Borehole wave particle motion in anisotropic formations

Leveille, Jacques P.; Seriff, A. J.

doi:10.1029/jb094ib06p07183

Cited by 12 publications

(7 citation statements)

References 7 publications

(7 reference statements)

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“…The parameter is obviously related to the difference in shear properties, but the parameter or equivalently, the modulus N, is a more complicated combination of moduli. Leveille and Seriff (1989) derived the tube-wave speed for a particular type of transversely isotropic medium with its axis perpendicular to the borehole. The general perturbation theory is compared with this exact case in Appendix B.…”

Section: Quasi-static Tube-and Torsional-wave Speedsmentioning

confidence: 99%

“…A more stringent test of our result occurs when there is true azimuthal anisotropy in the formation. This situation was considered by Leveille and Seriff (1989) who drew upon results of Savin (1961).…”

Section: Appendix a Some Tube Wave Integralsmentioning

confidence: 99%

“…In addition to Thomsen (1986), several other authors have discussed the implications of anisotropy for elastic wave propagation in applications relevant to exploration geophysics. Leveille and Seriff (1989) examined the possibility that the tube wave in a borehole might have a preferential polarization in the presence of azimuthal anisotropy, and concluded that the degree of polarization eccentricity was not significant. Nicoletis et al (1990) used a combination of analytical and numerical methods to compute the tube-wave speed in anisotropic formations.…”

Section: Introductionmentioning

confidence: 99%

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Weak elastic anisotropy and the tube wave

Norris

Sinha

1993

GEOPHYSICS

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Tube‐wave speed in the presence of a weakly anisotropic formation can be expressed in terms of an effective shear modulus for an equivalent isotropic formation. When combined with expressions for the speeds of the SH‐ and quasi‐SV‐waves along the borehole axis, a simple inversion procedure can be obtained to determine three of the five elasticities of a transversely isotropic (TI) formation tilted at some known angle with respect to the borehole axis. Subsequently, a fourth combination of elastic moduli can be estimated from the expression for the qP‐wave speed along the borehole axis. The possibility of determining all five elasticities of a TI formation based on an assumed correlation between two anisotropy parameters is discussed.

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Section: Quasi-static Tube-and Torsional-wave Speedsmentioning

confidence: 99%

Section: Appendix a Some Tube Wave Integralsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Weak elastic anisotropy and the tube wave

Norris

Sinha

1993

GEOPHYSICS

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“…Most of our knowledge comes from the perturbation solution. On the other hand, field data observations in the anisotropic formation are available, e.g., borehole waves generated from a vertical seismic profile (Barton and Zoback, 1988; Leveille and Seriff, 1989) and borehole dipole logging (Esmersoy et al, 1994).…”

Section: Introductionmentioning

confidence: 99%

Decomposition and particle motion of acoustic dipole log in anisotropic formation

Cheng¹,

Cheng²

1995

SEG Technical Program Expanded Abstracts 1995

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For linear wave propagation in anisotropic media, the principle of superposition still holds. The decomposition of the acoustic dipole log is based on this principle. In the forward decomposition inline and crossline acoustic dipole logs at any azimuthal angle the projection of measurements is along the principal direction of the formation. In the inverse decomposition the measurements along the principal direction can be constructed from the orthogonal pair of inline and crossline acoustic dipole log. The analytic formulas for both forward and inverse decompositions of the dipole laaa ssssaog are derived in this paper. The inverse decomposition formula is the solution in the least-square sense. Numerical examples are demonstrated for the acoustic dipole log decomposition in isotropic and anisotropic formations. The synthetic dipole log is calculated by the 3-D finite difference method. The numerical examples also show that the inverse decomposition formula works very well with noisy data. This inverse decomposition formula will be useful to process the field acoustic logging data in anisotropic formations. It can provide the direction of the formation anisotropy as well as the degree of anisotropy. Because acoustic dipole logging is in the near field distance, the particle motion is complicated. The particle motion is linearly polarized only in the principle direction. The initial particle motion with a dipole source at an arbitrary azimuthal angle tends to point in the fast shear wave direction. However, it will be difficult to use this information to find a stable estimation of a fast shear wave direction. 2-1 Cheng and Cheng

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“…Recently, some researchers have focused on transverse isotropy when the symmetry axis is perpendicular to the borehole. Leveille and Seriff (1989) determined the particle motion of the tube wave at the zero frequency limit, and they studied the horizontal displacement on the inner wall of a finite length, cylindrical shell which has be excited by a horizontal point force. Nicoletis et al (1990) determined the phase velocity and particle displacements of a tube wave at the zero frequency limit.…”

Section: Introductionmentioning

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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Borehole wave particle motion in anisotropic formations

Cited by 12 publications

References 7 publications

Weak elastic anisotropy and the tube wave

Weak elastic anisotropy and the tube wave

Decomposition and particle motion of acoustic dipole log in anisotropic formation

Elastic wave propagation along a borehole in an anisotropic medium

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