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Unformatted text preview: Aligned vertical fractures, HTI reservoir symmetry, and Thomsen seismic anisotropy parameters James G. Berryman E-mail: [email protected] University of California, Lawrence Berkeley National Laboratory, 1 Cyclotron Road, MS 90R1116, Berkeley, CA 94720, USA Abstract : The Sayers and Kachanov (1991) crack-influence parameters are shown to be directly related to Thomsen (1986) weak-anisotropy seismic parameters for fractured reservoirs when the crack density is small enough. These results are then applied to seismic wave propagation in reservoirs having HTI symmetry due to aligned vertical fractures. The approach suggests a method of inverting for fracture density from wave speed data. INTRODUCTION Aligned vertical fractures provide a commonly recognized source of azimuthal (surface angle dependent) seismic anisotropy in oil and gas reservoirs (Lynn et al. , 1995). For analysis, VTI earth media are much easier to understand and analyze than HTI media. Nevertheless, when the source of the anisotropy is aligned vertical fractures, we can make very good use of the simpler case of horizontal fracture analysis by making a rather minor change of our point of view that easily gives all the needed results. We can also understand very directly the sources of the anisotropy due to fractures by considering a method introduced by Sayers and Kachanov (1991). Elastic constants, and therefore the Thomsen (1986) parameters, can be conveniently expressed in terms of the Sayers and Kachanov (1991) formalism. Furthermore, in the low crack density limit [which is also consistent with the weak anisotropy approach of Thomsen (1986)], we obtain direct links between the Thomsen parameters and the fracture properties. These links suggest a method of inverting for fracture density from wave speed data. THOMSEN'S SEISMIC WEAK ANISOTROPY METHOD Thomsen's weak anisotropy method (Thomsen, 1986), being an approximation designed specifically for use in velocity analysis for exploration geophysics, is clearly not exact. Approximations incorporated into the formulas become most apparent for greater angles g from the vertical, especially for compressional and vertically polarized shear velocities G ¡ ¢g£ and G ¤¥ ¢g£ , respectively. Angle g is measured from the ¦-vector pointing into the earth. Exact velocity formulas for P , SV , and SH seismic waves at all angles in a VTI elastic medium are known and available in many places (Ruger, 2002; Musgrave, 2003), so will not be listed here. Expressions for phase velocities in Thomsen's weak anisotropy limit can also be found in many places, including Thomsen (1986) and Ruger (2002). The pertinent expressions for phase velocities in VTI media as a function of angle g are: G ¡ ¢g£ § G ¡ ¢u£¢U ¨ © ª«¬ g ®¯ª g ¨ ° ª«¬ ± g£² ¢U£ G ¤¥ ¢g£ § G ¤ ¢u£³U ¨ ´ G ¡ ¢u£ G ¤ ¢u£ µ¢° ¶ ©£ ª«¬ g ®¯ª g·² ¢¸£ and G ¤¹ ¢g£ § G ¤ ¢u£¢U ¨ ºª«¬ g£» ¢¼£ In our present context,...
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- Spring '11
- Seismic wave, Thomsen, crack density, crack densities