Index of content:
Volume 91, Issue 6, June 1992

The effect of a viscous fluid on Love waves in a layered medium
View Description Hide DescriptionThis paper describes a theoretical study pertaining to the effect of the viscosity and density of an adjacent viscous fluid on the characteristics of Love waves propagating in a layered half‐space medium. Expressions for the Love wave velocity and attenuation are obtained as functions of the viscosity and density of the fluid by exact and asymptotic analyses. The valid range of the asymptotic solution is identified by comparing it with the exact solution.

On multidimensional ultrasonic scattering in an inhomogeneous elastic background
View Description Hide DescriptionThis work is concerned with the modeling of elastic wave scattering by solid or fluid‐filled objects embedded in an i n h o m o g e n e o u selastic background. The medium is probed by a monochromatic force and the scattered field is computed (forward problem) or observed (inverse problem) at some known receiver locations. Based on vector integral equations for elasticscattering, a general framework is developed, independent of both the problem geometry and the transmitter–receiver characteristics. This framework encompasses both forward and inverse modeling. In the forward model, a Born approximation for an inhomogeneous background is applied to obtain a closed form expression for the scattered field. In the inverse model, this approximation is also invoked to linearize for the mutliparameter characteristic of the object. Finally, an iterative inversion scheme alternating forward and inverse modeling is proposed to improve the resolution and accuracy of the reconstruction algorithm.

Acoustic scattering by a rigid sphere in the field of waves emanating from a circular concave radiator
View Description Hide DescriptionThis paper presents a new method for calculating the velocity potential Φ of scatteredultrasonicwaves from a rigid sphere placed in the field of waves emanating from a circular concave radiator in an infinite baffle. The solution Φ is given in the form of an infinite series of spherical surface harmonics as a function of reduced quantities k a, k r _{ c }, k b, k z _{0}, etc., where k is the wave number, a is the radius of the circular concave vibrator, r _{ c } is the radius of curvature of it, b is the radius of the sphere, and z _{0} is the distance from the piston to the center of the sphere. The present theoretical framework has the advantages that it includes no numerical integrations and that it is applicable to elastic or compressible sphere cases with slight modifications of the boundary conditions.

Radiation or scattering from multiple axisymmetric cylinders
View Description Hide DescriptionThe boundary‐element method is applied to solve for the radiation or scattering from multiple cylinders having given surface normal velocity distributions. The axisymmetric case is considered where all cylinders have the same axis of symmetry with an arbitrary surface velocity field. The algorithm is applied to solve for scattering from rigid cylinders with hemispherical endcaps. Numerical results are presented for different two‐ or three‐cylinder configurations with a plane wave incident from various directions. The dependence of the scattered field on the distance between two identical cylinders is examined as well as scattering from one large and one small cylinder.

Wave propagation interaction with free and fluid‐loaded piezoelectric substrates
View Description Hide DescriptionA unified analytical treatment is presented that is supported with numerical illustrations of the interactions of ultrasonicwaves with piezoelectricanisotropic half‐space substrates. The solids are allowed to possess up to monoclinic anisotropic symmetry and associated piezoelectric coupling. The solids are also assumed to be loaded with water and subjected to incident acoustic beams at arbitrary polar and azimuthal angles. Simple analytical expressions for the reflection and transmission coefficients are derived from which all propagation characteristics are identified. Such expressions contain, as a by‐product, the secular equation for the propagation of free harmonic waves on the piezoelectric substrate. It is found that piezoelectric coupling, as well as water, influence both types of modes. Higher symmetry, such as orthotropic, transverse isotropic, and cubic, are contained implicitly in this analysis. This paper also demonstrates that the motion of the surface and S H modes uncouple for propagation along axis of symmetry. For such cases, however, piezoelectric coupling can influence one of these types of modes depending upon the type of piezoelectric model adopted.

The validity of the linear orifice impedance model for predicting the impedance of a tube
View Description Hide DescriptionThe orifice impedance model usually works well for modelingsound transmission through an orifice. However, for a long orifice or for an orifice with a large load impedance, the standard impedance model may be invalid. The goal of this paper is to establish when the orifice impedance model gives a valid estimate of the impedance of a tube in series with a load impedance. The method involved a comparison of the orifice impedance model with a transmission line model. Comparison showed that if both ‖Γk l‖<0.1 and ‖Z _{ L }/Z _{ c }‖ <0.1, then the orifice impedance model is valid (Γ is the propagation coefficient, k is the wave number, l is the tube length, and Z _{ L }/Z _{ c } is dimensionless load impedance). If either of these limits is unsatisfied, then the validity of the orifice impedance model depends on six variables. Numerical comparisons of the two models showed the effects of these variables. Computations were restricted to air, and most calculations were in the shear wave‐number range of 1≤S≤100 [S=r _{0}(ω/ν)^{1} ^{/} ^{2}, where r _{0} is tube radius, ω is frequency, and ν is kinematicviscosity]. Graphical results show the limits of validity of the orifice impedance model.

Harmonic generation in finite amplitude sound beams from a rectangular aperture source
View Description Hide DescriptionTheoretical analysis and some experiments are performed on nonlinearly generated harmonic components in bounded sound beams emitted from a rectangular aperture source. The Khokhlov–Zabolotskaya–Kuznetsov equation, which takes account of nonlinearity, dissipation, and diffractioneffects in the beams, is numerically solved by means of the alternating direction implicit difference method. Using a planar source of size 24×44 cm, axial sound pressures and beam patterns of the first three harmonics are measured in air for initially sinusoidal ultrasounds of 25‐ and 30‐kHz frequency, and are compared with the theory. They are in relatively good agreement. Deformation of the source face from circular to rectangular shape results in the unclear appearance of pressure peaks and dips with propagation. Within the framework of these studies, the harmonic pressure levels in the far field are almost the same as from a circular aperture source with equal face area and equal initial pressure, independent of the source levels.

Separation devices based on forced coincidence response of fluid‐filled pipes
View Description Hide DescriptionA separation process based on the acoustic radiation force created in stationary fields produced by a forced coincidence excitation at ultrasonic frequencies of fluid‐filled pipes has been developed. The efficacy of this method for the collection and manipulation of fine secondary phases in flowing suspensions will be compared to equivalent operations in stationary fields generated in acoustic interferometer chambers operated without coincidence effects. The basis for the axial translation of the phases concentrated at the pressure nodes to either end of the cell as a result of an applied periodic sweep in the driving frequency will be examined.

Simulation of drop dynamics in an acoustic positioning chamber
View Description Hide DescriptionTo support experiments scheduled for the First United States Microgravity Laboratory (USML‐1) shuttle mission, experimental and computer simulation methods have been developed which allow ground‐based investigation of the translational, rotational, and vibrational motions of single and dual liquid drops in an external acoustic field in a microgravity environment. The acoustic fields used are the 3‐D orthogonal resonant modes of a rectangular chamber. Hardware and software development are described in detail. Results for the translation of single and dual drops are presented, and semi‐automated schemes for controlled translation are proposed, tested, and evaluated.

Sonoluminescence and bubble dynamics for a single, stable, cavitation bubble
View Description Hide DescriptionHigh‐amplitude radial pulsations of a single gas bubble in several glycerine and water mixtures have been observed in an acoustic stationary wave system at acoustic pressure amplitudes on the order of 150 kPa (1.5 atm) at 21–25 kHz. Sonoluminescence(SL), a phenomenon generally attributed to the high temperatures generated during the collapse of cavitationbubbles, was observed as short light pulses occurring once every acoustic period. These emissions can be seen to originate at the geometric center of the bubble when observed through a microscope. It was observed that the light emissions occurred simultaneously with the bubble collapse. Using a laser scattering technique, experimental radius‐time curves have been obtained which confirm the absence of surface waves, which are expected at pressure amplitudes above 100 kPa. [S. Horsburgh, Ph.D. dissertation, University of Mississippi (1990)]. Also from these radius‐time curves, measurements of the pulsation amplitude, the timing of the major bubble collapse, and the number of rebounds were made and compared with several theories. The implications of this research on the current understanding of cavitation related phenomena such as rectified diffusion, surface wave excitation, and sonoluminescence are discussed.

Sound propagation over a surface with varying impedance: A parabolic equation approach
View Description Hide DescriptionThis paper describes modifications to a finite element solution for the wide angle parabolic equation (PE). The modifications to the PE allow the computationally efficient solution of the problem of sound propagation over ground whose impedance varies with range. In particular, the set of linear algebraic equations that propagate the field outward in range is solved with a U L (upper, lower triangular) decomposition, instead of the standard L U (lower, upper triangular) scheme. This approach allows the change in impedance to affect only a single element in the decomposition. Consequently, all previous calculations in the decomposition can be saved in proceeding from one range step to the next. Results are presented for several cases, in which the ground suffers an abrupt change in acoustic impedance at some distance along the propagation path. Comparisons to existing experimental data are made and the method presented here matches the published data quite well. Other diffraction cases are presented for which no experimental data are available, however the results are fairly self‐consistent and serve to indicate the versatility of this method. The approach described in this paper represents an accurate and efficient method for solving problems involving sound propagation over ground having a range‐dependent surface impedance.

Examination of three‐dimensional effects using a propagation model with azimuth‐coupling capability (FOR3D)
View Description Hide DescriptionA three‐dimensional wave propagationmodel of parabolic approximation type (FOR3D) is used to examine 3‐D ocean environmental variations. The background theory and characteristics of the model are reviewed briefly. Propagation situations that are classified as 3‐D, N×2‐D, and 2‐D are described in connection with FOR3D and are interpreted in several ways. An analytic exact solution is used to demonstrate the model’s accuracy and its capability for treating fully 3‐D propagation, when coupling exists between solutions in adjacent vertical planes of constant azimuth. It is also employed to illustrate a procedure for using approximate conditions at vertical side boundaries in a 3‐D calculation. An application is made to an Atlantic Ocean shelf‐slope environment with realistic bottom topographic variations and sound‐speed profiles. The occurrence of significant azimuthal coupling is demonstrated in propagation loss versus range curves. It follows that, while the N×2‐D approximation of no azimuthal coupling is useful in many situations, not all 3‐D ocean acoustics problems can be adequately solved without a fully 3‐D propagation model.

Volume scattering in a shallow channel
View Description Hide DescriptionUsing a generalization of the modal coherence equations previously developed by Sutton and McCoy [J. Math. Phys. 1 8, 1052 (1977)], the effect of volume scattering in a shallow channel is treated. The difference between the range behavior of the cross‐modal coherence functions and the previously studied self‐modal coherence functions is shown. In particular, calculations are made to evaluate the characteristic scales that govern the range decay of the cross‐modal coherence functions. A particular example is given to illustrate the effect of the choice of different parameters.

Ocean acoustics turbulence study: Acoustic scattering from a buoyant axisymmetric plume
View Description Hide DescriptionLimited i n s i t umeasurements from high‐frequency underwater acoustic echosounders have suggested that there may be circumstances in which acoustic scattering from ocean temperature variability is sufficiently intense to be observable over volume reverberation due to biologics. A new laboratory program, the ocean acousticsturbulence study (OATS), has been undertaken to quantify such scattering. The laboratory employs a very precise computer‐controlled positioning system and allows a scattering geometry from a near forward‐scattering angle, 5°, to a near backscattering angle, 160°. This article reports on results of an initial set of experiments utilizing a 1‐MHz, 1‐cycle transmitted pulse scattering from a temperature anomaly field produced by a laminar buoyant plume. The objective of this experiment is to compare observations of acoustic scattering from the temperature anomaly with that predicted by the Bragg scattering condition. A parameter regime is chosen such that the laminar plume has an approximately axisymmetric and Gaussian temperature profile. For the two‐dimensional axisymmetric case, the Bragg scattering condition allows prediction of an acoustically derived two‐dimensional Fourier transform of the temperature field. The acoustically derived two‐dimensional Fourier transform and the one derived directly from i n s i t u temperature measurements are in good agreement, except at the higher frequency range of the bandwidth of the scattered signal. Discussion of the possibility of inverting such measurements for a direct calculation of the temperature field is presented.

Waveform inversion for the geoacoustic parameters of the ocean bottom
View Description Hide DescriptionThe geoacoustic properties of ocean sediments in deep water environments are important parameters necessary to predict low‐frequency acoustic fields in the water column. A full wave method for obtaining the geoacoustic parameters from the acoustic field measured as a function of range with a cw source is presented. By assuming horizontal stratification, the unknown geoacoustic parameters are reduced to functions of one variable, i.e., depth. The problem of estimating the geoacoustic properties of the ocean floor is then cast as a parameter estimation problem in which a cost function φ(m), where m is a vector containing the unknown parameters, is minimized. This problem is then solved using a nonlinear optimization algorithm. This algorithm requires the determination of the derivative ∂φ/∂m. For a fluid bottom model an efficient algorithm for obtaining these partial derivatives is presented. The performance of the inversion algorithm is studied using noise free and noisy synthetic data. These inversions are carried out using the complex pressure field and the magnitude of the field as data. For the noise‐free case, both approaches yield estimates close to the true value.
In the case of noisy data, inversions carried out using the magnitude of the pressure field as data do not perform as well as inversions where the data are the complex pressure field. However, in both cases the algorithm is stable. The effect of modeling errors on the estimates is studied and it is shown that even small errors in source/receiver location lead to significant errors in the estimates. The effect of modeling the sediment as a fluid on the estimation of its geoacoustic properties is studied. In the case where the sediment shear speed is much smaller than compressional wave speed, the fluid approximation has no significant effect on the estimate of the compressional wave speeds. On the other hand, if the shear speed is such that considerable conversion exists, the fluid bottom model leads to a poor estimate of the compressional wave speed. In both cases the estimates of compressional wave attenuation and density are significantly affected by the fluid approximation. Finally this method is applied to data obtained in a field experiment and an estimate of the compressional wave speed profile in the sediment layers is obtained. This result is compared with the model obtained by iteration of forward models [G. V. Frisk e t a l., J. Acoust. Soc. Am. 8 0, 591–600 (1986)].

Estimation of sediment volume scattering cross section and absorption loss coefficient
View Description Hide DescriptionA simple theoreticalmodel for estimating the sediment volume scattering cross section and the absorption loss coefficient from the reverberation tail of an acoustic pulse observed by a point receiver within the ocean sediment is described. This model assumes an infinite plane wave entering the sediment at normal incidence and scattering isotropically from a uniform field of random point scatterers. The model predicts the magnitude and decay rate of the volume scattering at a point receiver in terms of the volume scattering cross section and the absorption coefficient of the medium. Experimental data were obtained from an array of in‐sediment acoustic probes deployed at a site near Jacksonville, Florida, and Kings Bay, Georgia. By fitting the predictions of the model to experimentally observed volume scattering data, the volume scattering cross sections and absorption coefficients of real sediments were inferred. The absorption coefficient and volume scattering cross‐section results were compared with attenuation measurements from core samples and with theoretical and experimental data from Hamilton [J. Acoust. Soc. Am. 6 8, 1313 (1980)], Nolle [J. Acoust. Soc. Am. 3 5, 1394–1408 (1963)], Turgut and Yamamoto [J. Acoust. Soc. Am. 8 7, 2376 (1990)], and Jackson e t a l. [J. Acoust. Soc. Am. 7 9, 1410 (1986)].

An equivalent fluid approximation for a low shear speed ocean bottom
View Description Hide DescriptionThe acoustic reflection coefficient for a homogeneous fluid over a homogeneous solid with a low shear speed is shown to be well approximated by replacing the solid with a fluid of different parameters. Explicit formulas for the density and attenuation coefficient of the equivalent fluid are given. Since the acoustic field in the upper fluid depends only on the reflection coefficient of the bottom, a uniform solid bottom with low shear speed can be approximated by assuming a fluid bottom with suitably chosen parameters. Shallow water examples are given.

Narrow‐band performance of phase‐conjugate arrays in dynamic random media
View Description Hide DescriptionThe theoretical narrow‐band performance of acoustic phase‐conjugate arrays in the presence of static and dynamic random media is presented. For a static random medium, analytical formulas are derived for the mean focus field of a Gaussian‐shaded volumetric phase‐conjugate array. The results suggest that random refraction allows phase‐conjugate arrays to ‘‘super focus,’’ that is, produce a focal region smaller than the free‐space diffraction limit. More specifically, vertical phase‐conjugate arrays are predicted to have horizontal directivity. In a dynamic random medium, phase‐conjugate array performance is degraded by changes in the medium that occur between the time that the acoustic signal is launched from its source and the time that the array’s transmission is received back at the source location (the round‐trip time delay). Formal results are obtained for an intrinsic signal‐to‐noise ratio for the signal sent from the phase‐conjugate array based on a combination of multiple scattering from static random refraction and single scattering from dynamic random refraction in the acoustic medium. These formal results are reduced to analytical formulas for a random medium characterized by the statistics of oceanic internal waves. The intrinsic signal‐to‐noise ratio is found to be proportional to: the inverse square of the round‐trip time delay, the inverse square of the acoustic frequency, the inverse first power of the array‐source range, and a simple function that combines the size of the array and the parameters of the random medium. For a typical deep‐water oceanic medium at acoustic frequencies near 10 kHz, phase‐conjugate array performance may be unaffected for round‐trip time delays as long as a minute.

Power‐law relationships between the dependence of ultrasonic attenuation on wavelength and the grain size distribution
View Description Hide DescriptionGrain size is one of the factors that influence mechanical properties of metals like strength and fracture toughness. Ultrasonicwaves propagating in polycrystalline materials are subject to attenuation dominated by grain boundaryscattering. The importance of grain size estimation for industrial applications warrants the investigation of alternative methods of nondestructive grain size determination. Analysis of the power‐law behavior of ultrasonic attenuation experimental data is used to link the wavelength dependence of the attenuation coefficient directly to the grain size distribution. The outcome is a simple relationship between the power law that describes the grain size distribution and the power‐law dependence of attenuation on wavelength. Careful attention is given to the limitations in terms of a practical grain size distribution with finite limits. Two types of measurements are presented to verify the theoretical development: grain size distribution and ultrasonic attenuation. Nickel samples were prepared using three different annealing durations. The attenuation exponent is experimentally shown to be an appropriate nondestructive measurement of the grain size distribution exponent.

A modified ray theory for predicting the V(x,z) response of a point‐focus acoustic microscope in the presence of a crack
View Description Hide DescriptionA modified geometric ray approach is used to predict the V(x,z) or the acoustic material signature of a circular point‐focus scanning acoustic microscope for an isotropic surface containing a surface‐breaking crack. The microscope response is assumed to consist of a specularly reflected geometric contribution, and the leaky contribution due in part to surface wavesscattered from the crack. The long thin straight crack is presumed to be characterized by symmetric reflection and transmission coefficients. This approach is numerically simple and can be used to evaluate the response of acoustic lenses of various geometries. The method is used to predict line scan V(x,z _{0}) response of a microscope in the vicinity of the crack for several defocus distances z _{0} and the results are compared with measurements.