Determining shear‐wave transverse isotropy from borehole stoneley waves

2001 ◽  
Author(s):  
X. M. Tang
Keyword(s):  
Shear Wave ◽  
Transverse Isotropy ◽  
Stoneley Waves

Determining formation shear‐wave transverse isotropy from borehole Stoneley‐wave measurements

Geophysics ◽  
2003 ◽  
Vol 68 (1) ◽  
pp. 118-126 ◽  
Author(s):  
Xiaoming Tang
Keyword(s):  
Shear Wave ◽  
Transverse Isotropy ◽  
Wave Spectrum ◽  
Weighted Average ◽  
Stoneley Wave ◽  
Fast Method ◽  
Actual Structure ◽  
Stoneley Waves ◽  
Wave Data ◽  
Shale Formation

Many rocks exhibit transversely isotropic (TI) characteristics. For determining the TI property using acoustic logging, Stoneley waves are the only borehole wave mode that has a significant sensitivity to TI effects, especially when the formation is acoustically slow compared to the borehole fluid. This study describes a method for deriving the formation shear‐wave TI parameter from the Stoneley wave data acquired by a logging tool. It is shown that the presence of the tool in the borehole can substantially affect the Stoneley wave propagation. Fortunately, for low‐frequency Stoneley waves, the tool effect can be satisfactorily modeled using an effective modulus, regardless of the actual structure of the tool. The modulus can be determined from a calibration procedure. In the inversion processing of the Stoneley wave data, the Stoneley wave slowness is related to the weighted average of the wave's dispersion curve over the frequency range occupied by the wave spectrum. This provides a fast method for the inversion. As a processing example, this method has been applied to estimate the shear‐wave TI parameter profile for the Lewis shale formation in Braggs, Wyoming. The resulting profile delineates the shear‐wave anisotropy magnitude and variation for this shale formation.

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.

Synthesis of multicomponent quasi-P and converted quasi-P-S seismograms for intersecting fracture systems

Geophysics ◽  
2000 ◽  
Vol 65 (4) ◽  
pp. 1261-1271 ◽  
Author(s):  
Andrey A. Ortega ◽  
George A. McMechan
Keyword(s):  
Shear Wave ◽  
Transverse Isotropy ◽  
Normal Incidence ◽  
Shear Wave Splitting ◽  
P Wave ◽  
Orthorhombic Symmetry ◽  
S Wave ◽  
Stiffness Constant ◽  
Wave Splitting ◽  
Vertical Fractures

Dynamic ray shooting with interpolation is an economical way of computing approximate Green’s functions in 3-D heterogeneous anisotropic media. The amplitudes, traveltimes, and polarizations of the reflected rays arriving at the surface are interpolated to synthesize three‐component seismograms at the desired recording points. The algorithm is applied to investigate kinematic quasi-P-wave propagation and converted quasi-P-S-wave splitting variations produced in reflections from the bottom of a layer containing two sets of intersecting dry vertical fractures as a function of the angle between the fracture sets and of the intensity of fracturing. An analytical expression is derived for the stiffness constant C16 that extends Hudson’s second‐order scattering theory to include tetragonal-2 symmetry systems. At any offset, the amount of splitting in nonorthogonal (orthorhombic symmetry) intersecting fracture sets is larger than in orthogonal (tetragonal-1 symmetry) systems, and it increases nonlinearly as a function of the intensity of fracturing as offset increases. Such effects should be visible in field data, provided that the dominant frequency is sufficiently high and the offset is sufficiently large. The amount of shear‐wave splitting at vertical incidence increases nonlinearly as a function of the intensity of fracturing and increases nonlinearly from zero in the transition from tetragonal-1 anisotropy through orthorhombic to horizontal transverse isotropy; the latter corresponds to the two crack systems degenerating to one. The zero shear‐wave splitting corresponds to a singularity, at which the vertical velocities of the two quasi‐shear waves converge to a single value that is both predicted theoretically and illustrated numerically. For the particular case of vertical fractures, there is no P-to-S conversion of vertically propagating (zero‐offset) waves. If the fractures are not vertical, the normal incidence P-to-S reflection coefficient is not zero and thus is a potential diagnostic of fracture orientation.

scholarly journals Seismic Short-Refraction Studies on the Ross Ice Shelf, Antarctica

1979 ◽  
Vol 24 (90) ◽  
pp. 313-319
Author(s):  
Joseph F. Kirchner ◽  
Charles R. Bentley
Keyword(s):  
Shear Wave ◽  
Transverse Isotropy ◽  
Compressional Wave ◽  
Least Squares Regression ◽  
Horizontal Shear ◽  
Ice Shelf ◽  
Compressional Waves ◽  
Ross Ice Shelf ◽  
Wave Velocities ◽  
Shear Wave Velocities

AbstractSeismic short-refraction studies were carried out at five stations on the Ross Ice Shelf during the 1976–77 summer season as part of the comprehensive Ross Ice Shelf Geophysical and Glaciological Survey. Measurements of the velocities of compressional waves were made at each location. Compressional wave velocities were measured along more than one azimuth at three sites, and shear wave velocities (both components) at two. Travel-time curves were fitted to an exponential expression by means of a non-linear least-squares regression technique. The errors in the apparent velocities are estimated to be about ±50 m s–1 at short distances, diminishing to about ±10 m s–1 near the ends of the profiles. Compressional-wave velocities show only slight variations with azimuth and only over certain depth intervals, showing that constant-velocity surfaces are essentially horizontal. Shear-wave velocities, however, exhibit large variations according to azimuth and polarization, indicating that transverse isotropy is violated at least in the upper 30–40 m of the ice shelf. It is believed that the anisotropy is caused by structural details in the firn perhaps modified by preferred crystal orientation and that it may arise at least partly from anisotropic stresses in the ice shelf.

3-D seismic modeling for cracked media: Shear‐wave splitting at zero‐offset

Geophysics ◽  
2000 ◽  
Vol 65 (1) ◽  
pp. 211-221 ◽  
Author(s):  
Jaime Ramos‐Martínez ◽  
Andrey A. Ortega ◽  
George A. McMechan
Keyword(s):  
Shear Wave ◽  
Effective Properties ◽  
Transverse Isotropy ◽  
Shear Waves ◽  
Crack Density ◽  
Shear Wave Splitting ◽  
Carbonate Reservoir ◽  
Vertical Crack ◽  
Wave Splitting ◽  
Zero Offset

Splitting of zero‐offset reflected shear‐waves is measured directly from three‐component finite‐difference synthetic seismograms for media with intersecting vertical crack systems. Splitting is simulated numerically (by finite differencing) as a function of crack density, aspect ratio, fluid content, bulk density, and the angle between the crack systems. The type of anisotropy symmetry in media containing two intersecting vertical crack systems depends on the angular relation between the cracks and their relative crack densities, and it may be horizontal transverse isotropy (HTI), tetragonal, orthorhombic, or monoclinic. The transition from one symmetry to another is visible in the splitting behavior. The polarities of the reflected quasi‐shear waves polarized perpendicular and parallel to the source particle motion distinguish between HTI and orthorhombic media. The dependence of the measured amount of splitting on crack density for HTI symmetry is consistent with that predicted theoretically by the shear‐wave splitting factor. In orthorhombic media (with two orthogonal crack systems), a linear increase is observed in splitting when the difference between crack densities of the two orthogonal crack systems increases. Splitting decreases nonlinearly with the intersection angle between the two crack systems from 0° to 90°. Surface and VSP seismograms are simulated for a model with several flat homogeneous layers, each containing vertical cracks with the same and with different orientations. When the crack orientation varies with depth, previously split shear waves are split again at each interface, leading to complicated records, even for simple models. Isotropic and anisotropic three‐component S-wave zero‐offset sections are synthesized for a zero‐offset survey line over a 2.5-D model of a carbonate reservoir with a complicated geometry and two intersecting, dipping crack sets. The polarization direction of the fast shear wave, propagating obliquely through the cracked reservoir, is predicted by theoretical approximations for effective properties of anisotropic media with two nonorthogonal intersecting crack sets.

Joint inversion of logging-while-drilling multipole acoustic data to determine formation shear-wave transverse isotropy

Geophysics ◽  
2020 ◽  
Vol 85 (4) ◽  
pp. D121-D132
Author(s):  
Yang-Hu Li ◽  
Song Xu ◽  
Can Jiang ◽  
Yuan-Da Su ◽  
Xiao-Ming Tang
Keyword(s):  
Shear Wave ◽  
Joint Inversion ◽  
Transverse Isotropy ◽  
Synthetic Data ◽  
Flexural Wave ◽  
Inversion Method ◽  
S Wave ◽  
Acoustic Data ◽  
Wave Data ◽  
Logging While Drilling

Seismic-wave anisotropy has long been an important topic in the exploration and development of unconventional reservoirs, especially in shales, which are commonly characterized as transversely isotropic ([TI] or vertical TI [VTI]) media. At present, the shear-wave (S-wave) TI properties have mainly been determined from monopole Stoneley- or dipole flexural-wave measurements in wireline acoustic logging, but the feasibility of those obtained from logging-while-drilling (LWD) acoustic data needs to be established. We have developed a joint inversion method for simultaneously determining formation S-wave transverse isotropy and vertical velocity from LWD multipole acoustic data. Our theoretical analysis shows that the presence of anisotropy strongly influences LWD Stoneley- and quadrupole-wave dispersion characteristics. Although the monopole Stoneley and quadrupole waves are sensitive to the formation S-wave TI parameters, they suffer from the typical nonuniqueness problem when using the individual-wave data to invert parameters alone. Thus, the respective dispersion data can be jointly used to estimate the formation S-wave TI properties. By the joint inversion, the nonuniqueness problem in the parameter inversion can also be effectively alleviated. The feasibility of the method has been verified by the processing results of theoretical synthetic data and field LWD acoustic-wave data. Therefore, the result offers an effective method for evaluating VTI formation anisotropy from acoustic LWD data.

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