Propagation of Sound Waves along Liquid Cylinders

Jacobi, William J.

doi:10.1121/1.1906475

Cited by 41 publications

(18 citation statements)

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“…That is, borehole waveforms must approach the liquid-liquid waveguide limit as shear velocity approaches zero (Jacobi, 1949). In this limit, the compressionai modes become undamped and dispersive in a manner closely analogous to the normal modes in hard formations.…”

Section: -8mentioning

confidence: 99%

“…They become important in the limit of vanishing shear velocity as the borehole becomes a liqUid-liquid waveguide. Several authors have used the analogy between shear normal modes and compressional normal modes in the two liquid cases to simplify the mathematics of mode theory (Jacobi, 1949;Rosenbaum, 1960;Aki and Richards, 1980). Phinney (1961) describes in detail the physical…”

Section: Paillet and Chengmentioning

confidence: 99%

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A numerical investigation of head waves and leaky modes in fluid‐filled boreholes

Paillet

Cheng

1986

GEOPHYSICS

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Although synthetic borehole seismograms routinely can be computed for a wide range of borehole conditions, the physical nature of shear and compressional head waves in fluid-filled boreholes is poorly understood. This paper presents a series of numerical experiments designed to provide insight into the physical mechanisms controlling head wave propagation in boreholes. These calculations demonstrate the existence of compressional normal modes equivalent to shear normal modes, or pseudo-Rayleigh waves, with sequential cutoff frequencies spaced between the cutoff frequencies for the shear normal modes. Major contributions to head wave spectra are shown to occur in discrete peaks at frequencies just below mode cutoff for both compressional and shear modes. This result is confirmed by calculations with synthetic waveforms at frequencies corresponding to mode cutoff, and by branch cut integrals designed to yield independent spectra for the compressional mode. In the case of soft formations where shear velocity falls below acoustic velocity in the borehole fluid, leaky compressional normal modes attain properties similar to those observed for shear normal modes in the hard rock case. This result is formally related to a fluid-fluid wavegUide with undamped compressional normal modes in the limit of vanishing shear velocity. Synthetic waveforms demonstrate that high amplitUde arrivals, traveling at velocities less than the acoustic veiocity of the borehole fluid, and at frequencies above a few kilohertz represent the Airy phase of the compressional mode and not a tUbe wave. Comparison of synthetic waveforms with waveforms obtained in soft sea sediments indicates that the predicted Airy phase arrivals are present in the experimental data.

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Section: -8mentioning

confidence: 99%

Section: Paillet and Chengmentioning

confidence: 99%

A numerical investigation of head waves and leaky modes in fluid‐filled boreholes

Paillet

Cheng

1986

GEOPHYSICS

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“…In very lossy pipe materials, the phase speeds and attenuations of propagating modes in the liquidfilled tube were theoretically and experimentally obtained. 11,12 However these investigations [4][5][6][7][8][9][10][11][12] were only limited to the axisymmetric modes. The propagation of nonaxisymmetric modes in a hollow pipe was theoretically described by Gazis.…”

Section: Introductionmentioning

confidence: 99%

“…However these analyses depend on assuming that the acoustic waves in the liquid and pipe materials 2,3 are uncoupled, or by use of a thin-wall approximation. [4][5][6] Del Grosso 7 calculated the dispersion relation for the phase speed of propagating modes inside the tube filled with inviscid liquid using exact elasticity equations which can be applied to any frequency and thickness of the tube. His predictions were experimentally verified by Lafleur and Shields 8 in the low frequency regime for a fluid-filled elastic tube.…”

Section: Introductionmentioning

confidence: 99%

Acoustic attenuation, phase and group velocities in liquid-filled pipes III: Nonaxisymmetric propagation and circumferential modes in lossless conditions

Baik

Jiang

Leighton

2013

The Journal of the Acoustical Society of America

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Equations for the nonaxisymmetric modes that are axially and circumferentially propagating in a liquid-filled tube with elastic walls surrounded by air/vacuum are presented using exact elasticity theory. Dispersion curves for the axially propagating modes are obtained and verified through comparison with measurements. The resulting theory is applied to the circumferential modes, and the pressures and the stresses in the liquid-filled pipe are calculated under external forced oscillation by an acoustic source. This provides the theoretical foundation for the narrow band acoustic bubble detector that was subsequently deployed at the Target Test Facility (TTF) of the Spallation Neutron Source (SNS) at Oak Ridge National Laboratory (ORNL), TN.

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“…n=-oo -00 -is found using the separation of variables technique (Jacobi, 1949;Ben-Menahem and Singh, 1981, p. 49-50;Tongtaow, 1982;White, 1983, p. 181-182). n is the azimuthal order number, k, the axial wavenumber, and w the radian frequency.…”

Section: A1 Propagation In the Fluidmentioning

confidence: 99%

Elastic wave propagation along a borehole in an anisotropic medium

Ellefsen

1990

SEG Technical Program Expanded Abstracts 1990

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In the first part of this thesis, several applications of perturbation theory are developed to study normal mode propagation along a borehole. This theory is used to relate first order perturbations in frequency, wavenumber, elastic moduli, densities, and locations of interfaces. Although the perturbation equation is derived for a general model with many fluid and solid layers which have any cross-sectional shape, the equation is applied to a two-layer model consisting of a fluid-filled borehole through a transversely isotropic solid (with its symmetry axis parallel to the borehole). Because analytical expressions for the displacements exist for this particular model, the terms in the perturbation equation simplify greatly. Formulas are derived to calculate (1) phase velocities for a model with slight, general anisotropy, (2) partial derivatives of either the wavenumber or frequency with respect to either an elastic modulus or density, (3) group velocity, and (4) phase velocities for a model with a slightly irregular borehole. These formulas are applicable also to models with an isotropic solid because it is a special case of a transversely isotropic solid.In the second part, the effects of anisotropy upon elastic wave propagation are determined. The wave equation is solved in the frequency-wavenumber domain with a variational method, and the solution yields the phase velocities, group velocities, pressures, and displacements for the normal modes. (The phase and group velocities obtained with this variational method match those obtained with the perturbation method indicating that both are correctly formulated and implemented.) These properties are studied for two cases: a transversely isotropic model for which the borehole has several different orientations with respect to the symmetry axis and an orthorhombic model for which the borehole is parallel to the intersection of two symmetry planes. The normal modes for these two cases show several effects which do not exist when the solid is isotropic or transversely isotropic with its symmetry axis parallel to the borehole:1. The phase velocities for the quasi-pseudo-Rayleigh, both quasi-flexural, and both quasi-screw waves do not exceed the phase velocity of the slowest qSwave. (The phase velocities of the leaky modes, which were not investigated, will exceed this threshold.)2. The two quasi-flexural waves have different phase and group velocities; the differences are greatest at low frequencies and diminish as the frequency increases. In general, the two quasi-screw waves behave similarly.3. The greater the difference between the the phase velocities of the qS-waves, the greater the difference between the phase velocities of the quasi-flexural waves at all frequencies. The two quasi-screw waves behave similarly.4. Near the limiting qS-wave velocity, the difference between the phase velocities of the two quasi-flexural waves is greater than that for the two quasi-screw waves.5. For the slow quasi-flexural wave, the particle displacements in the plane perpe...

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Propagation of Sound Waves along Liquid Cylinders

Cited by 41 publications

References 0 publications

A numerical investigation of head waves and leaky modes in fluid‐filled boreholes

A numerical investigation of head waves and leaky modes in fluid‐filled boreholes

Acoustic attenuation, phase and group velocities in liquid-filled pipes III: Nonaxisymmetric propagation and circumferential modes in lossless conditions

Elastic wave propagation along a borehole in an anisotropic medium

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