3D velocity reconstruction in shale derived from limited number of measurements

Bayuk, I.; Dyaur, Nikolay; Mohamed, Y.; Ammerman, Mike; Chesnokov, Evgeni M.

doi:10.1190/1.2792788

Cited by 2 publications

(4 citation statements)

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“…The stiffness tensor of shale was reconstructed from a limited number of measurements insufficient for the standard determination of the shale's stiffness tensor from the Green‐Christoffel equation. Thus, Bayuk et al . (2007) demonstrated a reconstruction of the stiffness tensor of shale for cases when only the compressional wave velocities are measured at a different direction in the normal‐to‐bedding plane.…”

Section: Theoretical Backgroundmentioning

confidence: 98%

“…The effective medium theory is widely applied to calculate the effective physical properties of shales (Rundle and Schuler 1981; Hornby, Schwartz and Hudson 1994; Sayers 1994, 1998; Jakobsen, Hudson and Johansen 2003; Bayuk et al . 2007, 2008; Sarout and Guéguen 2008b).…”

Section: Theoretical Backgroundmentioning

confidence: 99%

“…At each stage of the model construction, the effective stiffness tensor is calculated with the help of methods of effective medium theory. In this study we apply the generalized singular approximation method whose theoretical background was described in detail by Shermergor (1977), Bayuk and Chesnokov (1998) and Bayuk et al . (2007, 2008).…”

Section: Theoretical Backgroundmentioning

confidence: 99%

“…We apply the inversion technique described above for both cases: a) the mineral composition is known and used for the inversion and b) the composition of silt minerals is unknown and only clay content is available. Since the measurements were performed under unloaded conditions, the values of the Thomsen parameters ɛ and γ can be greater than 0.7 (Bayuk et al . 2007).…”

Section: Theoretical Backgroundmentioning

confidence: 99%

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Determination of shale stiffness tensor from standard logs

Chesnokov

Bayuk

Ammerman

2010

Geophysical Prospecting

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A B S T R A C TA technique allowing inversion of the shale stiffness tensor from standard logging data: sonic velocities, density, porosity and clay content is developed. The inversion is based on the effective medium theory. The testing of the technique on laboratory measurements of the elastic wave velocities in shale samples shows that the inversion makes it possible to predict the elastic wave velocities V P , V S1 and V S2 in any direction within an error of a few per cent.The technique has been applied for the stiffness tensor inversion along a well penetrating a shale formation of the Mississippian age altered by thin layers of limestone. It is demonstrated that the symmetry of a stiffness tensor inverted at the sonic frequency (2 kHz) is slightly orthorhombic and taking into account the experimental errors, can be related to the vertical transverse isotropy symmetry. For the productive interval of the shale formation, the Thomsen parameters ε, γ , and δ average, respectively, 0.32, 0.25 and 0.21, which indicate anelliptic behaviour of the velocities in this shale. The coefficients of anisotropy of this shale interval are around 24% and 20% for the compressional and shear waves, respectively. The values of the inverted velocities in the bedding plane for this interval are in good agreement with the laboratory measurements. The technique also allows inversion of the water saturation of the formation (Sw) and the inverted values are in agreement with the Sw values available for this formation.A Backus-like upscaling of the inverted stiffness tensors is carried out for the lower and upper bounds of the frequency band used in the crosswell tomography (100 Hz and 500 Hz). These results can serve as an initial velocity model for the microearthquake location during hydrofracking of the shale formation.

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Section: Theoretical Backgroundmentioning

confidence: 98%