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

Journal Article · Wed Dec 12 04:00:00 EST 2007 · Geophysical Prospecting

OSTI ID:929768

Berryman, James G

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.

• Research Organization: Ernest Orlando Lawrence Berkeley NationalLaboratory, Berkeley, CA (US)
• Sponsoring Organization: USDOE Director. Office of Science. Basic EnergySciences
• DOE Contract Number: AC02-05CH11231
• OSTI ID: 929768
• Report Number(s): LBNL--63659; BnR: KC0303010
• Journal Information: Geophysical Prospecting, Journal Name: Geophysical Prospecting Journal Issue: 0 Vol. 0; ISSN GPPRAR; ISSN 0016-8025
• Country of Publication: United States
• Language: English

Related Subjects

54 ENVIRONMENTAL SCIENCES
ANISOTROPY
FRACTURED RESERVOIRS
FRACTURES
SEISMIC WAVES
SYMMETRY
VELOCITY
fractures reservoirs HTI Thomsen seismic anisotropy polarmedia