Table of Contents
ISRN Geophysics
Volume 2013, Article ID 258492, 10 pages
http://dx.doi.org/10.1155/2013/258492
Research Article

Propagation and Attenuation of Elastic Waves in a Double Porosity Medium

1Department of Mathematics, M.D. University, Rohtak 124001, India
2Department of Mathematics, Government College Kalka, Kalka 133302, India

Received 5 December 2012; Accepted 26 December 2012

Academic Editors: G. Casula, H. Perroud, and A. Streltsov

Copyright © 2013 J. S. Nandal and T. N. Saini. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. G. I. Barenblatt, I. P. Zheltov, and I. N. Kochina, “Basic concepts in the theory of seepage of homogeneous liquids in fissured rocks,” Journal of Applied Mathematics and Mechanics, vol. 24, no. 5, pp. 1286–1303, 1960. View at Google Scholar · View at Scopus
  2. J. E. Warren and P. J. Root, “The behavior of naturally fractured reservoirs,” Society of Petroleum Engineers Journal, vol. 3, pp. 245–255, 1963. View at Google Scholar
  3. M. A. Biot, “Theory of propagation of elastic waves in a fluid-saturated porous solid. I. Low frequency range. II. Higher frequency range,” Journal of the Acoustical Society of America, vol. 28, pp. 168–191, 1956. View at Google Scholar
  4. M. A. Biot, “Mechanics of deformation and acoustic propagation in porous media,” Journal of Applied Physics, vol. 33, no. 4, pp. 1482–1498, 1962. View at Publisher · View at Google Scholar · View at Scopus
  5. M. A. Biot, “Generalized theory of acoustic propagation in porous dissipative media,” Journal of the Acoustical Society of America, vol. 34, pp. 1254–1264, 1962. View at Google Scholar
  6. R. I. O'Connell and B. Budiansky, “Viscoelastic properties of fluid saturated cracked solids,” Journal of Geophysical Research, vol. 82, pp. 5719–5735, 1977. View at Google Scholar
  7. G. M. Mavko and A. Nur, “Wave attenuation in partially saturated rocks,” Geophysics, vol. 44, no. 2, pp. 161–178, 1979. View at Google Scholar · View at Scopus
  8. G. Mavko and D. Jizba, “Estimating grain-scale fluid effects on velocity dispersion in rocks,” Geophysics, vol. 56, no. 12, pp. 1940–1949, 1991. View at Google Scholar · View at Scopus
  9. J. Dvorkin and A. Nur, “Dynamic poroelasticity: a unified model with the squirt and the Biot mechanisms,” Geophysics, vol. 58, no. 4, pp. 524–533, 1993. View at Google Scholar · View at Scopus
  10. L. Thomsen, “Elastic anisotropy due to aligned cracks in porous rock,” Geophysical Prospecting, vol. 43, no. 6, pp. 805–829, 1995. View at Google Scholar · View at Scopus
  11. M. D. Sharma, “Surface-wave propagation in a cracked poroelastic half-space lying under a uniform layer of fluid,” Geophysical Journal International, vol. 127, no. 1, pp. 31–39, 1996. View at Google Scholar · View at Scopus
  12. R. K. Wilson and E. C. Aifantis, “On the theory of consolidation with double porosity,” International Journal of Engineering Science, vol. 20, pp. 1009–1035, 1982. View at Google Scholar
  13. R. K. Wilson and E. C. Aifantis, “A double porosity model for acoustic wave propagation in fractured-porous rock,” International Journal of Engineering Science, vol. 22, no. 8–10, pp. 1209–1217, 1984. View at Google Scholar · View at Scopus
  14. T. F. Cho, M. E. Plesha, and B. C. Haimson, “Continuum modelling of jointed porous rock,” International Journal for Numerical & Analytical Methods in Geomechanics, vol. 15, no. 5, pp. 333–353, 1991. View at Google Scholar · View at Scopus
  15. M. Bai, D. Elsworth, and J. C. Roegiers, “Modeling of naturally fractured reservoirs using deformation dependent flow mechanism,” International Journal of Rock Mechanics and Mining Sciences and, vol. 30, no. 7, pp. 1185–1191, 1993. View at Google Scholar · View at Scopus
  16. J. G. Berryman and H. F. Wang, “The elastic coefficients of double-porosity models for fluid transport in jointed rock,” Journal of Geophysical Research, vol. 100, no. 12, pp. 611–627, 1995. View at Google Scholar · View at Scopus
  17. J. G. Berryman and H. F. Wang, “Elastic wave propagation and attenuation in a double-porosity dual-permeability medium,” International Journal of Rock Mechanics and Mining Sciences, vol. 37, no. 1-2, pp. 63–78, 2000. View at Google Scholar · View at Scopus
  18. S. R. Pride and J. G. Berryman, “Linear dynamics of double-porosity dual-permeability materials. I. Governing equations and acoustic attenuation,” Physical Review E, vol. 68, no. 3, Article ID 036603, 10 pages, 2003. View at Google Scholar · View at Scopus
  19. S. R. Pride and J. G. Berryman, “Linear dynamics of double-porosity dual-permeability materials. II. Fluid transport equations,” Physical Review E, vol. 68, no. 3, Article ID 036604, 10 pages, 2003. View at Google Scholar · View at Scopus
  20. A. W. Skempton, “The pore-pressure coefficients A and B,” Geotechnique, vol. 4, pp. 143–147, 1954. View at Google Scholar
  21. R. D. Stoll and G. M. Bryan, “Wave attenuation in saturated sediments,” Journal of the Acoustical Society of America, vol. 47, pp. 1440–1147, 1970. View at Google Scholar
  22. R. D. Stoll, “Marine sediment acoustics,” Journal of the Acoustical Society of America, vol. 77, no. 5, pp. 1789–1799, 1985. View at Google Scholar · View at Scopus
  23. M. D. Sharma and M. L. Gogna, “Seismic wave propagation in a viscoelastic porous solid saturated by viscous liquid,” Pure and Applied Geophysics, vol. 135, no. 3, pp. 383–400, 1991. View at Publisher · View at Google Scholar · View at Scopus
  24. P. M. Morse and H. Feshback, Methods of Theoretical Physics, McGraw-Hill, New York, NY, USA, 1953.