Measurements and modeling of acoustic scattering from partially and completely buried spherical shells

Sound scattering and radiation suppression by pressurized spherical shells

Thin-shell models offer important insights into the complex process of sound-structure interaction but are found to be inconsistent with the rigorous thick-shell theory for fluid-loaded spherical shells. Here, linearized equations of motion of fluid-loaded, thin, spherical shells are re-derived from the first principles. The shell may be prestressed due to the difference in the static pressures in the internal and external fluids. Differences in the fluid-loading terms from previously proposed ad hoc models are identified and their significance is analyzed. Analytic solutions are derived of the problems of spherical sound wave scattering by a fluid-filled, prestressed spherical shell and resonant vibrations of the shell. The results reduce to a number of known exact and asymptotic solutions in appropriate limiting cases. The mathematical model of the shell vibrations is applied to characterize the influence of the shell's material properties and the prestress on passive suppression of low-frequency underwater sound radiation due to diffraction on an acoustically compliant sphere, such as an encapsulated gas bubble. Using soft rubber as the encapsulating membrane is found to preserve the sound suppression qualities of the free gas bubble.

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.

Compressive synthetic aperture sonar imaging with distributed optimization

Synthetic aperture sonar (SAS) provides high-resolution acoustic imaging by processing coherently the backscattered acoustic signal recorded over consecutive pings. Traditionally, object detection and classification tasks rely on high-resolution seafloor mapping achieved with widebeam, broadband SAS systems. However, aspect- or frequency-specific information is crucial for improving the performance of automatic target recognition algorithms. For example, low frequencies can be partly transmitted through objects or penetrate the seafloor providing information about internal structure and buried objects, while multiple views provide information about the object's shape and dimensions. Sub-band and limited-view processing, though, degrades the SAS resolution. In this paper, SAS imaging is formulated as an ℓ₁-norm regularized least-squares optimization problem which improves the resolution by promoting a parsimonious representation of the data. The optimization problem is solved in a distributed and computationally efficient way with an algorithm based on the alternating direction method of multipliers. The resulting SAS image is the consensus outcome of collaborative filtering of the data from each ping. The potential of the proposed method for high-resolution, narrowband, and limited-aspect SAS imaging is demonstrated with simulated and experimental data.

Enhanced backscattering in water by partially exposed cylinders at free surfaces associated with an acoustic Franz wave

When a smooth curved object is lowered into water, the initial specular contribution to high frequency backscattering of sound is weak before the specular point on the object becomes illuminated by incident sound. The associated transition in reflection from a metallic cylinder viewed at grazing incidence was previously studied [Baik and Marston, IEEE J. Ocean. Eng. 33, 386-396 (2008)]. The present research involves analogous measurements of backscattering performed using short tone bursts facilitating improved temporal resolution of distinct mechanisms contributing to the backscattering. The measurements reveal the presence of a delayed contribution to the backscattering that evolves in time in a way consistent with a scattering contribution of an acoustic Franz wave. The wave appears to be partially reflected at the free surface after having been excited on the cylinder by the incident acoustic wave. For slightly exposed cylinders viewed at grazing incidence, the Franz wave mechanism dominated the observed backscattering.

Quantifying the effects of roughness scattering on reflection loss measurements

Seafloor reflection loss and roughness measurements were taken at the Experimental Validation of Acoustic Modeling Techniques experiment in 2006. The magnitude and phase of the reflection loss was measured at frequencies from 5 to 80 kHz and grazing angles from 7° to 77°. Approximately 1500 samples were taken for each angle. The roughness was measured with a laser profiler. Geoacoustic parameters such as water and sediment sound speed and density were measured concurrently. The reflection loss data were compared with three models: A flat interface elastic model based on geoacoustic measurements; a flat interface poro-elastic model based on the Biot/Stoll model; and a rough interface model based on the measured interface roughness power spectrum. The data were most consistent with the poro-elastic model including scattering. The elastic model consistently predicted values for the reflection loss which were higher than measured. The data exhibited more variability than the model due to layering and fluctuations in the propagating medium.

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.

Discriminating resonant targets from clutter using Lanczos iterated single-channel time reversal

Power iterated single-channel time-reversal is extended to employ Lanczos iterations. The properties of these algorithms are studied in the presence of varying levels of noise and broadband clutter. It is shown the Lanczos iterated method possesses superior convergence properties in comparison to the standard power iterated technique. Results demonstrate that such algorithms provide an efficient means through which to isolate and extract the properties of resonant scatterers in the presence of noise and coherent interference.

Isolating scattering resonances of an air-filled spherical shell using iterative, single-channel time reversal

Iterative, single-channel time reversal is employed to isolate backscattering resonances of an air-filled spherical shell in a frequency range of 0.5-20 kHz. Numerical simulations of free-field target scattering suggest improved isolation of the dominant target response frequency in the presence of varying levels of stochastic noise, compared to processing returns from a single transmission and also coherent averaging. To test the efficacy of the technique in a realistic littoral environment, monostatic scattering experiments are conducted in the Gulf of Mexico near Panama City, Florida. The time reversal technique is applied to returns from a hollow spherical shell target sitting proud on a sandy bottom in 14 m deep water. Distinct resonances in the scattering response of the target are isolated, depending upon the bandwidth of the sonar system utilized.

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.

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.

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

Understanding acoustic scattering from objects placed on the interface between two media requires incorporation of scattering off the interface. Here, this class of problems is studied in the particular context of a 61 cm long, 30.5 cm diameter solid aluminum cylinder placed on a flattened sand interface. Experimental results are presented for the monostatic scattering from this cylinder for azimuthal scattering angles from 0 degrees to 90 degrees and frequencies from 1 to 30 kHz. In addition, synthetic aperture sonar (SAS) processing is carried out. Next, details seen within these experimental results are explained using insight derived from physical acoustics. Subsequently, target strength results are compared to finite-element (FE) calculations. The simplest calculation assumes that the source and receiver are at infinity and uses the FE result for the cylinder in free space along with image cylinders for approximating the target/interface interaction. Then the effect of finite geometries and inclusion of a more complete Green's function for the target/interface interaction is examined. These first two calculations use the axial symmetry of the cylinder in carrying out the analysis. Finally, the results from a three dimensional FE analysis are presented and compared to both the experiment and the axially symmetric calculations.

Classification of a cylindrical target buried in a thin sand-water mixture using acoustic spectra

A number of papers have shown that it is possible to characterize an air-filled cylindrical shell immersed in water using data obtained from a backscattering spectrum. The scattered impulse time signal is constituted of echoes linked to the reradiation of waves circumnavigating around the cylindrical target. In the first part of this work, the scattered signal is calculated and then measured under conditions where the cylindrical shell is immersed in water. In the second part, the cylindrical shell is buried in a thin sand-water mixture. It is insonified perpendicularly to its axis and perpendicularly to the water mixture interface. The scattered impulse time signal is recorded and processed using a Fourier transform algorithm to obtain a resonance spectrum. Among all the resonances that are established in the explored frequency band, only those related to the circumferential S(0) wave are observed on the resonance spectrum of a cylindrical shell buried in the sand-water mixture. Resonances of the circumferential A wave also called A0- wave seem to have vanished. The resonance spectrum obtained by the Method of Isolation and Identification of Resonances (MIIR) reveals that it is possible to detect and classify an object buried in thin sand-water mixture in laboratory conditions.

Sensing a buried resonant object by single-channel time reversal

Scaled laboratory experiments are conducted to assess the efficacy of iterative, single-channel time reversal for enhancement of monostatic returns from resonant spheres in the free field and buried in a sediment phantom. Experiments are performed in a water tank using a broad-band piston transducer operating between 0.4 and 1.5 MHz and calibrated using free surface reflections. Solid and hollow metallic spheres, 6.35 mm in diameter, are buried in a consolidation of 128-microm-mean- diameter spherical glass beads. The procedure consists of exciting the target object with a broadband pulse, sampling the return using a finite time window, reversing the signal in time, and using this reversed signal as the source waveform for the next interrogation. Results indicate that the spectrum of the returns rapidly converges to the dominant mode in the backscattering response of the target. Signal-to-noise enhancement of the target echo is demonstrated for a target at several burial depths. Images generated by scanning the transducer over the location of multiple buried targets demonstrate the ability of the technique to distinguish between targets of differing type and to yield an enhancement of different modes within the response of a single target as a function of transducer position and processing bandwidth.

Benchmark problems for acoustic scattering from elastic objects in the free field and near the seafloor

Results from a workshop organized in 2006 to assess the state of the art in target scatter modeling are presented. The problem set includes free-field scenarios as well as scattering from targets that are proud, half-buried, or fully buried in the sediment. The targets are spheres and cylinders, of size O(1 m), which are insonified by incident plane waves in the low-frequency band 0.1-10 kHz. In all cases, the quantity of interest is the far-field target strength. The numerical techniques employed fall within three classes: (i) finite-element (FE) methods and (ii) boundary-element (BE) techniques, with different approaches to computing the far field via discretizations of the Helmholtz-Kirchhoff integral in each case, and (iii) semianalytical methods. Reference solutions are identified for all but one of the seven test problems considered. Overall, FE- and BE-based models emerge as those being capable of treating a wider class of problems in terms of target geometry, with the FE method having the additional advantage of being able to deal with complex internal structures without much additional effort. These capabilities are of value for the study of experimental scenarios, which can essentially be envisioned as variations of the problem set presented here.

Tank measurements of scattering from a resin-filled fiberglass spherical shell with internal flaws

This paper presents results of acoustic inversion and structural health monitoring achieved by means of low to midfrequency elastic scattering analysis of simple, curved objects, insonified in a water tank. Acoustic elastic scattering measurements were conducted between 15 and 100 kHz on a 60-mm-radius fiberglass spherical shell, filled with a low-shear-speed epoxy resin. Preliminary measurements were conducted also on the void shell before filling, and on a solid sphere of the same material as the filler. These data were used to estimate the constituent material parameters via acoustic inversion. The objects were measured in the backscatter direction, suspended at midwater, and insonified by a broadband directional transducer. From the inspection of the response of the solid-filled shell it was possible to detect and characterize significant inhomogeneities of the interior (air pockets), the presence of which were later confirmed by x-ray CT scan and ultrasound measurements. Elastic wave analysis and a model-data comparison study support the physical interpretation of the measurements.

Computing the far field scattered or radiated by objects inside layered fluid media using approximate Green's functions

A numerically efficient technique is presented for computing the field radiated or scattered from three-dimensional objects embedded within layered acoustic media. The distance between the receivers and the object of interest is supposed to be large compared to the acoustic wavelength. The method requires the pressure and normal particle displacement on the surface of the object or on an arbitrary circumscribing surface, as an input, together with a knowledge of the layered medium Green's functions. The numerical integration of the full wave number spectral representation of the Green's functions is avoided by employing approximate formulas which are available in terms of elementary functions. The pressure and normal particle displacement on the surface of the object of interest, on the other hand, may be known by analytical or numerical means or from experiments. No restrictions are placed on the location of the object, which may lie above, below, or across the interface between the fluid media. The proposed technique is verified through numerical examples, for which the near field pressure and the particle displacement are computed via a finite-element method. The results are compared to validated reference models, which are based on the full wave number spectral integral Green's function.

Target detection and location with ambient noise

By placing a vertical array in an ambient noise field and forming an upward and a downward beam one obtains two time series which can be cross correlated to reveal a subbottom profile of the seabed [Siderius et al., J. Acoust. Soc. Am. 120, 1315-1323 (2006)]. Here the cross-correlation approach is applied to the location in range and bearing of a point target. An experiment was designed using floats and weights mounted (and dismounted) on the same cable as the vertical array. Careful measurements were made of the location of all likely floats, ballast weights, array terminations, and so on. After suitable coherent averaging, peaks were seen at delays (correlation offsets) agreeing with the reflector positions and were shown to be absent when reflectors were removed. A trivial extension of the theory developed in Harrison and Siderius [J. Acoust. Soc. Am. 123, 1282-1296 (2008)] is used to explain the rough amplitudes of the reflections. The approach differs from "acoustic daylight" principally in having a capability to determine a target range.

Subcritical scattering from buried elastic shells

Buried objects have been largely undetectable by traditional high-frequency sonars due to their insignificant bottom penetration. Further, even a high grazing angle sonar approach is vastly limited by the coverage rate dictated by the finite water depth, making the detection and classification of buried objects using low frequency, subcritical sonar an interesting alternative. On the other hand, such a concept would require classification clues different from the traditional high-resolution imaging and shadows to maintain low false alarm rates. A potential alternative, even for buried targets, is classification based on the acoustic signatures of man-made elastic targets. However, the elastic responses of buried and proud targets are significantly different. The objective of this work is to identify, analyze, and explain some of the effects of the sediment and the proximity of the seabed interface on the scattering of sound from completely and partially buried elastic shells. The analysis was performed using focused array processing of data from the GOATS98 experiment carried out jointly by MIT and SACLANTCEN, and a new hybrid modeling capability combining a virtual source-or wave-field superposition-approach with an exact spectral integral representation of the Green's functions for a stratified ocean waveguide, incorporating all multiple scattering between the object and the seabed. Among the principal results is the demonstration of the significant role of structural circumferential waves in converting incident, evanescent waves into backscattered body waves, emanating to the receivers at supercritical grazing angles, in effect making the target appear closer to the sonar than predicted by traditional ray theory.