Characterizing the effect of elastic interactions on the effective elastic properties of porous, cracked rocks

References

1. BakulinA., GrechkaV. and TsvankinI.2000. Estimation of fracture parameters from reflection seismic data – Part I: HTI model due to a single fracture set. Geophysics65, 1788–1802.
   [Google Scholar]
2. BerrymanJ.G.1980a. Long‐wavelength propagation in composite elastic media. I Spherical inclusions. Journal of the Acoustical Society of America68, 1809–1819.
   [Google Scholar]
3. BerrymanJ.G.1980b. Long‐wavelength propagation in composite elastic media. II Ellispoidal inclusions. Journal of the Acoustical Society of America68, 1820–1831.
   [Google Scholar]
4. BerrymanJ.G.1992. Single‐scattering approximations for coefficients in Biot's equations of poroelasticity. Journal of the Acoustical Society of America91, 551–571.
   [Google Scholar]
5. BerrymanJ.G.1995. Mixture theories for rock properties. In: Rock Physics and Phase Relations: A Handbook of Physical Constants, (ed. T.J.Ahrens), pp. 205–228. American Geophysical Union, Washington, D.C.
   [Google Scholar]
6. BudianskyB.1965. On the elastic moduli of some heterogeneous materials. Journal of the Mechanics and Physics of Solids13, 223–227.
   [Google Scholar]
7. EshelbyJ.D.1957. The determination of the elastic field of an ellipsoidal inclusion and related problems. Proceedings of the Royal Society of London, Series, A, Mathematical and Physical Sciences241, 376–396.
   [Google Scholar]
8. GrechkaV. and KachanovM.2006. Effective elasticity of cracked rocks: A snapshot of the work in progress. Geophysics71(6), W45–W58.
   [Google Scholar]
9. GuéguenY. and KachanovM.2011. Effective elastic properties of cracked and porous rocks – An overview. Mechanics of Crustal Rocks, CISM Courses and Lectures533, 73–125.
   [Google Scholar]
10. HillL.R.1965. A self‐consistent mechanics of composite materials. Journal of the Mechanics and Physics of Solids13, 213–222.
    [Google Scholar]
11. HornbyB.E., SchwartzL.M. and HudsonJ.A.1994. Anisotropic effective‐medium modeling of the elastic properties of shales. Geophysics59, 1570–1583.
    [Google Scholar]
12. HuY. and McMechanG.A.2009. Comparison of effective stiffness and compliance for characterizing cracked rocks. Geophysics74(2), D49–D55.
    [Google Scholar]
13. HudsonJ.A.1980. Overall properties of a cracked solid. Mathematical Proceedings of the Cambridge Philosophical Society88, 371–384.
    [Google Scholar]
14. HudsonJ.A.1981. Wave speeds and attenuation of elastic waves in material containing cracks. Geophysical Journal of the Royal Astronomical Society64, 133–150.
    [Google Scholar]
15. HudsonJ.A.1994. Overall properties of a material with inclusions or cavities. Geophysical Journal International117, 555–561.
    [Google Scholar]
16. HudsonJ.A. and LiuE.1999. Effective elastic properties of heavily faulted structures. Geophysics64, 479–485.
    [Google Scholar]
17. JaegerJ., CookN.G. and ZimmermanR.2007. Fundamentals of Rock Mechanics, 4th edn. Malden, MA, Blackwell Ltd.
    [Google Scholar]
18. JakobsenM.2004. The interacting inclusion model of wave‐induced fluid flow. Geophysical Journal International158, 1168–1176.
    [Google Scholar]
19. JakobsenM. and ChapmanM.2009. Unified theory of global flow and squirt flow in cracked porous media. Geophysics74(2), WA65–WA76.
    [Google Scholar]
20. JakobsenM., HudsonJ.A. and JohansenT.A.2003. T‐Matrix approach to shale acoustics. Geophysical Journal International154, 533–558.
    [Google Scholar]
21. KachanovM.1992. Effective elastic properties of cracked solids: Critical review of some basic concepts. Applied Mechanics Reviews45, 304–335.
    [Google Scholar]
22. KachanovM., ShafiroB. and TsukrovI.2003. Handbook of Elasticity Solutions. Kluwer Academic Publishers.
    [Google Scholar]
23. KachanovM., TsukrovI. and ShafiroB.1994. Effective moduli of solids with cavities of various shapes. Applied Mechanics Reviews47(1), S151–S174.
    [Google Scholar]
24. KusterG.T. and ToksözM.N.1974. Velocity and attenuation of seismic waves in two‐phase media: Part I. Theoretical formulations. Geophysics39, 587–606.
    [Google Scholar]
25. LiuE., HudsonJ.A. and PointerT.2000. Equivalent medium representation of fractured rock. Journal of Geophysical Research105, 2981–3000.
    [Google Scholar]
26. MavkoG. and NurA.1978. The effect of nonelliptical cracks on the compressibility of rocks. Journal of Geophysical Research83, 4459–4468.
    [Google Scholar]
27. MavkoG., MukerjiT. and DvorkinJ.2009. The Rock Physics Handbook, Tools for Seismic Analysis in Porous Media. Cambridge University Press
    [Google Scholar]
28. MavkoG. and VanorioT.2008. Observation and limitations of effective medium models for pore shape. Stanford Rock Physics & Borehole Geophysics Project Annual report114(B9), 1–14
    [Google Scholar]
29. MuraT.1987. Micromechanics of Defects in Solid. Martinus Nijhoff Publishers.
    [Google Scholar]
30. NishizawaO.1982. Seismic velocity anisotropy in a medium containing oriented cracks –Transversely isotropic case. Journal of Physics of the Earth30, 331–347.
    [Google Scholar]
31. NorrisA.N.1985. A differential scheme for the effective moduli of composites. Mechanics of Materials4, 1–16.
    [Google Scholar]
32. O'ConnellR.J. and BudianskyB.1974. Seismic velocities in dry and saturated cracked solids. Journal of Geophysical Research79, 5412–5426.
    [Google Scholar]
33. Ponte CastañedaP. and WillisJ.R.1995. The effect of spatial distribution on the effective behavior of composite materials and cracked media. Journal of Mechanics and Physics of Solids43, 1919–1951.
    [Google Scholar]
34. RügerA.1997. P‐wave reflection coefficients for transversely isotropic models with vertical and horizontal axis of symmetry. Geophysics62, 713–722.
    [Google Scholar]
35. SayersC.M. and KachanovM.1995. Microcrack‐induced elastic wave anisotropy of brittle rocks. Journal of Geophysical Research100, 4149–4156.
    [Google Scholar]
36. SchoenbergM.1980. Elastic wave behavior across linear slip interfaces. Journal of the Acoustic Society of America68, 1516–1521.
    [Google Scholar]
37. SchoenbergM.1983. Reflection of elastic waves from periodically stratified media with interfacial slip. Geophysical Prospecting31, 265–292.
    [Google Scholar]
38. SchoenbergM. and DoumaJ.1988. Elastic wave propagation in media with parallel fractures and aligned cracks. Geophysical Prospecting36, 571–590.
    [Google Scholar]
39. SchoenbergM. and SayersC.M.1995. Seismic anisotropy of fractured rock. Geophysics60, 204–211.
    [Google Scholar]
40. TsvankinI.1997. Reflection moveout and parameter estimation for horizontal transverse isotropy. Geophysics62, 614–629.
    [Google Scholar]
41. VernikL. and KachanovM.2010. Modeling elastic properties of siliciclastic rocks. Geophysics75(6), E171–E182.
    [Google Scholar]
42. WalshJ.1965. The effects of cracks on the compressibility of rocks. Journal of Geophysical Research70, 381–389.
    [Google Scholar]
43. WuT.T.1966. The effect of inclusion shape on the elastic moduli of a two‐phase material. International Journal of Solids and Structures2, 1–8.
    [Google Scholar]
44. XuS.1998. Modelling the effect of fluid communication on velocities in anisotropic porous rocks. International Journal of Solids and Structures35, 4685–4707.
    [Google Scholar]
45. ZimmermanR.W.1991. Elastic moduli of a solid containing spherical inclusions. Mechanics of Materials12, 17–24.
    [Google Scholar]