passive manner for existing high-frequency SONAR systems (potentially mounted on autonomous underwater vehicles), which naturally operate in a narrow frequency band and can also be used over significantly longer ranges compared to optically-based systems.

Multistatic acoustic characterization of seabed targets

One application for autonomous underwater vehicles (AUVs) is detecting and classifying hazardous objects on the seabed. An acoustic approach to this problem has been studied in which an acoustic source insonifies seabed target while receiving AUVs with passive sensing payloads discriminate targets based on features of the three dimensional scattered fields. The OASES-SCATT simulator was used to study how scattering data collected by mobile receivers around targets insonified by mobile sources might be used for sphere and cylinder target characterization in terms of shape, composition, and size. The impact of target geometry on these multistatic scattering fields is explored, and a discrimination approach developed in which the source and receiver circle the target with the same radial speed. The frequency components of the multistatic scattering data at different bistatic angles are used to form models for target characteristics. Data are then classified using these models. Classification accuracies were greater than 98% for shape and composition. Regression for target volume showed potential, with 90% chance of errors less than 15%. The significance of this approach is to make classification using low-cost vehicles plausible from scattering amplitudes and the relative angles between the target, source, and receiver vehicles.

Spectral analysis of bistatic scattering from underwater elastic cylinders and spheres

Far field sound scattering from underwater elastic spheres and finite cylinders is considered over the full range of scattering angles. Three models for the frequency response of the scattered field are evaluated: a hybrid finite element/propagation simulation for a finite cylinder with broadside illumination, an approximate solution for the finite cylinder, and the exact solution for a sphere. The cylinder models are shown to give comparable results, attesting to the strength of the finite cylinder approximate solution. Interference and resonance structure present in the frequency response of the targets is identified and discussed, and the bistatic spectra for a variety of elastic sphere materials are presented. A thorough understanding of the complicated angle and frequency dependence of the scattering from simple elastic targets is helpful for interpretation of backscattering data from targets at or near an interface, or for scattering data taken by moving automated underwater vehicles, acoustic arrays, or other forms of data collection involving bistatic scattering.

Buried targets in layered media: A combined finite element/physical acoustics model and comparison to data on a half buried 2:1 cylinder

Previously, a combined finite element/physical acoustics model for proud targets [K. L. Williams, S. G. Kargl, E. I. Thorsos, D. S. Burnett, J. L. Lopes, M. Zampolli, and P. L. Marston, J. Acoust. Soc. Am. 127, 3356-3371 (2010)] was compared to both higher fidelity finite element models and to experimental data for a proud 2:1 aluminum cylinder. Here that expression is generalized to address the case of a target buried in a layered media. The result is compared to data acquired for the same 2:1 cylinder but half buried in a mud layer that covers the sand sediment (considered here as infinite in extent below the mud layer). The generalized expression reduces to both the previous proud result and to the result for a target buried in an infinite medium under the appropriate limiting conditions. The model/data comparisons shown include both the previous proud model and data results along with the ones for the half buried cylinder. The comparison quantifies the reduction in target strength as a function of frequency in the half buried case relative to the proud case.

A Fourier-based total-field/scattered-field technique for three-dimensional broadband simulations of elastic targets near a water-sand interface

The numerical simulation of acoustic scattering from elastic objects near a water-sand interface is critical to underwater target identification. Frequency-domain methods are computationally expensive, especially for large-scale broadband problems. A numerical technique is proposed to enable the efficient use of finite-difference time-domain method for broadband simulations. By incorporating a total-field/scattered-field boundary, the simulation domain is restricted inside a tightly bounded region. The incident field is further synthesized by the Fourier transform for both subcritical and supercritical incidences. Finally, the scattered far field is computed using a half-space Green's function. Numerical examples are further provided to demonstrate the accuracy and efficiency of the proposed technique.

High frequency imaging and elastic effects for a solid cylinder with axis oblique relative to a nearby horizontal surface

The calibrated acoustic backscattering spectrum versus aspect angle, also called the "acoustic color" or "acoustic template," of solid cylinders located near a flat interface was previously studied for the case where the cylinder axis was vertically oblique relative to the interface and was insonified by a beam at a non-zero grazing angle. The presence of the interface allows for multiple paths by which sound is backscattered. These multipaths are highly dependent on the relative orientations of the target, the interface, and the source/receiver. In this work, the effects of vertical obliquity on the reconstructed synthetic aperture acoustic images is presented. Several robust orientation dependent features are considered and the physical mechanisms responsible identified through geometric arguments. Information about a target's three-dimensional orientation and size may be gleaned from these images, aiding the interpretation of features within the target's acoustic template. Specific features observed in the reconstructed image are associated with features in the acoustic color. The coupling conditions for surface elastic waves are also considered.

Model-based waveform design for optimal detection: A multi-objective approach to dealing with incomplete a priori knowledge

This work considers the design of optimal, energy-constrained transmit signals for active sensing for the case when the designer has incomplete or uncertain knowledge of the target and/or environment. The mathematical formulation is that of a multi-objective optimization problem, wherein one can incorporate a plurality of potential targets, interference, or clutter models and in doing so take advantage of the wide range of results in the literature related to modeling each. It is shown, via simulation, that when the objective function of the optimization problem is chosen to maximize the minimum (i.e., maxmin) probability of detection among all possible model combinations, the optimal waveforms obtained are advantageous. The advantage results because the maxmin waveforms judiciously allocate energy to spectral regions where each of the target models respond strongly and each of the environmental models affect minimal detection performance degradation. In particular, improved detection performance is shown compared to linear frequency modulated transmit signals and compared to signals designed with the wrong target spectrum assumed. Additionally, it is shown that the maxmin design yields performance comparable to an optimal design matched to the correct target/environmental model. Finally, it is proven that the maxmin problem formulation is convex.

High frequency backscattering by a solid cylinder with axis tilted relative to a nearby horizontal surface

The backscattering spectrum versus azimuthal angle, also called the "acoustic color" or "acoustic template," of solid cylinders located in the free water column have been previously studied. For cylinders lying proud on horizontal sand sediment, there has been progress in understanding the backscattering spectrum as a function of grazing angle and the viewing angle relative to the cylinder's axis. Significant changes in the proud backscattering spectrum versus the freefield case are associated with the interference of several multipaths involving the target and the surface. If the cylinder's axis has a vertical tilt such that one end is partially buried in the sand, the multipath structure is changed, thus modifying the resulting spectrum. Some of the changes in the template can be approximately modeled using a combination of geometrical and physical acoustics. The resulting analysis gives a simple approximation relating certain changes in the template with the vertical tilt of the cylinder. This includes a splitting in the azimuthal angle at which broadside multipath features are observed. A similar approximation also applies to a metallic cylinder adjacent to a flat free surface and was confirmed in tank experiments.

Scattering from a finite cylinder near an interface

In this paper, a Boundary Integral Equation Method (BIEM) is described for the computation of scattering from a finite, rigid, cylinder near a pressure release interface. The cylinder lies parallel or tilted with respect to the interface plane so that the azimuthal symmetry of the problem is destroyed. The scattering solution is first described in terms of an azimuthally symmetric free space solution. The multiple interactions of the scattered field with the interface are accounted for by an azimuthal-conversion matrix. In Sec. III, the method of this paper is benchmarked using wavefield superposition for a sphere near a pressure-release surface. Computed scattered spectra are shown for a finite cylinder, parallel and tilted with respect to the interface, and for a variety of source/receiver geometries. The differences resulting from not including multiple target/interface interactions (single scatter solution) and from including all interactions are presented. The problem of irregular frequencies for the single-scatter and the fully coupled BIEM are discussed and numerically examined.

Fast nearfield to farfield conversion algorithm for circular synthetic aperture sonar

Monostatic circular synthetic aperture sonar (CSAS) images are formed by processing azimuthal angle dependent backscattering from a target at a fixed distance from a collocated source/receiver. Typical CSAS imaging algorithms [Ferguson and Wyber, J. Acoust. Soc. Am. 117, 2915-2928 (2005)] assume scattering data are taken in the farfield. Experimental constraints may make farfield measurements impractical and thus require objects to be scanned in the nearfield. Left uncorrected this results in distortions of the target image and in the angular dependence of features. A fast approximate Hankel function based algorithm is presented to convert nearfield data to the farfield. Images and spectrograms of an extended target are compared for both cases.

Acoustic scattering from a water-filled cylindrical shell: measurements, modeling, and interpretation

Understanding the physics governing the interaction of sound with targets in an underwater environment is essential to improving existing target detection and classification algorithms. To illustrate techniques for identifying the key physics, an examination is made of the acoustic scattering from a water-filled cylindrical shell. Experiments were conducted that measured the acoustic scattering from a water-filled cylindrical shell in the free field, as well as proud on a sand-water interface. Two modeling techniques are employed to examine these acoustic scattering measurements. The first is a hybrid 2-D/3-D finite element (FE) model, whereby the scattering in close proximity to the target is handled via a 2-D axisymmetric FE model, and the subsequent 3-D propagation to the far field is determined via a Helmholtz integral. This model is characterized by the decomposition of the fluid pressure and its derivative in a series of azimuthal Fourier modes. The second is an analytical solution for an infinitely long cylindrical shell, coupled with a simple approximation that converts the results to an analogous finite length form function. Examining these model results on a mode-by-mode basis offers easy visualization of the mode dynamics and helps distinguish the different physics driving the target response.

Subspace array processing using spatial time-frequency distributions: applications for denoising structural echoes of elastic targets

Structural echoes of underwater elastic targets, used for detection and classification purposes, can be highly localized in the time-frequency domain and can be aspect-dependent. Hence such structural echoes recorded along a distributed (synthetic) aperture, e.g., using a moving receiver platform, would not meet the stationarity and multiple snapshots requirements of common subspace array processing methods used for denoising array data based on their estimated covariance matrix. To address this issue, this article introduces a subspace array processing method based on the space-time-frequency distribution (STFD) of single-snapshots of non-stationary signals. This STFD is obtained by computing Cohen's class time-frequency distributions between all pairwise combination of the recorded signals along an arbitrary aperture array. This STFD is interpreted as a generalized array covariance matrix which automatically accounts for the inherent coherence across the time-frequency plane of the received nonstationary echoes emanating from the same target. Hence, identifying the signal's subspace from the eigenstructure of this STFD provides a means for denoising these non-stationary structural echoes by spreading the clutter and noise power in the time-frequency domain; as demonstrated here numerically and experimentally using the structural echoes of a thin steel spherical shell measured along a synthetic aperture.

Computation of dispersion curves for embedded waveguides using a dashpot boundary condition

In this paper a numerical approach is presented to compute dispersion curves for solid waveguides coupled to an infinite medium. The derivation is based on the scaled boundary finite element method that has been developed previously for waveguides with stress-free surfaces. The effect of the surrounding medium is accounted for by introducing a dashpot boundary condition at the interface between the waveguide and the adjoining medium. The damping coefficients are derived from the acoustic impedances of the surrounding medium. Results are validated using an improved implementation of an absorbing region. Since no discretization of the surrounding medium is required for the dashpot approach, the required number of degrees of freedom is typically 10 to 50 times smaller compared to the absorbing region. When compared to other finite element based results presented in the literature, the number of degrees of freedom can be reduced by as much as a factor of 4000.

Sonar target enhancement by shrinkage of incoherent wavelet coefficients

Background reverberation can obscure useful features of the target echo response in broadband low-frequency sonar images, adversely affecting detection and classification performance. This paper describes a resolution and phase-preserving means of separating the target response from the background reverberation noise using a coherence-based wavelet shrinkage method proposed recently for de-noising magnetic resonance images. The algorithm weights the image wavelet coefficients in proportion to their coherence between different looks under the assumption that the target response is more coherent than the background. The algorithm is demonstrated successfully on experimental synthetic aperture sonar data from a broadband low-frequency sonar developed for buried object detection.

A rail system for circular synthetic aperture sonar imaging and acoustic target strength measurements: design/operation/preliminary results

A 22 m diameter circular rail, outfitted with a mobile sonar tower trolley, was designed, fabricated, instrumented with underwater acoustic transducers, and assembled on a 1.5 m thick sand layer at the bottom of a large freshwater pool to carry out sonar design and target scattering response studies. The mobile sonar tower translates along the rail via a drive motor controlled by customized LabVIEW software. The rail system is modular and assembly consists of separately deploying eight circular arc sections, measuring a nominal center radius of 11 m and 8.64 m arc length each, and having divers connect them together in the underwater environment. The system enables full scale measurements on targets of interest with 0.1° angular resolution over a complete 360° aperture, without disrupting target setup, and affording a level of control over target environment conditions and noise sources unachievable in standard field measurements. In recent use, the mobile cart carrying an instrumented sonar tower was translated along the rail in 720 equal position increments and acoustic backscatter data were acquired at each position. In addition, this system can accommodate both broadband monostatic and bistatic scattering measurements on targets of interest, allowing capture of target signature phenomena under diverse configurations to address current scientific and technical issues encountered in mine countermeasure and unexploded ordnance applications. In the work discussed here, the circular rail apparatus is used for acoustic backscatter testing, but this system also has the capacity to facilitate the acquisition of magnetic and optical sensor data from targets of interest. A brief description of the system design and operation will be presented along with preliminary processed results for data acquired from acoustic measurements conducted at the Naval Surface Warfare Center, Panama City Division Test Pond Facility. [Work Supported by the U.S. Office of Naval Research and The Strategic Environmental Research and Development Program.].

Time and frequency constrained sonar signal design for optimal detection of elastic objects

In this paper, the task of model-based transmit signal design for optimizing detection is considered. Building on past work that designs the spectral magnitude for optimizing detection, two methods for synthesizing minimum duration signals with this spectral magnitude are developed. The methods are applied to the design of signals that are optimal for detecting elastic objects in the presence of additive noise and self-noise. Elastic objects are modeled as linear time-invariant systems with known impulse responses, while additive noise (e.g., ocean noise or receiver noise) and acoustic self-noise (e.g., reverberation or clutter) are modeled as stationary Gaussian random processes with known power spectral densities. The first approach finds the waveform that preserves the optimal spectral magnitude while achieving the minimum temporal duration. The second approach yields a finite-length time-domain sequence by maximizing temporal energy concentration, subject to the constraint that the spectral magnitude is close (in a least-squares sense) to the optimal spectral magnitude. The two approaches are then connected analytically, showing the former is a limiting case of the latter. Simulation examples that illustrate the theory are accompanied by discussions that address practical applicability and how one might satisfy the need for target and environmental models in the real-world.

Acoustic identification of buried underwater unexploded ordnance using a numerically trained classifier (L)

Using a finite element-based structural acoustics code, simulations were carried out for the acoustic scattering from an unexploded ordnance rocket buried in the sediment under 3 m of water. The simulation treated 90 rocket burial angles in steps of 2°. The simulations were used to train a generative relevance vector machine (RVM) algorithm for identifying rockets buried at unknown angles in an actual water/sediment environment. The trained RVM algorithm was successfully tested on scattering measurements made in a sediment pool facility for six buried targets including the rocket at 90°, 120°, and 150°, a boulder, a cinderblock, and a cinderblock rolled 45° about its long axis.

Bistatic, above-critical angle scattering measurements of fully buried unexploded ordnance (UXO) and clutter

Laboratory grade bistatic scattering measurements are conducted in order to examine the acoustic response of realistic fully buried unexploded ordnance (UXO) from above-critical angle insonification, between 2 and 40 kHz. A 127 mm diameter rocket UXO, a 155 mm diameter artillery shell, a natural rock of approximately the same size, and a cinder block are fully buried in water-saturated medium grained sand (mean grain diameter, 240 μm) at depths of 10 cm below the water-sediment interface. A two-dimensional array of bistatic scattering measurements is generated synthetically by scanning a single hydrophone in steps of 3 cm over a 1 m × 1 m patch directly above the targets at a height of 20 cm above the water-sediment interface. Three-dimensional volumetric acoustic images generated from the return waveforms reveal scattering components attributed to geometric and elastic scattering, as well as multiple-scattering interactions of returns between the sediment-water interface and the buried objects. The far-field target strength of the objects is estimated through extrapolation of the angular spectrum. Agreement is found between experimental data and simulated data generated from a finite-element-based, three-dimensional time-harmonic model (2-25 kHz). Separation of the measured UXO from the clutter objects is demonstrated through exploitation of structural-acoustics-based features.

Time-frequency analysis of the bistatic acoustic scattering from a spherical elastic shell

The development of low-frequency sonar systems, using, for instance, a network of autonomous systems in unmanned vehicles, provides a practical means for bistatic measurements (i.e., when the source and receiver are widely separated) allowing for multiple viewpoints of the target of interest. Time-frequency analysis, in particular, Wigner-Ville analysis, takes advantage of the evolution time dependent aspect of the echo spectrum to differentiate a man-made target, such as an elastic spherical shell, from a natural object of the similar shape. A key energetic feature of fluid-loaded and thin spherical shell is the coincidence pattern, also referred to as the mid-frequency enhancement (MFE), that results from antisymmetric Lamb-waves propagating around the circumference of the shell. This article investigates numerically the bistatic variations of the MFE with respect to the monostatic configuration using the Wigner-Ville analysis. The observed time-frequency shifts of the MFE are modeled using a previously derived quantitative ray theory by Zhang et al. [J. Acoust. Soc. Am. 91, 1862-1874 (1993)] for spherical shell's scattering. Additionally, the advantage of an optimal array beamformer, based on joint time delays and frequency shifts is illustrated for enhancing the detection of the MFE recorded across a bistatic receiver array when compared to a conventional time-delay beamformer.

Acoustic quasi-holographic images of scattering by vertical cylinders from one-dimensional bistatic scans

When synthetic aperture sonar (SAS) is used to image elastic targets in water, subtle features can be present in the images associated with the dynamical response of the target being viewed. In an effort to improve the understanding of such responses, as well as to explore alternative image processing methods, a laboratory-based system was developed in which targets were illuminated by a transient acoustic source, and bistatic responses were recorded by scanning a hydrophone along a rail system. Images were constructed using a relatively conventional bistatic SAS algorithm and were compared with images based on supersonic holography. The holographic method is a simplification of one previously used to view the time evolution of a target's response [Hefner and Marston, ARLO 2, 55-60 (2001)]. In the holographic method, the space-time evolution of the scattering was used to construct a two-dimensional image with cross range and time as coordinates. Various features for vertically hung cylindrical targets were interpreted using high frequency ray theory. This includes contributions from guided surface elastic waves, as well as transmitted-wave features and specular reflection.

Boundary effects on backscattering by a solid aluminum cylinder: experiment and finite element model comparisons (L)

Backscattering of sound by a solid aluminum cylinder was measured in the free field and with the cylinder near a flat surface. The target was suspended just below the surface of a water tank to simulate some aspects of backscattering when resting on the seabed. Measurements were compared with predictions made by an approximate hybrid approach based on multiple two-dimensional finite element calculations and the use of images. Many of the spectral features present in the tank data were present in the model. Comparing numerical model predictions with experimental data serves to build credibility for the modeling approach and can assist in developing insight into the underlying physical processes.

Structural-acoustic modeling for three-dimensional freefield and littoral environments with verification and validation

This paper describes a high-order, finite-element-based, three-dimensional time-harmonic model for large-scale exterior structural-acoustics problems. It is applicable to both freefield and littoral environments. For the freefield case, the infinite exterior is treated as a homogeneous linear acoustic medium. For littoral applications, the water or air and the sediment domains are each treated as linear homogeneous, semi-infinite half-spaces with piecewise-constant properties. Both domains admit complex-valued wave speeds to enable the inclusion of damping. The finite element formulation uses a variational statement which naturally incorporates the transmission-condition at the water or air-sediment interface. The truncation of the infinite exterior is realized using an infinite-element for the freefield case, and the perfectly-matched-layer approximation for littoral applications. Computation of the farfield quantities is done based on an integral representation which, for the littoral cases, uses efficient approximations for the appropriate Green's function. Numerical computations are presented for a series of progressively more complex problems, and are used to verify the model against analytic and other numerical solutions and validate it based on the experimental data for scattering from elastic scatterers as measured in freefield and sediment pool laboratory facilities.