Estimation of vertical fracturing from measured elastic moduli

Hood, Julie A.; Schoenberg, Michael

doi:10.1029/jb094ib11p15611

Cited by 33 publications

(14 citation statements)

References 13 publications

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“…Hood and Schoenberg (1989) showed how, when certain constraints on the moduli of an orthorhombic medium were satisfied, it was possible to find the fracture parameters of a set of vertical fractures and the elastic moduli of a transversely isotropic background with a vertical axis of symmetry. This was done by subtracting an unknown fracture group element from the group element of the TI medium and insisting that the remaining group element transform back into the moduli of a transversely isotropic medium.…”

Section: Decomposition Of a Fractured Mediummentioning

confidence: 99%

“…Much analytical work on the anisotropic behavior of fractured or cracked heterogenous rock masses has been done, e.g., Hudson (1981), Nishizawa (1982), Crampin (1984), Schoenberg (1983), Schoenberg and Muir (1989), and Hood and Schoenberg (1989). The assumption of a linear model of fracture behavior proposed by Schoenberg (1980) renders the analysis straightforward.…”

Section: Introductionmentioning

confidence: 98%

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Elastic waves through a simulated fractured medium

1993

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Ultrasonic velocities were measured on a block composed of lucite plates with roughened surfaces pressed together with a static normal stress to simulate a fractured medium. The measurements, normal, parallel, and oblique to the fractures, show that for wavelengths much larger than the thickness of an individual plate, the block can be modeled as a particular type of transversely isotropic (TI) medium that depends on four parameters. This TI medium behavior is the same as that of an isotropic solid in which are embedded a set of parallel linear slip interfaces, specified by (1) the excess compliance tangential to the interfaces and (2) the excess compliance normal to the interfaces. At all static stress levels, we inverted the data for the background isotropic medium parameters and the excess compliances. The background parameters obtained were basically independent of stress level and agreed well with the bulk properties of the lucite. The excess compliances decreased with increasing static closing stress, implying that increasing static stress forces asperities on either side of a fracture into greater contact, gradually eliminating the excess compliance that gives rise to the anisotropy. A medium with such planes of excess compliance has been shown, theoretically, to describe the behavior of a medium with long parallel joints, as well as a medium with embedded parallel microcracks.

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Section: Decomposition Of a Fractured Mediummentioning

confidence: 99%

Section: Introductionmentioning

confidence: 98%

Elastic waves through a simulated fractured medium

1993

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“…Then, one could, using the group formulation , "subtract" the fractures (with three unknown compliances). Specifically, the condition that the remaining background must be TI, with the symmetry axis parallel to the fractures (in the 3-direction), could be used to solve for the three unknown fracture compliances and hence the five background TI stiffnesses (Hood and Schoenberg, 1989). It stands to reason that the axes of the permeability tensor have the same orientation as the eigenvalues of the fracture compliance matrix, equation (6), and that the magnitude of the permeability anisotropy depends on the degree of fracturing.…”

Section: Vertically Fractured Medium: the Orthorhombic Modelmentioning

confidence: 99%

“…If they do, the stiffness matrix can be decomposed into the stiffnesses of the unfractured background rock and the fracture compliances (Hood and Schoenberg, 1989). From the fracture compliances, some information can be deduced on the degree of fracturing and on the texture and fluid content of the fractures (see, e.g., Schoenberg and Sayers, 1995;Hudson, 1981;Schoenberg and Douma, 1988).…”

Section: Introductionmentioning

confidence: 99%

Orthorhombic media: Modeling elastic wave behavior in a vertically fractured earth

Schoenberg

Helbig²

1997

GEOPHYSICS

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Vertical fractures and horizontal fine layering combine to form a long, wavelength equivalent orthorhombic medium. Such media constitute a subset of the set of all orthorhombic media. Orthorhombic elastic symmetry is the lowest symmetry for which the slowness surface (the solution of the Christoffel equation) is bicubic rather sextic. Various properties of orthorhombic media, such as the number and location of conical points and longitudinal directions, may be derived from the slowness surface or, because of its bicubic character, the squared slowness surface, which is a cubic surface. From the occurrence and angular orientation of some of these distinctive features, conclusions can be drawn with respect to the properties of the medium and to the parameters of the assumed underlying causes of the anisotropy. The estimation of these more subtle properties gains greater importance with the proliferation of multiazimuthal seismic surveys and the ability to drill along ever more complicated 3‐D well trajectories.

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“…Displacements across such interfaces are not continuous ͑i.e., the contacts between thin layers are not welded͒, whereas the stress ͑traction across the interface͒ should be continuous. Models with similar interface conditions have been used since the 1970s in geophysics and in other areas, including nondestructive testing ͑Tattersal, 1973; Angel and Achenbach, 1985;Drinkwater et al, 1996;Quinn et al, 2002;Brotherhood et al, 2003͒. The LS theory, proposed by Schoenberg for a single interface in 1980 and for a periodically stratified elastic medium in the longwavelength limit in 1983, is further developed by Schoenberg and his co-workers in a series of publications ͑Schoenberg and Douma, 1988;Hood and Schoenberg, 1989;Hsu and Schoenberg, 1993;Schoenberg and Sayers, 1995;Schoenberg and Nakagawa, 2006͒. The validity of the LS theory was proven experimentally by measuring compressional ͑P͒ and shear ͑S͒-wave velocities in a block composed of Lucite™ plates pressed together to simulate a fractured medium ͑Hsu and Schoenberg, 1993͒. The possibility of extending LS theory to viscoelastic media was first mentioned by Schoenberg ͑1980͒.…”

Section: Introductionmentioning

confidence: 97%

Attenuation anisotropy in the linear-slip model: Interpretation of physical modeling data

et al. 2009

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This study attempts to validate a mathematical formalism of introducing attenuation into Schoenberg's linear slip model. This formalism is based on replacing the real-valued weaknesses by complex-valued ones. During an ultrasonic experiment, performed at a central frequency of 100 kHz on a plate-stack model with 1-mm-thick Plexiglas™ plates, the velocity and attenuation ͑inverse of the quality factor Q͒ of P-, SH-, and SV-waves are measured in directions from 25°to 90°with the symmetry axis for dry and oil-saturated models and loading uniaxial pressures of 2 and 4 MPa. The velocity and attenuation data are fitted by the derived theoretical functions. The values of the real and imaginary parts of the complex-valued weaknesses are estimated. The real parts of the weaknesses, which have a clear physical meaning ͑they affect the weakening of the material͒, are three times larger for the dry model than for the oil-saturated one. The imaginary parts of the weaknesses are responsible for attenuation; their values are an order of magnitude smaller than the real parts. The derived expressions for angle-dependent velocities and attenuations can be used to distinguish between dry and oil-saturated fractures. In particular, the P-wave attenuation function in the symmetry-axis direction ͑normal to fracture planes͒ is different in dry and saturated media. The experiment shows that the platestack model is inhomogeneous because of the nonuniform pressure distribution, which degrades the experimental results and creates difficulties in the inversion for the complex-valued weaknesses -particularly in joint inversion of P-and S-wave data.

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Estimation of vertical fracturing from measured elastic moduli

Cited by 33 publications

References 13 publications

Elastic waves through a simulated fractured medium

Elastic waves through a simulated fractured medium

Orthorhombic media: Modeling elastic wave behavior in a vertically fractured earth

Attenuation anisotropy in the linear-slip model: Interpretation of physical modeling data

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