A finite difference model of an acoustic logging tool: the borehole in a horizontally layered geologic medium

Bhasavanija, Khajohn; Nicoletis, L.; Young, Terence K.

doi:10.1190/1.1826951

Cited by 12 publications

(17 citation statements)

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“…Full waveform acoustic logging offers an effective tool for characterizing these structures. The current technique for modelling borehole acoustic wave propagation with heterogeneous formation structures is the finite-difference method (Bhashvanija 1983; Steven, Paper read at the 53rd EAEG meeting, Florence, May 1991;received November 1991, revision accepted August 1992 Pardo-Casas and Cheng 1985;Kostek 1991), which can handle heterogeneity quite easily. However the implementation of the method to a permeable porous formation is still a topic of research.…”

Section: Introductionmentioning

confidence: 99%

BOREHOLE STONELEY WAVE PROPAGATION ACROSS PERMEABLE STRUCTURES¹

Tang¹,

Cheng²

1993

Geophysical Prospecting

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TANG, X.M. and CHENG, C.H. 1993. Borehole Stoneley wave propagation across permeable structures. Geophysical Prospecting 41, 165-187.This study investigates the propagation of borehole Stoneley waves across permeable structures. By modelling the structure as a zone intersecting the borehole, a simple 1D theory is formulated to treat the interaction of the Stoneley wave with the structure. This is possible because the Stoneley wave is a guided wave, with no geometric spreading as it propagates along the borehole. The interaction occurs because the zone and the surrounding formation possess different Stoneley wavenumbers. Given appropriate representations of the wavenumber, the theory can be applied to treat a variety of structures, including a fluid-filled fracture. Of special interest are the cases of permeable porous zones and fracture zones. The results show that, while Stoneley wave reflections are generated, strong Stoneley wave attenuation is produced across a very permeable zone. This result is particularly important in explaining the observed strong Stoneley wave attenuation at major fractures where it has been difficult to explain the attenuation in terms of the single planar fracture theory. In addition, by using a simple and sufficiently accurate theory to model the effects of the permeable zone, a fast and efficient method is developed to characterize the fluid transport properties of a permeable fracture zone.

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Section: Introductionmentioning

confidence: 99%

BOREHOLE STONELEY WAVE PROPAGATION ACROSS PERMEABLE STRUCTURES¹

Tang¹,

Cheng²

1993

Geophysical Prospecting

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“…It is distinguished from previous finite-difference models (Chang, 1982;Bhasavanija, 1983;Stephen et aI., 1985)in several ways. First, we employ a velocity-stress finite-difference (vs-fd) formulation (Virieux, 1986), resulting in a simple numerical implementation of irregular fluid-solid interfaces.…”

Section: Introductionmentioning

confidence: 98%

Multipole borehole acoustic waveforms: Synthetic logs with beds and borehole washouts

Randall

Scheibner²,

Wu³

1991

GEOPHYSICS

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We give a two‐dimensional (2-D) velocity‐stress finite‐difference (vs-fd) formulation for the multipole borehole acoustic logging problem. Irregular boreholes, horizontal bedding, and axially varying alteration are encompassed by the model. Excellent agreement is obtained with transform techniques for constant radius boreholes and homogeneous formations. The method is used to generate waveforms for many positions of transmitter and receiver array relative to beds and washouts as in logging. First motion and semblance techniques are applied to the waveforms to extract formation slownesses, resulting in synthetic multipole logs which demonstrate the response of ideal multipole logging tools and signal processing to several environmental effects. For monopole, compressional, first‐motion logs, residual slowness errors remain at borehole washouts after borehole compensation. These errors increase as the effective measure point in the waveforms is moved back in time from true first motion, admitting greater interference from reflected and mode‐converted waves. Errors at bed boundaries are typically smaller than those at washouts. Stoneley slowness logs are obtained by narrow‐band filtering of low frequency monopole waveforms and application of the semblance slowness extraction algorithm STC. Similar processing applied to low frequency dipole waveforms yields flexural mode slowness logs. A small correction satisfactorily accounts for flexural mode dispersion properties, yielding formation shear slowness. Slowness errors for both Stoneley and dipole shear logs at washouts and bed boundaries are quite small, typically on the order of a few percent. Borehole compensation is of marginal benefit for both of these logs since they are based on modes of the borehole rather than head‐waves.

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“…The complications include permeable rock (Rosenbaum, 1974;Schmitt, 1988a;Schmitt et al, 1988;Norris, 1989;Schmitt 1989), a damaged or invaded zone around the borehole or a cased borehole (Chan and Tsang, 1983;Tubman et al, 1984;Stephen et al, 1985;Tubman et al, 1986;Burns, 1986;Schmitt, 1988a;Schmitt, 1988b;Schmitt, 1989), a viscous fluid (Burns, 1988), a borehole with an irregular cross section (Willen, 1983;Nicoletis et al, 1990), a borehole in which the diameter changes along the axis (Bouchon and Schmitt, 1989), fractures intersecting the borehole (Bhasavanija, 1983;Mathieu, 1984;Stephen et al, 1985), and anisotropy. Tongtaow (1980), White and Tongtaow (1981), Tongtaow (1982), Chan and Tsang (1983), and Schmitt (1989) focused on the special case of transversely isotropy with the symmetry axis aligned with the borehole.…”

Section: Extendedmentioning

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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A finite difference model of an acoustic logging tool: the borehole in a horizontally layered geologic medium

Cited by 12 publications

References 0 publications

BOREHOLE STONELEY WAVE PROPAGATION ACROSS PERMEABLE STRUCTURES¹

BOREHOLE STONELEY WAVE PROPAGATION ACROSS PERMEABLE STRUCTURES¹

Multipole borehole acoustic waveforms: Synthetic logs with beds and borehole washouts

Elastic wave propagation along a borehole in an anisotropic medium

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A finite difference model of an acoustic logging tool: the borehole in a horizontally layered geologic medium

Cited by 12 publications

References 0 publications

BOREHOLE STONELEY WAVE PROPAGATION ACROSS PERMEABLE STRUCTURES1

BOREHOLE STONELEY WAVE PROPAGATION ACROSS PERMEABLE STRUCTURES1

Multipole borehole acoustic waveforms: Synthetic logs with beds and borehole washouts

Elastic wave propagation along a borehole in an anisotropic medium

Contact Info

Product

Resources

About

BOREHOLE STONELEY WAVE PROPAGATION ACROSS PERMEABLE STRUCTURES¹

BOREHOLE STONELEY WAVE PROPAGATION ACROSS PERMEABLE STRUCTURES¹