{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

LBNL-63016 - Aligned vertical fractures HTI reservoir...

Info icon This preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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,...
View Full Document

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern