scholarly journals Stoneley wave propagation in a fluid‐filled borehole with a vertical fracture

1989 ◽  
Author(s):  
Xiaoming Tang ◽  
C. H. Cheng ◽  
M. Nafi Toksöz
Keyword(s):  
Wave Propagation ◽  
Stoneley Wave ◽  
Vertical Fracture

scholarly journals Stoneley‐wave propagation in a fluid‐filled borehole with a vertical fracture

Geophysics ◽  
1991 ◽  
Vol 56 (4) ◽  
pp. 447-460 ◽  
Author(s):  
X. M. Tang ◽  
C. H. Cheng ◽  
M. N. Toksöz
Keyword(s):  
Boundary Condition ◽  
Wave Propagation ◽  
Wave Attenuation ◽  
Perturbation Technique ◽  
Quantitative Relationship ◽  
Acoustic Properties ◽  
Stoneley Wave ◽  
Fracture Aperture ◽  
Stoneley Waves ◽  
Vertical Fracture

The propagation of Stoneley waves in a fluid‐filled borehole with a vertical fracture is investigated both theoretically and experimentally. The borehole propagation excites fluid motion in the fracture and the resulting fluid flow at the fracture opening perturbs the fluid‐solid interface boundary condition at the borehole wall. By developing a boundary condition perturbation technique for the borehole situation, we studied the effect of this change in the boundary condition on the Stoneley propagation. Cases of both hard and soft formations have been investigated. The fracture has minimal effects on the Stoneley velocity, except in the very low frequency range in which the Stoneley velocity drastically decreases with decreasing frequency. Significant Stoneley‐wave attenuation is produced because of the energy dissipation into the fracture. The quantitative behavior of these effects depends not only on fracture aperture and borehole radius, but also on the acoustic properties of the formation and fluid. Ultrasonic experiments were performed to measure Stoneley propagation in laboratory fracture borehole models. Aluminum and lucite were used to simulate a hard and a soft formation, respectively. Array data for wave propagation were obtained and were processed using Prony’s method to give velocity and attenuation of Stoneley waves as a function of frequency. In both hard and soft formation cases, the experimental results agreed with the theoretical predictions. The important result of this study is that it presents a quantitative relationship between the Stoneley propagation and the fracture character in conjunction with formation and fluid properties. This relationship provides a method for estimating the characteristics of a vertical fracture by means of Stoneley wave measurements.

Wave Propagation in a Two-Layered Medium

1964 ◽  
Vol 31 (2) ◽  
pp. 213-222 ◽  
Author(s):  
J. P. Jones
Keyword(s):  
Wave Propagation ◽  
Elastic Wave ◽  
Rayleigh Waves ◽  
Layered Medium ◽  
Elastic Wave Propagation ◽  
Flexural Wave ◽  
Stoneley Wave ◽  
Sh Waves ◽  
The Waves

Elastic wave propagation in a medium consisting of two finite layers is considered. Two types of solutions are treated. The first is a Rayleigh train of waves. It is seen that for this case, when the wavelength becomes short, the waves approach two Rayleigh waves plus a possible Stoneley wave. When the wavelength becomes large, there are two waves; i.e., a flexural wave and an axial wave. Calculations are presented for this case. The propagation of SH waves is treated, but no calculations are presented.

BOREHOLE STONELEY WAVE PROPAGATION ACROSS PERMEABLE STRUCTURES1

1993 ◽  
Vol 41 (2) ◽  
pp. 165-187 ◽  
Author(s):  
X. M. TANG ◽  
C. H. CHENG
Keyword(s):  
Wave Propagation ◽  
Stoneley Wave

Simulation of borehole sonic waveforms in dipping, anisotropic, and invaded formations

Geophysics ◽  
2011 ◽  
Vol 76 (4) ◽  
pp. E127-E139 ◽  
Author(s):  
Robert K. Mallan ◽  
Carlos Torres-Verdín ◽  
Jun Ma
Keyword(s):  
Wave Propagation ◽  
Shear Modulus ◽  
Symmetry Axis ◽  
Transverse Isotropy ◽  
Cutoff Frequency ◽  
Dispersion Curves ◽  
Flexural Wave ◽  
Stoneley Wave ◽  
Stoneley Waves ◽  
The Impact

A numerical simulation study has been made of borehole sonic measurements that examined shoulder-bed, anisotropy, and mud-filtrate invasion effects on frequency-dispersion curves of flexural and Stoneley waves. Numerical simulations were considered for a range of models for fast and slow formations. Computations are performed with a Cartesian 3D finite-difference time-domain code. Simulations show that presence of transverse isotropy (TI) alters the dispersion of flexural and Stoneley waves. In slow formations, the flexural wave becomes less dispersive when the shear modulus (c44) governing wave propagation parallel to the TI symmetry axis is lower than the shear modulus (c66) governing wave propagation normal to the TI symmetry axis; conversely, the flexural wave becomes more dispersive when c44 > c66. Dispersion decreases by as much as 30% at higher frequencies for the considered case where c44 < c66. Dispersion of Stoneley waves, on the other hand, increases in TI formations when c44 > c66 and decreases when c44 < c66. Dispersion increases by more than a factor of 2.5 at higher frequencies for the considered case where c44 < c66. Simulations also indicate that the impact of invasion on flexural and Stoneley dispersions can be altered by the presence of TI. For the case of a slow formation and TI, where c44 decreases from the isotropic value, separation between dispersion curves for cases with and without the presence of a fast invasion zone increases by as much as 33% for the flexural wave and by as much as a factor of 1.4 for the Stoneley wave. Lastly, presence of a shoulder bed intersecting the sonic tool at high dip angles can alter flexural dispersion significantly at low frequencies. For the considered case of a shoulder bed dipping at 80°, ambiguity in the flexural cutoff frequency might lead to shear-wave velocity errors of 8%–10%.

Acoustic wave propagation in a fluid‐filled borehole surrounded by a formation with stress‐relief‐induced anisotropy

Geophysics ◽  
1993 ◽  
Vol 58 (9) ◽  
pp. 1257-1269 ◽  
Author(s):  
Lasse Renlie ◽  
Arne M. Raaen
Keyword(s):  
Wave Propagation ◽  
Acoustic Wave ◽  
Shear Wave ◽  
Transverse Isotropy ◽  
Shear Velocity ◽  
Stress Relief ◽  
Stoneley Wave ◽  
Acoustic Wave Propagation ◽  
Damaged Zone ◽  
Compressional Velocity

The stress relief associated with the drilling of a borehole may lead to an anisotropic formation in the vicinity of the borehole, where the properties in the radial direction differ from those in the axial and tangential directions. Thus, axial and radial compressional acoustic velocities are different, and similarly, the velocity of an axial shear‐wave depends on whether the polarization is radial or tangential. A model was developed to describe acoustic wave propagation in a borehole surrounded by a formation with stress‐relief‐induced radial transverse isotropy (RTI). Acoustic full waveforms due to a monopole source are computed using the real‐axis integration method, and dispersion relations are found by tracing poles in the [Formula: see text] plane. An analytic expression for the low‐frequency Stoneley wave is developed. The numerical results confirm the expectations that the compressional refraction is mainly given by the axial compressional velocity, while the shear refraction arrival is due to the shear wave with radial polarization. As a result, acoustic logging in an RTI formation, will indicate a higher [Formula: see text] ratio than that existing in the virgin formation. It also follows that the shear velocity may be a better indicator of a mechanically damaged zone near the borehole than the compressional velocity. The Stoneley‐wave velocity was found to decrease with the increasing degree of RTI.

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