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Volume 97, Issue 5, May 1995

Time dependence of multiply scattered diffuse ultrasound in polycrystalline media
View Description Hide DescriptionTime domain results are presented for the multiply scattered longitudinal intensity backscattered from a polycrystalline medium. The results are solutions to the ultrasonicradiative transfer equation (URTE), the derivation of which is based upon radiative transfer theory. Unlike steady‐state solutions obtained previously, time domain solutions will more closely correspond to experiments that use tone burst sources. This paper is concerned with the time dependence of the backscattered longitudinal intensity from a polycrystalline medium excited by a normally incident longitudinal wave idealized as an impulsive deposition of energy. It is shown that multiple scattering effects become significant at times on the order of a mean free time or less. It is anticipated that this work may be applicable to microstructural characterization of polycrystalline, geophysical and other random media in which multiple scattering effects are important.

The inverse problem for scattering by an ellipsoidal boss
View Description Hide DescriptionThe inverse problem of determining the semiaxes and orientation of an ellipsoidal boss on a base plane is considered. For low‐frequency plane‐wave excitation of a rigid surface, it is shown that four measurements of the leading order coefficient of the imaginary part of the scattering amplitude are sufficient to specify the boss. At high frequencies, a measurement of the time of flight of the backscatteredwave together with geometrical considerations is used to construct a supporting plane at the point of specular reflection on the boss. Knowledge of four such planes corresponding to four directions of incidence is then used to solve the inverse problem. The method applies for both rigid and acoustically soft surfaces. For either excitation, a priori knowledge of the boss, e.g., its orientation, reduces the number of required measurements.

The scattering of sound from a spatially distributed axisymmetric cylindrical source by a circular cylinder
View Description Hide DescriptionGeneral expressions for the scattering of sound from a spatially distributed cylindrical source by a circular cylinder are given. The incident field is determined using a Hankel transform. The scattered fields are determined by matching the pressure and radial velocity at the surface of the cylinder. Examples of total and scattered pressure fields are given for a cylindrical line source and a axisymmetric source with a Gaussian spatial distribution. An example is also given for a circular disk source.

Acoustical source characterization by using recursive Wiener filtering
View Description Hide DescriptionThis paper discusses a feedback iteration technique that provides the enhancement of backward reconstruction in acoustical imaging.Reconstruction of a vibrating surface motion from acoustic holographic data causes computational difficulties because the problem is ill posed. In order to deal with these difficulties, a method is developed based on a recursive algorithm, where the inverse problem is converted to a well‐posed forward propagation problem. An initial guess regarding the source images is required to activate the iterative inversion method. Then, the tentative image is propagated forward to the hologram plane and the residue is determined. Next, a feedback operator is used to process the residue by which the image is updated. Two types of feedback operators were investigated: (1) a Wiener suboptimal operator, and (2) a dynamic, optimal operator (designed subject to minimum mean‐square‐error optimization criteria). The performance of these iteration methods was investigated by numerical simulations of the holographicreconstruction of a baffled piston field. Both iteration methods provided satisfactory convergence and were found to be relatively insensitive to the choice of initial guess and noise parameters used in the feedback operators.

Active noise cancellation by using the linear quadratic Gaussian independent modal space control
View Description Hide DescriptionThe objective of this study is to develop an active noisecontroller based on optimal control approaches for enclosed Gaussian noise fields. By independent modal space control, the individual mode in the acoustic field is suppressed by the corresponding modal control exerted by loudspeakers. The formulation of the modal controller is considerably simplified because modal coupling is neglected. For the Gaussian noises considered in this study, the linear quadratic Gaussian algorithm in conjunction with the Kalman–Bucy filter is employed to perform state feedback and estimation. The developed controller is validated by simulations for a duct and a rectangular room. The results indicate that the technique will yield significant noise reduction if one uses the same number of controlled modes, microphones, and loudspeakers. Satisfactory performance is possible if one carefully avoids placing microphones and loudspeakers at the nodal points.

Multipole radiation of seismic waves from explosions in nonspherical cavities and its application to signal identification
View Description Hide DescriptionA new method, named ‘‘spherical mapping approximation’’ (SMA), is developed for the evaluation of displacement fields of body waves and surface waves from explosions in nonspherical cavities embedded in elastic media. Under SMA, the explosion‐generated stress distribution on the surface of an arbitrary cavity is mapped onto the surface of an equivalent virtual spherical cavity having the volume of the true cavity. The analytical results express the displacement field in terms of a multipole double‐sum expansion of spherical eigenvectors with coefficients in the form of a finite Legendre transform of the components of the normal vector of the cavity boundary. These ‘‘cavity integrals’’ can be evaluated exactly for spheroidal and cylindrical inclusions. In the long‐wave far‐field approximation, symmetric finite cavities are shown to be equivalent to a linear combination of point dipoles directed along the principal cavity axes.
The ensuing radiation patterns yield, in general, four‐lobe patterns for Swaves, two‐lobe patterns for Pwaves, and single to two‐lobe Rayleigh‐wave pattern, independent of the details of the cavities’ shape. However, all radiation patterns are modulated by a frequency‐dependent ‘‘cavity factor’’ that embodies the boundary conditions on the cavity surface. Moreover, it is shown that the radiation pattern for Pwaves from a nonspherical symmetrical cavity in the long‐wave far‐field approximation is always dipolar. Since the radiation pattern of radiated Pwaves from a standard earthquake is always quadrupolar, the cavity explosion behaves like a non‐double‐couple earthquake. Thus the examination of the deviatoric moment tensor of a given seismic event enables one, in principle, to state whether it is a standard earthquake or perhaps (if the S‐wave pattern is quadrupolar) an evasion of the test‐ban treaty. It is shown that SMA can be easily fitted to a multilayered elastic half‐space if the equivalent source is placed in one of the layers. In that case, Love waves will be generated in addition to P, S, and Rayleigh waves. Displacement patterns for body and surface waves are calculated for spheroidal and cylindrical cavities for a wide range of aspects ratios and corresponding aperture angles, exhibiting the whole gamut of cavity shapes from a line source to a disk.
The moments of the equivalent dipoles are shown to depend on the corresponding cavity integrals, the elastic constants of the medium in the neighborhood of the source, and the initial energy injection. All nonspherical cavities generate strong shear waves except for special aperture angles at which a spherical Pwave is generated, unaccompanied by Swaves. The wave‐spectra of body waves(surface waves) exhibit a corner frequency (peak frequency) at a wavelength equal to the radius of the equivalent sphere. This enables one to deduce the size of the cavity from the spectrum of its far‐field displacement signals, provided that the explosion is fully decoupled and that the interaction of the shock wave with the medium occurred in the elastic regime. The results of the present research are applicable to the detection and identification of seismic signals from clandestine underground nuclear explosions.

Measurement and interpretation of the impulse response for backscattering by a thin spherical shell using a broad‐bandwidth source that is nearly acoustically transparent
View Description Hide DescriptionA novel source was developed to produce a plane‐wave unipolar pressure impulse with a wide range of frequency components. The source consisted of a PVDF sheet with water in contact with both sides. The PVDF was driven by a step voltage. This source is nearly acoustically transparent and was used for backscattering from an empty stainless‐steel spherical shell. The shell was placed in the near field of the source where it experienced a plane‐wave pressure impulse followed much later by edge contributions resulting from the finite source size. A hydrophone was placed in the far field of the scatterer on the opposite side of the source. Prominent features in the shell’s calculated impulse response are observed over a wide frequency interval. Time records reveal an approximately Gaussian wave packet from the excitation of the subsonic a _{0−}wave associated with the backscattering enhancement near the coincidence frequency (≊309 kHz). Superposed on the same records are large contributions from the low‐frequency excitation of the a _{0−}wave and from the s _{0}wave. A bipolar feature of the initial response was found to be associated with the finite inertia of the shell and the null frequency. An approximate theory predicts that the associated relaxation time depends on the mass per area of the shell and the density and sound speed of the surrounding water. The shell used in the experiment has a thickness to radius ratio of 2.3% and the scattering phenomena of interest occur between 8 and 450 kHz corresponding to ka from approximately 1 to 70. The 10‐kHz ringing of the target associated with the a _{0−}wave is quite pronounced.

Sound radiation from two semi‐infinite dissimilar plates subject to a harmonic line force excitation in mean flow. I. Theory
View Description Hide DescriptionFormulations are derived for predicting sound radiation from two semi‐infinite dissimilar plates subject to a line force excitation at the joint in the presence of mean flow using the Wiener–Hopf technique and Fourier transformations. The acoustic pressure is solved in the frequency‐wave‐number domain first in terms of the decomposition factors and parameters associated with displacements, slopes, bending moments, and shear forces at the joint of two plates. The decomposition factors are evaluated via contour integrations, and the parameters are determined by a set of simultaneous equations derived from boundary conditions and the finiteness requirement imposed at the joint. It is shown that the set of equations reduces to a 2×2 matrix for a welded joint, a 3×3 matrix for a hinged joint, and a 4×4 matrix for a free–free joint, i.e., two plates being mechanically unconnected. The frequency‐domain acoustic pressure is subsequently obtained by taking an inverse Fourier transformation and evaluated by using the residue theory and contour integrals along the branch cut. Asymptotic behaviors of the plate flexural displacement and radiated acoustic pressure in the frequency‐wave‐number domain are obtained. Effects of mean flow on resulting sound radiation are examined.

Sound radiation from two semi‐infinite dissimilar plates subject to a harmonic line force excitation in mean flow. II. Asymptotics and numerical results
View Description Hide DescriptionAsymptotic formulations are derived for describing far‐field acoustic radiation from two semi‐infinite dissimilar plates subject to an harmonic line force excitation at the joint in the presence of mean flow.Analysis shows that mean flow affects the acoustic pressure in three ways: (1) It enhances the wave number and amplitude of an acoustic wave propagating in the upstream direction, while it suppresses those of an acoustic wave propagating in the downstream direction; (2) it reduces the decay rate of the upstream propagating wave, while it increases that of the downstream propagating wave as they propagate in the plate normal direction; and (3) it rotates the radiation beam angles toward the downstream direction. The effects of mean flow are obvious when the excitation frequency is above the plate coincidence frequency, but decays significantly at low frequencies. The condition at the joint of two plates does not change the characteristics of the radiation pattern, but merely the amplitude of the radiated acoustic pressure. The looser the joint, for example, two plates being mechanically unconnected, the higher the amplitude of the resulting acoustic pressure.

Improved method for the measurement of acoustic properties of a sound absorbent sample in the standing wave tube
View Description Hide DescriptionThis paper introduces a novel way of reconstructing the one‐dimensional acoustic field in the tube from multiple pressure measurements. It presents a detailed derivation for estimating the best fitted, in a least‐squares sense, incident and reflected wave components at the sample surface. This attempt reveals that their estimation is no longer independent of the number of pressure data and their measurement positions. The best condition for selecting these two experimental factors is proposed for a finite number of microphone positions. The singular condition and spatial aliasing are shown to arise from their inadequate choice in space and their protection schemes are also presented. These results lead to the logical ways of improving the accuracy of experimentally assessed acoustic properties. Furthermore, the proposed estimation method of the wave components allows the experimental reconstruction of the pressure pattern existing in the tube from measurement. It also presents the clear understanding of acoustic field itself existing in the tube. Experimental results are illustrated to make these points clear.

Acoustic streaming induced in focused Gaussian beams
View Description Hide DescriptionAxisymmetric flow equations for a viscous incompressible fluid are transformed into the vorticity transport and Poisson’s equations. They are numerically solved via a finite difference method imposing appropriate initial and boundary conditions. A model source of 1‐cm radius and 5‐cm focal length with Gaussian amplitude distribution radiates 5‐MHz ultrasound beams in water. Numerical examples are shown for buildup of acoustic streaming along and across the acoustic axis. Evidently, hydrodynamic nonlinearity has an essential effect on the streaming generation in comparison with a linear flow case; the nonlinearity reduces the streaming velocity in the focal and prefocal region, whereas it tends to accelerate the flow in the postfocal region.

Calculation of acoustic radiation force generated by focused beams using the ray acoustics approach
View Description Hide DescriptionRadiation force applied on an absorbing disk due to a focused circular beam generated by a focusing transducer is calculated using the ray acoustics approach. It is found that the radiation force is a function of the acoustic power of the beam, the f number of the source transducer, the normalized radius of the absorbing disk relative to the radius of aperture of the source transducer, the separation between the disk and the source transducer, the ratio between the speed of sound in the medium and that in the disk material, and the ratio between the characteristicacoustic impedance of the disk material and that of the medium.

On resonant features of supersonic jets at off‐design flow regimes
View Description Hide DescriptionAcoustic excitation of supersonic jets emitting a discrete tone at off‐design flow regimes is considered. It has been shown that in the case of action by sufficiently high‐intensity sound on the jet, Powell’s mechanism of discrete tone emission is broken down and there arises some other mechanism of discrete tone emission. This mechanism is related to sound radiation by disturbances moving with supersonic convectionvelocity along the irradiated jet boundary. At a definite value of the external sound‐pressure level that depends on the total pressure in the jet, both these mechanisms of sound radiation can exist simultaneously. Supersonic jets at off‐design flow regimes have no resonant features due to external acoustic excitation.

Influence of geoacoustic modeling on predictability of low‐frequency propagation in range‐dependent, shallow‐water environments
View Description Hide DescriptionIn a previous study of predictability of relative intensity and horizontal wave numbers by the authors, parabolic approximations were used in range‐independent shallow‐water waveguides. Uncertainties in sediment properties were found to be the most significant factor limiting prediction accuracy. In this paper, models of bottom sound‐speed profiles that take into account sediment consolidation are developed, and their effects on propagation model predictions in range‐dependent environments are examined. Modeling of low‐frequency results from a New Jersey shelf experiment is the focus of our efforts. Using borehole data and Biot–Stoll theory, the porosity profiles for homogeneous consolidated sediments are derived, and corresponding sound‐speed profiles for different sediment types are then constructed. Predictions from models with consolidated sediment layers throughout the bottom are compared with results from cases where bottom sound speed is comprised of piecewise linear segments. In addition, bottom sound‐speed range dependence is shown to be significant in the area of the experiment, and different geoacoustic models for it are examined. Comparisons of experimental data with model predictions incorporating range dependence are illustrated and show the influence of the bottom model.

Beach acoustics
View Description Hide DescriptionThe parabolic equation method is modified to handle problems involving waveguides with sloping boundaries and applied to solve ocean acoustics problems in beach environments. Energy from a source in the ocean may propagate beyond the beach and be detectable several kilometers inland. Energy from a source buried several kilometers inland may couple into the oceanwaveguide and be detectable many kilometers out to sea.

New full‐wave approximation for ocean acoustic travel time predictions
View Description Hide DescriptionA new full‐wave parabolic approximation is introduced that is valid for a wide range of grazing angles. By Fourier synthesis it yields travel times of ocean acoustic multipaths that are insensitive to a reference speed of sound. After depths and sound speeds are transformed to new coordinates, the highly efficient ‘‘split‐step Fourier’’ algorithm is used to solve the new approximate wave equation for forward propagation. Accuracy of the new approximation has been tested by comparison to a broadband normal mode model in a range‐independent environment. At 1000 km range and with a pulse of resolution 20 ms at center frequency 75 Hz, computed travel times of 24 multipaths agreed with maximum difference 3.4 ms, mean difference 0.9 ms, and rms difference 1.5 ms. This approximation may prove to be an efficient method for accurate travel time predictions of multipaths over a wide range of acoustic frequencies and for basin scale distances.

Spatial correlation of acoustic waves scattered from a random ocean bottom
View Description Hide DescriptionAcoustic wave scattering from a random bottom is studied. The bottom is modeled as a fluid medium with a layer where the sound speed is composed of a small random component superimposed upon a constant background sound speed. Emphasis is placed on the spatial correlation of the scattered field. It is found that the spatial correlation length of the scattered acoustic field is related to the correlation length of the random sound speed in the bottom, and by sweeping acoustic frequencies, it is possible to invert for the bottom correlation length through measuring the spatial correlation of the scattered field by using a receiving array. Also studied is the influence of anisotropy of the bottom scatterer. A comparison is made to the Born approximation.

A shallow‐water normal‐mode reverberation model
View Description Hide DescriptionA practical model to compute shallow‐water boundary reverberation is described. Normal modes are used to calculate the acoustic energy propagating from the source to the scattering area, and from the scattering area to the receiver. At the scattering patch each mode is decomposed into up‐ and down‐going waves, then ray‐mode analogies and empirical scattering functions can be used to compute the scattered energy. The method was first described by Bucker and Morris [J. Acoust. Soc. Am. 44, 827–828 (1968)], and papers which first appeared in the Chinese literature. Their work is extended here by using group velocities to obtain the travel times for each mode pair, and by further developing the ray‐mode analogy. The effects of summing the modes coherently or incoherently and of including the time spreading due to the modal group velocities are examined. This paper deals with the range‐independent monostatic case, although the technique is extendible to bistatic geometries and range‐dependent environments. Calculations show excellent agreement with some ray‐based models, and, using the Lambert bottom‐scattering coefficient as the only adjustable parameter, good agreement is obtained with some measured shallow‐water reverberation.

Floquet waves and classical plane waves in an anisotropic periodically multilayered medium: Application to the validity domain of homogenization
View Description Hide DescriptionThe aim of this paper is to better understand the correspondence between classical plane waves propagating in each layer of an anisotropic periodically multilayered medium and Floquet waves. The last are linear combinations of the classical plane waves. Their wave number is obtained from the eigenvalues of the transfer matrix of one cell of the medium. A Floquet polarization which varies with its position in the periodically multilayered medium has been defined. This allows one to define a Floquet wave displacement by analogy with the displacement of classical plane waves, and to check the equality of the two displacements at any interface separating two layers. The periodically multilayered medium is then an equivalent material, considered as homogeneous, and one can draw dispersion curves and slowness surfaces which are dispersive. In the low‐frequency range, when the relation between the Floquet wave numbers and the frequency is linear, the multilayered medium can be homogenized; the Floquet polarization at different interfaces tends to a limit which is the polarization of the classical plane wave in the homogenized medium.

Conversion of an SH wave into a Stoneley wave under weak distortion of the elastic isotropic space material of a crystal lattice
View Description Hide DescriptionThe problem of the conversion of a volume SHwave propagating in an isotropic elastic space into a Stoneley wave as a consequence of the conversion of this space into a three‐layered medium by small variations in material elastic moduli in a portion of the space is considered. Three‐layered medium of two types have been investigated: A weakly anisotropic layer of cubic symmetry between two isotropic half‐spaces and an isotropic layer between two slightly anisotropic half‐spaces of cubic symmetry. The elastic moduli of the isotropic material and the isotropic parts of the moduli of the weakly anisotropic material are the same. Small anisotropic values added to the isotropic elastic moduli are introduced by various means, in such a manner that velocities of the SHwaves in the slightly anisotropic materials with cubic symmetry may be smaller, bigger, or equal to the velocity of the SHwave in the corresponding isotropic material. It is shown that in cases when the Stoneley wave exists it refers to a weakly inhomogeneous quasitransverse wave of SH type, because among three displacement components weakly decaying with depth, the transverse one parallel to the interface of three mediums predominates.