Calculation of phase and group angles, slowness surfaces and ray tracing in transversely isotropic media

  • Karen Pachano Peláez Technology Cooperation Agreement: Ecopetrol S.A. - Instituto Colombiano del Petróleo, A.A. 4185 Bucaramanga , Santander , Colombia
  • Miguel Duarte Ballesteros Technology Cooperation Agreement: Ecopetrol S.A. - Instituto Colombiano del Petróleo, A.A. 4185 Bucaramanga , Santander , Colombia
  • Hernando Altamar Mercado Technology Cooperation Agreement: Ecopetrol S.A. - Instituto Colombiano del Petróleo, A.A. 4185 Bucaramanga , Santander , Colombia
  • Carlos Piedrahita Escobar Geophysical Group, Research Unit, Ecopetrol S.A. – Instituto Colombiano del Petróleo.
  • Trino Salinas Garnica Geophysical Group, Research Unit, Ecopetrol S.A. – Instituto Colombiano del Petróleo.
  • Zuly Calderón Carrillo Universidad Industrial de Santander- Professor School of Petroleum Engineering
Keywords: anisotropy, phase angle, seismic wave, ray path, wave propagation, symmetry, isotropy, group velocity, elasticity, mathematical model

Abstract

This paper presents some fundamental concepts of seismic anisotropy specifically those which have hexagonal symmetry (ordinarily called transversely isotropic in geophysics jargon).  There were made calculations of phase and group angles at a planar interface separating an anisotropic media, using routines written in Matlab ® and Maple ® language. The slowness surfaces of the qP, qSV and SH wave, as well as the ray paths in these two media were also estimated.  Although only the simplest situations are discussed, this paper is useful as a first step in understanding the fractured media, because it contains examples, software routines, and a reviewing of the basic concepts and formulas of wave propagation.

References

Bakulin, A., Grechka, V., & Tsvankin, I. (2000). Estimation of fracture parameters from reflection seismic data - Part I: HTI model due to a single fracture set. Geophysics, 65 (6): 1788-1802. https://doi.org/10.1190/1.1444863

Cerveny, V. (2001). Seismic Ray Theory. Cambridge University Press. https://doi.org/10.1017/CBO9780511529399

Chen, W. (1995). AVO in Azimuthally anisotropic media fracture detection using P-Wave data and seismic study of naturally fractured tight gas reservoir. Ph. D. Thesis. Department of Geophysics, School of Earth Sciences, Stanford University, Stanford, California, 143 pp.

Crampin, S. (1980). A review of wave motion in anisotropic an cracked elastic media. Wave motion, 3: 343-391. https://doi.org/10.1016/0165-2125(81)90026-3

Duarte , M., Piedrahita, C., Salinas , T., Altamar, H., & Pachano, K. (2004). Slowness surface calculation for different media using the symbolic mathematics language Maple ®. Earth Sciences Research Journal, 8 (1), 63-67.

Evans, R., Gaucher E., & Randall, N. (2000). Borehole seismic supplying answers to fractured reservoir questions. SPE 58994. https://doi.org/10.2118/58994-MS

Garnica, M. (2003). AVOA analysis and fracture characterization: Clair Field, West of Shetlands. M. Sc. Thesis. School of Earth Sciences , The University of Leeds , Leeds , England , 90 pp.

Hudson, J.A. (1980). Overall properties of a cracked solid. Math. Proc. Camb. Phil. Soc., 88: 371-384. https://doi.org/10.1017/S0305004100057674

Mase, G.E. (1970). Theory and Problems of Continuum Mechanics. Schaum's Outline Series, McGraw-Hill.

Rüger, A. (2002). Reflection Coefficients and Azimuthal AVO Analysis in Anisotropic Media, Geophysical Monograph Series. SEG - Society of Exploration Geophysicists, 10: 189 Tulsa , OK . https://doi.org/10.1190/1.9781560801764

Rüger, A.,& Tsvankin I. (1997). Using AVO for fracture detection: analytic basis and practical solutions. The Leading Edge, 1429-1434. https://doi.org/10.1190/1.1437466

Schoenberg, M., & Douma, J. (1988). Elastic wave propagation in media with parallel fractures and aligned cracks. Geophysical Prospecting, 39: 571-590. https://doi.org/10.1111/j.1365-2478.1988.tb02181.x

Schoenberg, M., & Sayers C. (1995). Seismic anisotropy of fractured rock. Geophysics, 60 (1): 204-211. https://doi.org/10.1190/1.1443748

Slawinski, M.A. (1996). On elastic-wave propagation in anisotropic media: reflection/refraction laws, ray tracing, and traveltime inversion. Ph. D. Thesis. Department of Geology and Geophysics. The University of Calgary , Calgary , Alberta . 223 pp.

Thomsen, L. (1986). Weak elastic anisotropy. Geophysics, 51 (9): 1954-196. https://doi.org/10.1190/1.1442051

How to Cite
Pachano Peláez, K., Duarte Ballesteros, M. ., Altamar Mercado, H., Piedrahita Escobar, C. ., Salinas Garnica, T., & Calderón Carrillo, Z. . (2006). Calculation of phase and group angles, slowness surfaces and ray tracing in transversely isotropic media. CT&F - Ciencia, Tecnología Y Futuro, 3(2), 41–56. https://doi.org/10.29047/01225383.489

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Published
2006-12-31
Section
Scientific and Technological Research Articles

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