Aligned vertical fractures, HTI reservoir symmetry, and Thomsenseismic anisotropy parameters for polar media

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Sayers and Kachanov (1991) defined crack-influence parameters that are shown to be directly related to Thomsen (1986) weak-anisotropy seismic parameters for fractured reservoirs when the crack/fracture density is small enough. These results are then applied to the problem of seismic wave propagation in polar (i.e., non-isotropic) reservoirs having HTI seismic wave symmetry due to the presence of aligned vertical fractures and resulting in azimuthal seismic wave symmetry at the earth's surface. The approach presented suggests one method of inverting for fracture density from wave-speed data. It is also observed that the angular location {theta}{sub ex} of the extreme value (peak ... continued below

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Berryman, James G. December 12, 2007.

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Sayers and Kachanov (1991) defined crack-influence parameters that are shown to be directly related to Thomsen (1986) weak-anisotropy seismic parameters for fractured reservoirs when the crack/fracture density is small enough. These results are then applied to the problem of seismic wave propagation in polar (i.e., non-isotropic) reservoirs having HTI seismic wave symmetry due to the presence of aligned vertical fractures and resulting in azimuthal seismic wave symmetry at the earth's surface. The approach presented suggests one method of inverting for fracture density from wave-speed data. It is also observed that the angular location {theta}{sub ex} of the extreme value (peak or trough) of the quasi-SV-wave speed for VTI occurs at an angle determined approximately by the formula tan{sup 2} {theta}{sub ex} {approx_equal} tan {theta}{sub m} = [(c{sub 33} - c{sub 44})/(c{sub 11}-c{sub 44})]{sup 1/2}, where {theta}{sub m} is an angle determined directly (as shown) from the c{sub ij} elastic stiffnesses, whenever these are known from either quasi-static or seismic wave measurements. Alternatively, {theta}{sub ex} is given in terms of the Thomsen seismic anisotropy parameters by tan {theta}{sub ex} {approx_equal} ([v{sub p}{sup 2}(0)-v{sub s}{sup 2}(0)]/[(1 + 2{epsilon})v{sub p}{sup 2}(0)-v{sub s}{sup 2}(0)]){sup 1/4}, where {epsilon} = (c{sub 11}-c{sub 33})/2c{sub 33}, v{sub p}{sup 2}(0) = c{sub 33}/{rho}, and v{sub s}{sup 2}(0) = c{sub 44}/{rho}, with {rho} being the background inertial mass density. The axis of symmetry is always treated here as the x{sub 3}-axis for either VTI symmetry (due, for example, to horizontal cracks), or HTI symmetry (due to aligned vertical cracks). Then the meaning of the stiffnesses is derived from the fracture analysis in the same way for VTI and HTI media, but for HTI the wave speeds relative to the earth's surface are shifted by 90{sup o} in the plane perpendicular to the aligned vertical fractures. Skempton's (1954) coefficient is used as a general means of quantifying the effects of fluids inside the fractures. Explicit formulas for Thomsen's parameters are also obtained for either drained or undrained fractures resulting in either VTI or HTI symmetry of the reservoir.

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  • Journal Name: Geophysical Prospecting; Journal Volume: 0; Journal Issue: 0; Related Information: Journal Publication Date: 0

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  • Report No.: LBNL--63659
  • Grant Number: DE-AC02-05CH11231
  • Office of Scientific & Technical Information Report Number: 929768
  • Archival Resource Key: ark:/67531/metadc897600

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  • December 12, 2007

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  • Sept. 27, 2016, 1:39 a.m.

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  • Oct. 31, 2016, 3:48 p.m.

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Berryman, James G. Aligned vertical fractures, HTI reservoir symmetry, and Thomsenseismic anisotropy parameters for polar media, article, December 12, 2007; Berkeley, California. (digital.library.unt.edu/ark:/67531/metadc897600/: accessed July 16, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.