Naval Research Laboratory Acoustics Division

Recent work has rendered possible the formulation of a rigorous model for the propagation of pressure waves in bubbly liquids. The derivation of this model is reviewed heuristically, and the predictions for the small-amplitude case are compared with the data sets of several investigators. The data concern the phase speed, attenuation, and transmission coefficient through a layer of bubbly liquid. It is found that the model works very well up to volume fractions of 1%–2% provided that bubble resonances play a negligible role. Such is the case in a mixture of many bubble sizes or, when only one or a few sizes are present, away from the resonant frequency regions for these sizes. In the presence of resonance effects, the accuracy of the model is severely impaired. Possible reasons for the failure of the model in this case are discussed.

The standard approach to the analysis of the pulsations of a driven gas bubble is to assume that the pressure within the bubble follows a polytropic relation of the form p=p0(R0/R)3κ, where p is the pressure within the bubble, R is the radius, κ is the polytropic exponent, and the subscript zero indicates equilibrium values. For nonlinear oscillations of the gas bubble, however, this approximation has several limitations and needs to be reconsidered. A new formulation of the dynamics of bubble oscillations is presented in which the internal pressure is obtained numerically and the polytropic approximation is no longer required. Several comparisons are given of the two formulations, which describe in some detail the limitations of the polytropic approximation.

White matter is composed primarily of myelinated axons which form fibrous, organized structures and can act as waveguides for the anisotropic propagation of sound. The evaluation of their elastic properties requires both knowledge of the orientation of these waveguides in space, as well as knowledge of the waves propagating along and through them. Here, we present waveguide elastography for the evaluation of the elastic properties of white matter tracts in the human brain, in vivo, using a fusion of diffusion tensor imaging, magnetic resonance elastography, spatial-spectral filtering, a Helmholtz decomposition, and anisotropic inversions, and apply this method to evaluate the material parameters of the corticospinal tracts of five healthy human volunteers. We begin with an Orthotropic inversion model and demonstrate that redundancies in the solution for the nine elastic coefficients indicate that the corticospinal tracts can be approximated by a Hexagonal model (transverse isotropy) comprised of five elastic coefficients representative of a medium with fibers aligned parallel to a central axis, and provides longitudinal and transverse wave velocities on the order of 5.7 m/s and 2.1 m/s, respectively. This method is intended as a new modality to assess white matter structure and health by means of the evaluation of the anisotropic elasticity tensor of nerve fibers.

We consider the inverse problem of identifying the location and shape of a finitely supported acoustic source function, separable with respect to space and frequency, from measurements of the acoustic field on a closed surface for many frequencies. A simple uniqueness proof and an error estimate for the unknown source function are presented. From the uniqueness proof an efficient numerical algorithm for the solution is developed. The algorithm is tested using numerically generated data in dimensions 2 and 3.

A Fresnel zone plate (FZP) lens of the Soret type creates a focus by constructive interference of waves diffracted through open annular zones in an opaque screen. For underwater sound below MHz frequencies, a large FZP that blocks sound using high-impedance, dense materials would have practical disadvantages. We experimentally and numerically investigate an alternative approach of creating a FZP with thin (0.4λ) acoustically opaque zones made of soft silicone rubber foam attached to a thin (0.1λ) transparent rubber substrate. An ultra-thin (0.0068λ) FZP that achieves higher gain is also proposed and simulated which uses low-volume fraction, bubble-like resonant air ring cavities to construct opaque zones. Laboratory measurements at 200 kHz indicate that the rubber foam can be accurately modeled as a lossy fluid with an acoustic impedance approximately 1/10 that of water. Measured focal gains up to 20 dB agree with theoretical predictions for normal and oblique incidence. The measured focal radius of 0.68λ (peak-to-null) agrees with the Rayleigh diffraction limit prediction of 0.61 λ/NA (NA = 0.88) for a low-aberration lens.

Waveguide invariant theory is applied to horizontal line array (HLA) beamformer output to localize moving broadband noise sources from measured acoustic intensity striation patterns. Acoustic signals emitted by ships of opportunity (merchant ships) were simultaneously recorded on a HLA and three hydrophones separated by 10 km during the RAGS03 (relationship between array gain and shelf-break fluid processes) experiment. Hough transforms are used to estimate both the waveguide invariant parameter "beta" and the ratio of source range at the closest point of approach to source speed from the observed striation patterns. Broadband (50-150-Hz) acoustic data-sets are used to demonstrate source localization capability as well as inversion capability of waveguide invariant parameter beta. Special attention is paid to bathymetric variability since the acoustic intensity striation patterns seem to be influenced by range-dependent bathymetry of the experimental area. The Hough transform method is also applied to the HLA beam-time record data and to the acoustic intensity data from three distant receivers to validate the estimation results from HLA beamformer output. Good agreement of the results from all three approaches suggests the feasibility of locating broadband noise sources and estimating waveguide invariant parameter beta in shallow waters.

Scattering from a cavity in a soft elastic medium, such as silicone rubber, resembles scattering from an underwater bubble in that low-frequency monopole resonance is obtainable in both cases. Arrays of cavities can therefore be used to reduce underwater sound transmission using thin layers and low void fractions. This article examines the role of cavity shape by microfabricating arrays of disk-shaped air cavities into single and multiple layers of polydimethylsiloxane. Comparison is made with the case of equivalent volume cylinders which approximate spheres. Measurements of ultrasonic underwater sound transmission are compared with finite element modeling predictions. The disks provide a deeper transmission minimum at a lower frequency owing to the drum-type breathing resonance. The resonance of a single disk cavity in an unbounded medium is also calculated and compared with a derived estimate of the natural frequency of the drum mode. Variation of transmission is determined as a function of disk tilt angle, lattice constant, and layer thickness. A modeled transmission loss of 18 dB can be obtained at a wavelength about 20 times the three-layer thickness, and thinner results (wavelength/thickness ∼ 240) are possible for the same loss with a single layer depending on allowable hydrostatic pressure.

The goal of this current study was to determine whether an MRI-based elastography (MRE) method can visualize and assess propagating mechanical waves within fluid-filled vessels and to investigate the feasibility of measuring the elastic properties of vessel walls and quantitatively assessing stenotic lesions by using MRE. The ability to measure the Young's modulus-wall thickness product was tested using a thin-walled latex vessel model. Also tested in vessel models was the ability to quantitate the degree of stenosis by measuring transmitted and reflected mechanical waves. This method was then applied to ex vivo porcine models and in vivo human arteries to further test its feasibility. The results provide preliminary evidence that MRE can be used to quantitatively assess the stiffness of blood vessels, and provide a non-morphologic method to measure stenosis. With further development, it is possible that the method can be implemented in vivo.

It is argued that a quantitative measure of incomplete environmental knowledge or information (i.e., environmental uncertainty) should be included in any simulation-based predictions linked to acoustic wave propagation. A method is then proposed to incorporate environmental uncertainty directly into the computation of acoustic wave propagation in ocean waveguides. In this regard, polynomial chaos expansions are chosen to represent uncertainty in both the environment and acoustic field. The sound-speed distribution and acoustic field are therefore generalized to stochastic processes, where uncertainty in the field is interpreted in terms of its statistical moments. Starting from the narrow angle parabolic approximation, a set of coupled differential equations is derived in which the coupling term links incomplete environmental information to the corresponding uncertainty in the acoustic field. Propagation of both the field and its uncertainty in an isospeed waveguide is considered as an example, where the sound speed is described by a random variable. The first two moments of the field are computed explicitly and compared to those obtained from independent Monte Carlo solution of the conventional (deterministic) parabolic equation that describes the acoustic wave properties.

A technique is described to image the vector intensity in the near field of a spherical array of microphones flush mounted in a rigid sphere. The spatially measured pressure is decomposed into Fourier harmonics in order to reconstruct the volumetric vector intensity outside the sphere. The theory for this reconstruction is developed in this paper. The resulting intensity images are very successful at locating and quantifying unknown exterior acoustic sources, ideal for application in noise control problems in interior spaces such as automobiles and airplanes. Arrays of varying numbers of microphones and radii are considered and compared and errors are computed for both theory and experiment. It is demonstrated that this is an ill-posed problem below a cutoff frequency depending on array design, requiring Tikhonov regularization below cutoff. There is no low frequency limit on operation, although the signal-to-noise ratio is the determining factor for high-spatial resolution at low frequencies. It is shown that the upper frequency limit is set by the number of microphones in the array and is independent of noise. The accuracy of the approach is assessed by considering the exact solution for the scattering of a point source by a rigid sphere. Several field experiments are presented to demonstrate the utility of the technique. In these experiments, the partial field decomposition technique is used and holograms of multiple exterior sources are separated and their individual volumetric intensity fields imaged. In this manner, the intensity fields of two uncorrelated tube sources in an anechoic chamber are isolated from one another and separated intensity maps are obtained from over a broad frequency range. In a practical application, the vector intensity field in the interior of an automobile cabin is mapped at the fundamental of the engine vibration using the rigid sphere positioned at the driver's head. The source regions contributing to the interior cabin noise are identified.

A new measurement system, consisting of a mobile array of 50 microphones that form a spherical surface of radius 0.2m, that images the acoustic intensity vector throughout a large volume is discussed. A simultaneous measurement of the pressure field across all the microphones provides time-domain holograms. Spherical harmonic expansions are used to convert the measured pressure into a volumetric vector intensity field on a grid of points ranging from the origin to a maximum radius of 0.4m. Displays of the volumetric intensity image are used to locate noise sources outside the volume. There is no restriction on the type of noise source that can be studied. An experiment inside a Boeing 757 aircraft in flight successfully tested the ability of the array to locate flow-noise-excited sources on the fuselage. Reference transducers located on suspected noise source locations can also be used to increase the ability of this device to separate and identify multiple noise sources at a given frequency by using the theory of partial field decompositions. The frequency range of operation is 0to1400Hz. This device is ideal for the diagnostic analysis of noise sources in commercial and military transportation vehicles in air, on land, and underwater.

Measurements of acoustical waves propagating in an unconsolidated water-saturated porous medium that involved the use of a two-dimensional synthetic array technique are presented. From these measurements, wave-front propagation is evaluated using time domain, wave-number frequency and two-dimensional spatial analysis techniques. First, a synthetic array measurement is employed to study sound penetration for a "smoothed" interface condition. This smoothed interface measurement is then compared to an identical synthetic array measurement with a "roughened" interface. A comparison of the smoothed and roughened interface measurements shows enhanced bottom penetration at shallow grazing angles as a result of the roughened interface. At shallow grazing angles, this scattered pressure from the roughened interface has the appearance of a wave front in the water-saturated porous medium that has a virtual wave speed of approximately 1200 m/s. Slower compressional waves in the sandy bottom are not observed.

Iron-based CO₂ catalysts have shown promise as a viable route to the production of olefins from CO₂ and H₂ gas. However, these catalysts can suffer from low conversion and high methane selectivity, as well as being particularly vulnerable to water produced during the reaction. In an effort to improve both the activity and durability of iron-based catalysts on an alumina support, copper (10-30%) has been added to the catalyst matrix. In this paper, the effects of copper addition on the catalyst activity and morphology are examined. The addition of 10% copper significantly increases the CO₂ conversion, and decreases methane and carbon monoxide selectivity, without significantly altering the crystallinity and structure of the catalyst itself. The FeCu/K catalysts form an inverse spinel crystal phase that is independent of copper content and a metallic phase that increases in abundance with copper loading (>10% Cu). At higher loadings, copper separates from the iron oxide phase and produces metallic copper as shown by SEM-EDS. An addition of copper appears to increase the rate of the Fischer-Tropsch reaction step, as shown by modeling of the chemical kinetics and the inter- and intra-particle transport of mass and energy.

A spiral wave front source produces an acoustic field that has a phase that is proportional to the azimuthal angle about the source. The concept of a spiral wave front beacon is developed by combining this source with a reference source that has a phase that is constant with the angle. The phase difference between these sources contains information about the receiver's azimuthal angle relative to the beacon and can be used for underwater navigation. To produce the spiral wave front, two sources are considered: a "physical-spiral" source, which produces the appropriate phase by physically deforming the active element of the source into a spiral, and a "phased-spiral" source, which uses an array of active elements, each driven with the appropriate phase, to produce the spiral wave front. Using finite element techniques, the fields produced by these sources are examined in the context of the spiral wave front beacon, and the advantages of each source are discussed.

Inversion of statistical parameters of a bottom/subbottom scattering model is investigated by using genetic algorithms for both synthetic and real data. The bottom/subbottom scattering model used in the calculations is a modified version of Lyons, Anderson, and Dwan [J. Acoust. Soc. Am. 79, 1410–1422 (1986)] in which correlation between subbottom density, compressibility, and sound-speed fluctuations is established through Wood’s equation [A Textbook of Sound (Macmillan, New York, 1941)], and volume inhomogeneities are described by von Karman type autocorrelation functions [T. von Karman, J. Mar. Res. 7, 252–264 (1948)]. The inversion is posed as an optimization problem which is solved (by a controlled Monte Carlo search using genetic algorithms) to find the optimum set of statistical parameters that minimizes the quadratic deviation between measured and calculated backscatter data. A posteriori probabilities calculated at the end of the search are used for error estimation and indication of relative importance of model parameters. This information helps to further assess the relative importance of two major scattering mechanisms due to bottom roughness and subbottom inhomogeneities. Such assessment is successfully demonstrated by using synthetic and real backscatter data for sandy, silty, and muddy sediments. Finally, inverted statistical parameters for a sandy site at Biscayne Bay, Florida confirm the results of simultaneous tomographic measurements indicating that scattering by subbottom inhomogeneities plays a minor role for this particular site.

This article describes the development and testing of a passive sonar, multitarget tracker, and adaptive behavior that enable an autonomous underwater vehicle (AUV) to detect and actively track nearby surface vessels. A planar hull-mounted hydrophone array, originally designed for active sonar, is repurposed for passive sonar use and provides acoustic data to a time-delay-and-sum beamformer that generates multiple angle-only contacts. A particle filter tracker assimilates these contacts with a single-hypothesis data association strategy to estimate the position and velocity of targets. Summary statistics of each track are periodically reported to an onboard database along with qualitative labels. To improve tracking performance, detections trigger an adaptive behavior that maneuvers the AUV to maintain multiple targets in the field of view by minimizing the worst case aspect angle deviation from broadside (across all targets). The tracking system is demonstrated through at-sea experiments in which a Bluefin-21 AUV adaptively tracks multiple surface vessels, including another autonomous platform, in the approaches to Boston Harbor.

Stochastic basis expansions are applied to formulate and solve the problem of including uncertainty in numerical models of acoustic wave propagation within ocean waveguides. As an example, a constrained least-squares approach is used to estimate the intensity of an acoustic field whose waveguide environment has uncertainty in both source depth and sound speed. The mean intensity, a second moment of the field, and its probability distribution are computed and compared with independent Monte-Carlo computations of these quantities. Very good agreement is obtained, indicating the potential of stochastic basis expansions for describing multiple sources of uncertainty and their effect on acoustic propagation.

Acoustic predictions of the recently developed traceo ray model, which accounts for bottom shear properties, are benchmarked against tank experimental data from the EPEE-1 and EPEE-2 (Elastic Parabolic Equation Experiment) experiments. Both experiments are representative of signal propagation in a Pekeris-like shallow-water waveguide over a non-flat isotropic elastic bottom, where significant interaction of the signal with the bottom can be expected. The benchmarks show, in particular, that the ray model can be as accurate as a parabolic approximation model benchmarked in similar conditions. The results of benchmarking are important, on one side, as a preliminary experimental validation of the model and, on the other side, demonstrates the reliability of the ray approach for seismo-acoustic applications.

The surface and interior response of a Cessna Citation fuselage section under three different forcing functions (10-1000 Hz) is evaluated through spatially dense scanning measurements. Spatial Fourier analysis reveals that a point force applied to the stiffener grid provides a rich wavenumber response over a broad frequency range. The surface motion data show global structural modes (approximately < 150 Hz), superposition of global and local intrapanel responses (approximately 150-450 Hz), and intrapanel motion alone (approximately > 450 Hz). Some evidence of Bloch wave motion is observed, revealing classical stop/pass bands associated with stiffener periodicity. The interior response (approximately < 150 Hz) is dominated by global structural modes that force the interior cavity. Local intrapanel responses (approximately > 150 Hz) of the fuselage provide a broadband volume velocity source that strongly excites a high density of interior modes. Mode coupling between the structural response and the interior modes appears to be negligible due to a lack of frequency proximity and mismatches in the spatial distribution. A high degree-of-freedom finite element model of the fuselage section was developed as a predictive tool. The calculated response is in good agreement with the experimental result, yielding a general model development methodology for accurate prediction of structures with moderate to high complexity.

A hybrid method coupling nonlinear and linear propagation codes is used to study the nonlinear signature of long-range acoustic propagation for high-amplitude sources in an ocean waveguide. The differences between linear and nonlinear propagation are investigated in deep and shallow water environments. The spectral reshaping that occurs in nonlinear propagation induces two main effects: in shallow water, an unusual arrival time structure in the lowest order modes is observed, and in both shallow and deep water environments, there is a tendency to have acoustic energy more uniformly distributed across modes. Further, parametric low-frequency generation in deep water is a candidate for the coupling between water and sediments for T-wave formation.