Volume 93, Issue 2, February 1993
Index of content:

Local principles of wave propagation in inhomogeneous media
View Description Hide DescriptionFour local principles are proven for waves propagating in a layered medium with a variable wave speed. These principles are (1) that inhomogeneities increase the amplitude of waves generated by a source of fixed strength, (2) that inhomogeneities reduce spatial oscillation, or increase the wavelength, (3) that inhomogeneities decrease transmission, or increase reflection, and (4) that transmission increases monotonically with frequency. Definitions of inhomogeneity, local wave function, and local reflection and transmission coefficients are made as a basis for stating these principles.

Scale model experiments on the validity of the matched asymptotic expansions theory for sound diffraction by curved surfaces of finite impedance
View Description Hide DescriptionScale modelexperiments have been conducted to study the diffraction of sound by a curved surface of finite impedance. The theory of matched asymptotic expansions (MAE) offers an alternative to Berry and Daigle’s generalized creeping wave series. [J. Acoust. Soc. Am. 8 3, 2047–2058 (1988)] Experimental results are in excellent agreement (less than 1 dB) with predictions from the MAE theory both in the deep shadow zone and in the penumbra along the line of sight.

Scattering by an open sphere: Exact solution and comparison with a boundary integral method
View Description Hide DescriptionThe objective of this paper is to extend the amount of exact solutions for acoustic scattering configurations available to validate numerical methods. The configuration chosen is the radiation of an acoustic point source located at the center of a rigid spherical shell having a circular aperture. In comparison to standard scattering problems, like diffraction of a plane wave by a closed sphere, this problem implies a more severe geometry including a sharp edge. The exact solution is derived using an expansion of the pressure field in terms of spherical Bessel functions and Legendre polynomials. The associated coefficients are the solution to an infinite linear system. The truncation of this system as a function of the reduced wave number k a is discussed. It is found that the system is stable with regard to the truncation and that only 4×k a coefficients are needed to get an accurate solution. Comparisons are made with solutions obtained using a boundary integral method developed by Hamdi [‘‘Formulation variationelle par équations intégrales pour le calcul de champs acoustiques linéaires proches et lointains,’’ doctoral thesis, Université de Compiègne (1982)]. A good agreement is obtained for various frequencies and aperture sizes (relative differences in the far field are of about 1%).

Elastic Helmholtz resonators
View Description Hide DescriptionThe influence of wall elasticity on the response of a Helmholtz resonator is examined by analyzing the canonical case of a thin elastic spherical shell with a circular aperture subject to plane wave excitation. By neglecting the thickness of the wall and representing the elasticity via a ‘‘thin shell’’ theory the problem is reduced to one of solving an integral equation over the aperture for the polarization velocity, which is related to, but distinct from, the radial particle velocity of the fluid. The integral equation can be solved by asymptotic methods for small apertures, yielding closed‐form expressions for the major resonator parameters. In general, wall compliance reduces the resonance frequency in comparison with an identically shaped rigid cavity. The Q value of the resonance is increased and the scattering strength of the cavity at resonance is enhanced by wall compliance. The asymptotic results are supported and supplemented by numerical calculations for thin steel shells in water.

A boundary element formulation for radiation of acoustic waves from axisymmetric bodies with arbitrary boundary conditions
View Description Hide DescriptionThis paper presents a computational technique using the boundary element method for the prediction of sound radiated by axisymmetric bodies with arbitrary boundary conditions. By taking advantage of the axisymmetric property of the body, the three‐dimensional integral formulation is reduced to a one‐dimensional integral along the generator of the body. The arbitrary boundary condition is expanded in a Fourier series with respect to the angle of revolution. The integral equation is solved using a superposition principle involving each term of the series. A numerical procedure is implemented using a curvilinear isoparametric element representation. Examples are given involving an oscillating sphere and a half vibrating sphere. The results are compared with the analytical solutions in which good agreement has been obtained.

Dipole logging in cased boreholes
View Description Hide DescriptionShear wave logging through casing can be challenging, especially when the surrounding formation is unconsolidated. This study identifies two possible causes of the problem using synthetic microseismograms, dispersion curves, signal processing scheme based on Prony’s method, and frequency‐dependent sensitivity coefficients with respect to the layers’ parameters. The first possible cause is eccentering of the tool when the cased hole is well bonded. The second possible cause is poor bonding, which is modeled by the presence of fluid annulus. An off‐center dipole source located in a well‐bonded cased hole generates a Stoneley wave that is poorly coupled to the surrounding formation and propagates at a velocity close to the compressional velocity of the borefluid. This Stoneley wave can obscure the formation shear wave signal associated with a slow (unconsolidated) formation. In a vertical well‐bonded cased hole, shear wave logging slow (unconsolidated) formations can be reliably performed despite the leaky character of the flexural mode if the tool is well centralized, and a low‐source frequency (around 2 kHz) is used. In a highly deviated or horizontal well, where the tool cannot be efficiently centralized, reliable measurements can still be obtained provided the directivities of the source and receivers are perpendicular to the direction of eccentricity. In poorly bonded cased holes, a dipole tool, regardless of its position, excites supplementary low‐velocity modes that are associated with vibrations of the steel casing and the presence of an external fluid annulus. The maximum excitation of these modes is located in the low‐frequency region, similar to that of unconsolidated formation signals. When the cement is not bonded to the casing, depending on the thickness of the fluid annulus, an unconsolidated formation signal may be corrupted, regardless of the tool’s position within the borehole. The Stoneley wave generated by the off‐center source is overpowered by the annulus mode. Even when no interference occurs, the supplementary mode exhibits high, low‐frequency energy due to a strong low‐frequency coupling with the casing which causes the formation signal to be weak, regardless of the type of formation (fast or slow).
As a consequence, the source must be powerful and the recording system must have a large dynamic range for the formation signal to be reliably detected. When the cement is well bonded to the casing but not to the formation, the effects of the presence of the annulus mode are less drastic.

Acoustic radiation from cylinders with a plane of symmetry using internal multipole line source distributions. I
View Description Hide DescriptionA new method is proposed to address the two‐dimensional exterior acoustic radiation problem from infinite cylinders with a plane of symmetry. This approach, which has its roots in fluid mechanics, is based on the use of internal monopole and dipole line source distributions within the surface. The monopole and dipole line source distributions are determined by prescribed normal velocity conditions over the surface of the shell and are subsequently used to determine the associated surface pressure. The exterior acoustic field is then simply calculated using the surface velocity and pressure via the usual surface Helmholtz integral equation. In contrast to earlier integral equation formulations of the problem the present method does not suffer from either nonuniqueness or result in hypersingular integral equations. Numerical results are presented to illustrate the accuracy of the new internal source density method for the case of a circular cylinder subjected to various specified normal velocityboundary conditions and frequencies. Additional numerical results are also presented for the exterior acoustic radiation problem for a strip on an elliptical cylinder. These results show the characteristics of the surface pressure as a function of the surface velocity and strip width.

Acoustic scattering from cylinders with a plane of symmetry using internal multipole line source distributions. II
View Description Hide DescriptionA general internal source density approach to evaluate the acoustic scattered field from rigid infinite cylinders that are symmetric about a plane is presented. The approach is based on the use of internal source density line distributions that are either monopoles or dipoles along the plane of symmetry of the surface. A least‐mean‐square error method is used to match the normal velocity field from the internal sources at the surface of interest with the normal surface velocity due to an incident wave field. The resultant procedure leads to sets of linear algebraic equations that can be easily solved for the monopole and dipole source strengths. The source strengths are subsequently used to obtain the scattered pressure on the surface. The pressure in the exterior field can then be simply determined by evaluating the surface Helmholtz integral formula via usual quadrature methods. Typical numerical results for the surface and far‐field pressures are presented for plane wavescattering by a circular cylinder and compared with closed form solutions. To illustrate the general applicability of the approach, plane wavescattering by elliptic cylinders of various aspect ratios is also addressed. These results indicate the characteristics of the scattered pressure as a function of frequency and aspect ratio.

Nonuniqueness of solutions to extended Kirchhoff integral formulations
View Description Hide DescriptionThis paper examines the nonuniqueness of solutions to an extended Kirchhoff integral formulation at certain discrete frequencies corresponding to the eigenfrequencies of the related interior boundary value problem. In particular, effects of surface motion and interaction between turbulence and vibrating surface in motion on nonuniqueness difficulties are investigated. It is shown that surface motion affects nonuniqueness difficulties in two ways: (1) it shifts the eigenfrequencies of the related interior boundary value problem and (2) it excites more eigenfrequencies at which nonuniqueness difficulties occur than the corresponding stationary case. The interaction between turbulence and vibrating surface in motion further shifts the eigenfrequencies. Although changes in these eigenfrequencies are small at low Mach numbers, they increase with the Mach number. It is also demonstrated that although an extended Kirchhoff integral equation fails to yield a unique solution at certain discrete frequencies, a combined extended surface Kirchhoff integral equation and an extended interior Kirchhoff integral equation always yield a unique solution for all frequencies. This is because there is only one set of solutions that satisfy both an extended surface Kirchhoff integral equation and an extended interior Kirchhoff integral equation.

Excitation of a fluid‐filled, submerged spherical shell by a transient acoustic wave
View Description Hide DescriptionA mathematical formulation and method of solution for the title problem are developed, and numerical results are presented for excitation by a plane step wave. The formulation is based on the familiar equations of motion for a thin spherical shell and the wave equation for the internal and external fluid domains. The Laplace transform is invoked, and the usual separation of variables method produces modal equations for each component of the Fourier–Legendre series solution. The modal equations are then restructured to facilitate transform inversion, yielding delayed differential equations in time for each response mode of the shell‐fluid system, which are integrated numerically in time. Complete response solutions then follow by modal superposition, with special techniques being employed to improve modal convergence. Transient response histories are shown for a step‐wave‐excited steel shell containing water and submerged in water. Also, these results are compared with their counterparts for an empty submerged steel shell.

Shape oscillations of bubbles in water driven by modulated ultrasonic radiation pressure: Observations and detection with scattered laser light
View Description Hide DescriptionSteady‐state quadrupole shape oscillations of air bubbles trapped in water were excited by amplitude modulation of the acoustic radiation pressure used for levitation. This method of exciting controlled shape oscillations may make possible noncontact dynamical measurements of the rheological properties of bubbles. Bubble sizes ranged from 1.6‐ to 12‐mm diameter corresponding to observed quadrupole mode frequenices of 190 to 17 Hz. Small‐amplitude oscillations were detected by interference of scattered laser light. Some larger amplitude oscillations were detected by the unaided eye or with a television camera. The structure of the acoustic field in the levitator needed for the levitation of large bubbles is discussed. In the absence of modulation the levitated bubbles had an oblate shape.

An exact Laplace transform formulation for a point source above a ground surface
View Description Hide DescriptionAn exact analysis is given for a point source in air above a ground surface. By representing the plane‐wave reflection coefficient as the Laplace transform of an image source distribution, a well‐behaved image integral, instead of the usual Sommerfeld integral, is obtained. The approach is valid for both locally and extended reacting surfaces. For a locally reacting ground surface, the image integral is an especially simple, rapidly convergent integral. The integral for local reaction is investigated analytically for a number of limiting cases. The resulting analytic solutions are compared with analytic solutions obtained from more standard approaches. Finally, the image integral for local reaction is analyzed numerically, and an upper limit on the numerical integration is given. It is shown that with realistic values of ground impedance, the prescribed integration limit allows the image integral to be easily and accurately computed numerically.

Determination of compressional wave and shear wave speed profiles in sea ice by crosshole tomography—Theory and experiment
View Description Hide DescriptionSea ice is a heterogeneous material whose acoustic properties are functions of time and space. Results of a crosshole tomography experiment conducted in multi‐year ice with the objective of determining the spatial structure of the compressional and shear wave speeds from travel time measurements made with high‐frequency pulses are presented here. The results of the experiment indicate that the wave speeds can be determined from such a crosshole experiment with good resolution. The compressional and shear wave speed contour maps indicate that the spatial variations of the wave speeds are complex with regions of low speed. Low‐speed regions observed are likely caused by high brine volume content. Resolution and variance studies performed on the estimates are also presented. Material properties such as Poisson’s ratio, salinity, and elastic and shear moduli of sea ice are obtained from the estimates of compressional and shear wave speeds. By measuring the amplitude of the transmitted and received signals along specific paths, estimates of the attenuation coefficients at different depth intervals are obtained. Spatial variability observed in the estimates is believed to be due to scattering by inhomogeneities in the material.

Modeling ambient noise in three‐dimensional ocean environments
View Description Hide DescriptionA model is developed for the calculation of the spatial properties of the surface‐generated noise in a three‐dimensional ocean. This is an extension of the work of Kuperman and Ingenito [J. Acoust. Soc. Am. 6 7, 1988–1996 (1980)], which used a normal‐mode representation of the noise field in a stratified ocean.Noise fields are simulated for both point receivers and vertical line receivers. These examples show how the spatial and directional characteristics of the noise field are affected by the ocean environment. For example, as is apparent in ambient noise data, surface noise propagating at high angles over a sloping ocean bottom is deflected into shallower angles. Also, matched‐field processing simulations in three‐dimensional ocean environments can be done in a consistent manner: signals and surface‐generated noise are modeled by propagating through the same environment with the same theory.

Effect of a rough seabed on the spectral composition of deep ocean infrasonic ambient noise
View Description Hide DescriptionIn deep water, the vertical separation of surfacenoisesources from the elastic bottom is too large for direct excitation of the experimentally observed seismicinterfacewaves in the frequency regime 1–10 Hz. It is here proposed that these strong seismic components are generated by scattering at rough elasticinterfaces in the bottom, thereby coupling the noise field produced by the primary surfacesources into evanescent waves in the bottom. This hypothesis is investigated by combining a previously developed perturbation theory of rough interfacescattering with a model for surface generated noise in a stratified ocean environment. The resulting theory predicts a spectral composition of the noise field near the seabed that is consistent with the spectral structure of relevant seismicnoise data recently collected in the Pacific. The present analysis, in combination with earlier analysis of a data set gathered in a shallow‐water region, makes it quite clear that waveguide propagation mechanisms have an extreme coloring effect on the spectral shape of ocean ambient noise; hence, these mechanisms must be subtracted from measured noise data before inferring the spectral level of surfacenoisesources.

Surface loss, scattering, and reverberation with the split‐step parabolic wave equation model
View Description Hide DescriptionMoore‐Head e t a l. [J. Acoust. Soc. Am. 8 6, 247–251 (1989)] have published a method to incorporate loss due to rough surfacescattering into split‐step parabolic wave equation (PE) codes which then has been extended by Dozier e t a l. [in O c e a n V a r i a b i l i t y a n d A c o u s t i c P r o p a g a t i o n, edited by J. Potter and A. Warn‐Varnas (Kluwer Academic, Dordrecht, 1991)] to include the incoherent scatter. A good agreement with other methods was reported in both cases. However, in the presence of sound‐speed gradients this approach is an approximate solution and errors may occur. This will be discussed for some examples. Using the same procedure to estimate the angular acoustic spectrum at the sea‐surface, the reverberation from the surface and/or bottom may be evaluated for any generic backscatter function. Two different approaches, based on either reciprocity or backpropagation, will be outlined, with both methods being applicable also to bistatic reverberation. The computationally simpler reciprocity approach has been programmed and results compare well with other models for range‐independent environments. A comparison for range‐dependent situations with a ray‐based model gives good agreement on the main features and all remaining deviations can be explained.

Wind dependence of deep ocean ambient noise at low frequencies
View Description Hide DescriptionA series of experiments has been carried out using a vertical line array to measure low‐frequency ambient noise at deep ocean sites in the Northeast Pacific Ocean. Data in the band from 13 to 300 Hz were processed to obtain the array response directed vertically upward in order to study the noise due to local winds. The results indicate that there are two regimes of behavior depending on the wind speed v, with the transition occurring at the onset of wave breaking, v∼10 kn. The noise level (NL) for a specific wind noise process was related to a power n of the wind speed according to the relationship NL=B+20n log v, and the model parameters were obtained by fitting the data. The average value over the band was n=0.3 for wind speeds <10 kn and n=1.33 for higher speeds. This latter value is significantly larger than the value n=1, which is observed in ambient noise data at higher frequencies above 1 kHz. This result suggests that the noise process in breaking waves may be different at low frequencies from that at higher frequencies. Assuming a uniform distribution of surface dipole sources, the source level for the wind‐generated noise was determined over the low‐frequency band for wind speeds from 10–30 kn. The values are consistent with those of a recent analysis of available noise data [Kewley e t a l., ‘‘Low‐frequency wind‐generated ambient noise source levels,’’ J. Acoust. Soc. Am. 8 8, 1894–1902 (1990)], and the model provides good agreement with wind noise measurements obtained with omni hydrophones in the southern oceans.

Tidal signals in basin‐scale acoustic transmissions
View Description Hide DescriptionTravel times of acoustic signals were measured between a bottom‐mounted source near Oahu and five bottom‐mounted receivers located near Washington, Oregon, and California in 1988 and 1989. This paper discusses the observed tidal signals. At three out of five receivers, observed travel times at M2 and S2 periods agree with predictions from a barotropic tide model to within ±30° in phase and a factor of 1.6 in amplitude. The discrepancies at the fourth and fifth receivers can largely be accounted for with a simple model for the generation of baroclinic tides by interactions between the barotropic tides and guyots in the Moonless mountains. These baroclinic tides are phase locked to the astronomical tide‐generating forces. A simple model is used to estimate the conversion of energy from barotropic to baroclinic tides by the world’s seamounts. At M2, the conversion amounts to about 1×10^{18} erg s^{−1}, or about 4% of the total dissipation at M2. Although this estimate is very approximate, it is similar to other published values.

Sound‐speed profile inversion using a large aperture vertical line array
View Description Hide DescriptionIn this paper, the single vertical slice ocean acoustictomography problem is investigated with a large aperture vertical line array and a narrow‐band low‐frequency acoustic source deployed at a known location. Within the framework of matched‐field processing and adiabatic normal modetheory, the self‐cohering technique of Bucker is shown to provide a smooth measure of sound‐speed mismatch. Simple simulation results lead to the development of a minimization procedure to invert for the sound‐speed profile using a good starting solution (e.g., based on historical data). The technique then is demonstrated with additional simulations for sound‐speed structures characteristic of the NE Pacific.

Acoustical properties of interacting particles
View Description Hide DescriptionAcoustical cross sections of random homogeneous dense systems of interacting Rayleigh particles are studied analytically. A model for the radial distribution function is proposed. The role of the far‐field and the near‐field effects on the acoustic characteristics is investigated. It is found that the near‐field effect on the scatteredsound is negligible compared to the far‐field effect. The validity of some assumptions is investigated. It is found that interaction among particles may increase or decrease the attenuation effect depending on the volume fraction and the properties of the particulate system.