摘要:

The role that thermo‐viscous effects play in the propagation of finite level sound in a waveguide has been reexamined from a fundamental perspective. In the past, nonlinear acoustic interactions have been described by energy conserving modulation of spectral amplitudes as wave packets travel axially down the waveguide. To account for thermo‐viscous effects in this modulation, investigators have included without formal justification into the modulation equations dissipative terms with a magnitude corresponding to the Kirchhoff rate of attenuation encountered in linear theory. In this investigation, the problem of the propagation of finite magnitude plane waves is analyzed in a different manner. As opposed to previous investigations, all three modes (acoustic, vorticity, and entropy) are considered from the outset. The boundary conditions are extended to include vanishing normal and tangential fluid velocity, as well as vanishing fluid temperature perturbations. A new solution at second order is presented (second order being the first correction due to nonlinearity), which is uniform in the spatial variables. As a consequence, it is shown that the thermo‐viscous effects are incorporated into the spectral amplitude modulation equations through one of the boundary conditions. These modulation equations apply to both plane and higher‐order modes, including the region arbitrarily near the cutoff frequency for the higher‐order modes. It is shown that the small parameter 1/(N)1/2, whereN=ρ0Dc/μ (the acoustic Reynolds number), is a special scale for analysis of nonlinear interactions in a waveguide. In particular, the relative magnitude of the sound source and 1/(N)1/2is a determining factor that predicts whether nonlinear interactions will be significant.

ISSN:0001-4966    

DOI:10.1121/1.402294

出版商:Acoustical Society of America    

年代:1991

数据来源: AIP

摘要:

Biot’s theory is employed to study the propagation of plane‐harmonic seismic waves in a transversely isotropic liquid‐saturated porous solid. Along withSHwave, the existence of three quasiwaves is discussed and analytical expressions for their velocities of propagation have been obtained. It has been observed that velocities of existing waves vary with the direction of propagation. Frequency equation for the propagation of Rayleigh‐type surface waves at the free surface of transversely isotropic liquid‐saturated porous solids has been obtained. Possibilities of existence of body waves and surface waves have been discussed numerically by assuming different sets of values of elastic constants. Dependence of the velocities of propagation on the direction of propagation has been exhibited.

ISSN:0001-4966    

DOI:10.1121/1.402295

出版商:Acoustical Society of America    

年代:1991

数据来源: AIP

摘要:

In the estimation of ultrasound attenuation in random scattering media, near‐field and near‐focus diffraction effects introduce bias because of their depth‐dependent filtering behavior. A new approach is proposed that is aimed at the prediction and correction of these effects. It is based on the concept of instantaneous time‐frequency representation of random signals, and it leads to a rigorous definition of the echographic diffraction filter. A thorough study is provided of this time‐varying filter for axisymmetric planar and focused transducers. In this last case the diffraction filter depends on five parameters (time, frequency, transducer radius, focal length, and sound velocity). Through the study of invariance properties of the diffraction impulse response, it is shown that the five parameters combine into a unique dimensionless variable. Hence the complete diffraction behavior is derived from the knowledge of a universal one‐variable function: thediffractionfunction. The physical origin of this property is discussed and a theoretical study of this function is presented. Also provided is a look up curve and a fitting rational approximation to allow easy diffraction‐correction implementation. Experimental calibration of an echographic diffraction filter shows good agreement with the predicted diffraction function.

ISSN:0001-4966    

DOI:10.1121/1.402296

出版商:Acoustical Society of America    

年代:1991

数据来源: AIP

摘要:

With the advent of large storage and high speed capabilities of digital computers, computations previously considered intractable have become feasible. One area in which this fact is especially relevant is in the numerical modeling of wave propagation. In this paper, a sequel to a previous one [T. J. Cavicchi, ‘‘Transient high‐order ultrasonic scattering,’’ J. Acoust. Soc. Am.88, 1132–1141 (1990)] a time‐domain moment method expansion is, through computer simulations, demonstrated to be capable of solving a temporal forward scattering problem for small, fairly strong cylindrical scatterers. It is, however, very computationally intensive, so detailed studies of the matrix structure are presented. Such studies are useful in optimizing the current method in order to make feasible more practical medical imaging studies.

ISSN:0001-4966    

DOI:10.1121/1.402297

出版商:Acoustical Society of America    

年代:1991

数据来源: AIP

摘要:

Solutions to two coupled half‐plane problems are derived. In the first, an exact solution to the canonical problem of acoustic plane‐wave diffraction from a pressure release (zero impedance) surface coupled to a perfectly rigid (infinite impedance) surface is given using the Wiener–Hopf method. The solution is expressed in terms of an angular spectrum of plane waves. In the second, the rigid surface is replaced by one characterized by a locally reacting finite impedance. Here, an approximate kernel to the Wiener–Hopf functional equation is used which leads to a complete and readily interpretable solution. This solution is expressed in terms of the canonical angular spectrum for the first problem multiplied by a function that depends on material parameters of the locally reacting surface. Polar plots of the far‐field amplitude level for the diffracted field are presented.

ISSN:0001-4966    

DOI:10.1121/1.402298

出版商:Acoustical Society of America    

年代:1991

数据来源: AIP

摘要:

Using the dereverberated‐source concept, the synthetic seismograms for stratified equal travel‐time layering for source and receiver at the surface as well as for a buried receiver as in the VSP data are derived. Here the simpler acoustic representation of seismograms is treated. These results are extended to data of equal vertical delay time, τ, and horizontal ray parameter,p. Since only time domain operators are used, it is not necessary to use Fourier transforms to compute the seismic response for any depth point, or any ray parameter. In addition to extending Goupillaud’s equal travel‐time layer synthetic seismogram method to a buried receiver and to the case of non‐normal incidence, the use of the dereverberated‐source concept intuitively illustrates the nature of the seismic impulse response for a one‐dimensional earth.

ISSN:0001-4966    

DOI:10.1121/1.402299

出版商:Acoustical Society of America    

年代:1991

数据来源: AIP

摘要:

The reflection and transmission coefficients of elastic waves are calculated numerically at the interface (solid–solid) for general anisotropic media oriented in any arbitrary direction. The plane‐wave solutions in anisotropic media are considered. The eigenvalues (slownesses) and the eigenvectors (polarizations) are computed from the 6×6 system matrixAof each medium using a numerical approach. Thezcomponent of the Pointing vector and the radiation condition are used to separate the up‐ and down‐going propagations. The solution of reflection and transmission coefficients at the interface are computed in terms of a scatterer operator approach (connecting the up‐ and down‐going wave components of the two sides of the interface). In this procedure, all the possible wave types (nine combinations as: @/iqP−qP, qP−S1, qP−S2, S1−qP, S1−S1, S1−S2, S2−qP, S2−S1,@/r andS2−S2) of the reflection and the transmission coefficients are at the interface. It is preferable to represent the coefficients as a function of slowness, rather than the conventional angle of incidence, because a common reference forPandSwaves can be used, thus displaying many of the characteristics more clearly. The coefficients depend, in general, on the polar and azimuthal angles of incidence, and the relative values of the elastic constants in the media on the two sides of the interface. Results for fractured media are presented. Some comparisons with the isotropic model are also presented to clarify the behavior of wave propagation in anisotropic media. Complete synthetic waveforms from an explosion source are computed to observe the effects of anisotropy on amplitude and phase at both sides of the interface.

ISSN:0001-4966    

DOI:10.1121/1.402300

出版商:Acoustical Society of America    

年代:1991

数据来源: AIP

摘要:

Accurate focusing in an inhomogeneous medium is difficult to implement. In order to focus on a reflective target we have extended the concept of optical phase‐conjugate mirrors, valid for monochromatic signals, to broadband pulses such as those used in ultrasound echography. The transducer’s linear response to the acoustic pressure allows one to replace the phase conjugation by a time reversal operation on the pulse echo signals. The time reversal mirror is an array of transmit–receive transducers. A first incident wave is reflected by the target. The received signals are stored in shift registers, reversed in time, and then reemitted. The main advantage of this process is that waves distorted by the propagation through an aberrating medium are corrected by the mirror operation and the back propagation through the medium. When the medium contains several reflectors, this time reversal process can be iterated in order to focus on the most reflective one. We present theoretical results on this principle, numerical simulations, and experimental results with a 1‐D array working at a central frequency of 3 MHz.

ISSN:0001-4966    

DOI:10.1121/1.402301

出版商:Acoustical Society of America    

年代:1991

数据来源: AIP

摘要:

Closed‐form expressions are derived for the Rayleigh–Rice and extinction‐theorem perturbation theories for the case of Dirichlet boundary conditions. It is shown that the two theories are related through the reciprocity transformation to all orders. It follows that a proof of invariance of either of the theories with respect to the reciprocity transformation would imply the formal equivalence of the two theories. Using the reciprocity relationship between the two theories, a recursion relation is derived for annth‐order term of the extinction‐theorem perturbation theory (similar to the one for the Rayleigh–Rice perturbation theory). In spite of considerable effort, no general proof of invariance of the terms of the two perturbation series with respect to the reciprocity transformation was obtained. Two possible approaches to such a proof are suggested. While the question of convergence of the two series is not examined in this work, it is possible that the formulas derived here will prove useful in such a study.

ISSN:0001-4966    

DOI:10.1121/1.402302

出版商:Acoustical Society of America    

年代:1991

数据来源: AIP

摘要:

A new formulation called the slowly varying method (SVM) is proposed in this paper to solve high‐frequency scalar scattering problems. It is well known in linear acoustics that, excited by a plane harmonic incident waveU0(x) impinging on a scatterer, the scattered fieldU(x) for a Neumann boundary value problem or ∂U(x)/∂nfor a Dirichlet boundary value problem is quickly varying on a scatterer whenka≫1, wherekis the wave number andais a typical scatterer dimension. The paper shows that for the samekathe functionV(x)=U*0(x)U(x) for the Neumann boundary condition andVn(x)=U*0(x)∂U(x)/∂nfor the Dirichlet boundary condition exhibit much slower variations on the scatterer compared with those ofU(x) and ∂U(x)/∂nfor some cases. Here,U*0(x) is the complex conjugate ofU0(x). The relations amongV(x),Vn(x) and the acoustic energy densities have been analyzed. A new boundary integral equation in terms of the unknown functionV(x) orVn(x) on the scatterer may be derived. This boundary integral equation can be either solved by the BEM or asymptotically simplified by the stationary phase method and other approximations. For the former case, the requirement that the boundary element dimension should be proportional to 1/(ka) may be waived for obtaining satisfactory numerical results. For the latter case, a non‐element numerical solution ofV(x) orVn(x) then may be obtained by an algebraic arithmetic without solving large‐dimensional linear‐algebraic equations. A few numerical results obtained by the SVM are presented in the paper as well as their comparison with the conventional BEM solutions.

ISSN:0001-4966    

DOI:10.1121/1.402017

出版商:Acoustical Society of America    

年代:1991

数据来源: AIP