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Izvestiya, Physics of the Solid Earth

, Volume 55, Issue 6, pp 927–935 | Cite as

On the Problem of Elastic Anisotropy Estimation in the Rocks with Quasi Orthotropic Symmetry

  • F. F. GorbatsevichEmail author
Article
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Abstract—The principles for estimating the degree of elastic anisotropy of the medium (the rocks) with transverse isotropic and orthorhombic symmetry are considered. Because of the structural heterogeneity, rocks cannot be considered as strictly having a single type of symmetry. With this fact taken into account, formulas are developed for estimating the elastic anisotropy of the rocks with quasi-orthotropic symmetry from the velocities of compressional and shear waves. The criteria for separating the media into weakly and strongly anisotropic are proposed. The developed parameters can be used for mass determinations of elastic anisotropy of rocks.

Keywords:

degree of elastic anisotropy transversely isotropic symmetry orthotropic symmetry 

Notes

FUNDING

The work was supported by the Russian Foundation for Basic Research under projects nos. 13-05-00125-a and 16-05-00026-a.

REFERENCES

  1. 1.
    Aleksandrov, K.S. and Prodaivoda, G.T., Anizotropya uprugikh svoistv mineralov i gornykh porod (Anisotropy of the Elastic Properties of Minerals and Rocks), Novosibirsk: SB RAS, 2000.Google Scholar
  2. 2.
    Allison, I.S., and Palmer, D.F., The Science of a Changing Earth.Seventh Edition, New York: McGraw-Hill, 1980.Google Scholar
  3. 3.
    Batugin, S.A. and Nirenburg, R.K., Approximate dependence between elastic constants of rocks and anisotropy parameters, Fiz.-Tekhm. Probl. Razpab. Polez. Iskop., 1972, vol. 7, no. 1, pp. 7–11.Google Scholar
  4. 4.
    Belikov, B.P., Aleksandrov, K.S., and Ryzhova, T.V., Uprugie svoistva porodoobrazuyushchikh mineralov i gornykh porod (Elastic Properties of Rock-Forming Minerals and Rocks), Moscow: Nauka, 1970. Google Scholar
  5. 5.
    Berryman, J.G., Long-wave elastic anisotropy in transversely isotropic media, Geophysics, l979, vol. 44, pp. 896–917.CrossRefGoogle Scholar
  6. 6.
    Bezukhov, N.I., Osnovy teorii uprugosti, plastichnosti i polzuchesti (Basic Theory of Elasticity, Plasticity, and Creep), Moscow: Vyssh. shk, 1968.Google Scholar
  7. 7.
    Birch, F., The velocity of compressional waves in rocks to 10 kbar: Part 2., J. Geophys. Res., 1961, vol. 66, pp. 2199–2224.CrossRefGoogle Scholar
  8. 8.
    Brace, W.F., Orientation of anisotropic minerals in a stress field: a discussion, Mem.–Geol. Soc. Amer., 1960, vol. 79, no. 9, pp. 9–20.Google Scholar
  9. 9.
    Brekhovskikh, L.M., Volny v sloistykh sredakh, izd. II (Waves in Layered Media), 2nd. ed., Moscow: Nauka, 1973.Google Scholar
  10. 10.
    Chesnokov, E.M., Seismicheskaya anizotropiya verkhnei mantii Zemli (Seismic Anisotropy of the Upper Mantle of the Earth), Moscow: Nauka, 1977.Google Scholar
  11. 11.
    Clark, A.V., Mignogna, P.B., and Sanford, R.J., Acoustoelastic measurements of stress and stress intensity factors around crack tips, Ultrasonics, 1983, vol. 3, pp. 57–64.CrossRefGoogle Scholar
  12. 12.
    Crampin, S., Evaluation of anisotropy by shear-wave splitting, Geophysics, 1985, vol. 50, no 1, pp. 142–152.CrossRefGoogle Scholar
  13. 13.
    Crampin, S., Peacock, S., Gao1, Y., and Chastin, S., The scatter of time-delays in shear-wave splitting above small earthquakes, Geophys. J. Int., 2004, vol. 156, pp. 39–44.CrossRefGoogle Scholar
  14. 14.
    Dellinger, J., and Vernik, L., Do traveltimes in pulse-transmission experiments yield anisotropic group or phase velocities?, Geophysics, 1994, vol. 59, pp. 1774–1779.CrossRefGoogle Scholar
  15. 15.
    Fedorov, F.I., Teoriya uprugikh voln v kristallakh (Theory of elastic waves in crystals), Moscow: Nauka, 1965.Google Scholar
  16. 16.
    Fizicheskie svoistva gornykh porod i poleznykh iskopaemykh (Physical Properties of Rocks and Minerals), Dortman, N.V., Ed., Moscow: Nedra, 1976.Google Scholar
  17. 17.
    Gorbatsevich, F.F., Absorption anisotropy of shear waves in rocks, Izv. Ross. Akad. Nauk,Fiz. Zemli, 1990, vol. 5, pp. 70–79.Google Scholar
  18. 18.
    Gorbatsevich, F.F., Akustopolyariskopiya gornykh porod (Acoustopolariscopy of Rocks), Apatity: Izd-vo KNTs RAN, 1995.Google Scholar
  19. 19.
    Gorbatsevich, F.F., Akustopolyariskopiya porodoobrazuyushchikh mineralov i kristallicheskikh porod (Acoustopolariscopy of Rock-Forming Minerals and Crystalline Rocks), Apatity: Izd. KNTs RAN, 2002.Google Scholar
  20. 20.
    Gorbatsevich, F., Reflection and Refraction Waves at the Interface, Salt Lake City: American Academic Press, 2016.Google Scholar
  21. 21.
    Gorbatsevich, F.F. and Basalaev, A.A., Experience of determining paleostress parameters using acoustopolarization method, Izv. Ross. Akad. Nauk,Fiz. Zemli, 1993, no. 7, pp. 24–31.Google Scholar
  22. 22.
    Hess, H.H., Seismic anisotropy of the uppermost mantle under oceans. Nature, 1964, vol. 203, no. 4945, pp. 629–631.CrossRefGoogle Scholar
  23. 23.
    Kern, H., Popp, T., and Schmidt, R., The effect of a deviatoric stress on physical rock properties, Surv. Geophys., 1994, vol. 15, pp. 467–479.CrossRefGoogle Scholar
  24. 24.
    Kern, H., Popp, T., Gorbatsevich, F., Zharikov, A., Lobanov, K.V., and Smirnov, Yu.P., Pressure and temperature dependence of Vp and Vs in rocks from the superdeep well and from surface analogues at Kola and the nature of velocity anisotropy, Tectonophysics, 2001, vol. 338, pp. 113–134.CrossRefGoogle Scholar
  25. 25.
    Kozhevnikov, V.N., Usloviya formirovaniya strukturno-metamorficheskikh paragenezisov v dokembriiskikh kompleksakh (Formation Conditions of Structural-Metamorphic Paragenesis in Precambrian Complexes), Leningrad: Nauka, 1982.Google Scholar
  26. 26.
    Musgrave, M.J.P., and Markham, M.F., Features of the elastic wave surface for a zinc crystal, Proc. Phys. Soc., 1961, vol. 77 no. 2, pp. 335–336.CrossRefGoogle Scholar
  27. 27.
    Nevskii, M.V., Kvazianizotropiya skorostei seismicheskikh voln (Quasi-Anisotropy of Seismic Wave Velocities), Moscow: Nauka, 1974.Google Scholar
  28. 28.
    Nye, J.F., Physical Properties of Crystals: Their Representation by Tensors and Matrices, Oxford: Clarendon, 1957. Google Scholar
  29. 29.
    Petrashen’, G.I., Rasprostranenie voln v anizotropnykh uprugikh sredakh (Wave Propagation in Anisotropic Elastic Media), Leningrad: Nauka, 1980.Google Scholar
  30. 30.
    Petrofizika. Spravochnik (Petrophysics: Reference Book), Dortman, N.B., Ed., Moscow: Nedra, 1992, vol. 1.Google Scholar
  31. 31.
    Petrov, V.P., Metamorfizm rannego proterozoya Baltiiskogo shchita (Metamorphism of the Early Proterozoic of the Baltic Shield), Apatity: Izd-vo KNTs RAN, 1999.Google Scholar
  32. 32.
    Raitt, R.W., Shor, G.G., Jr., Francis, T.J.G., and Morris, G.B., Anisotropy of the Pacific upper mantle, J. Geophys. Res., 1969, vol. 74, no. 12, pp. 3095–3109.CrossRefGoogle Scholar
  33. 33.
    Ranganathan, Sh. I. and Ostoja-Starzewski, M., Universal elastic anisotropy index, Phys. Rev. Lett., 2008, vol. 101, paper ID 055504.Google Scholar
  34. 34.
    Seleznev, V.S., Solov’ev, V.M., and Nikitenko, A.B., Determination of seismic anisotropy parameters of the Earth’s crust in Western Yakutia, Rus.Geol. Geofiz., 1986, no. 8i, pp. 90–98.Google Scholar
  35. 35.
    Slawinski, M.A., On elastic-wave propagation in anisotropic media: reflection/refraction laws, raytracing, and traveltime inversion, Ph.D. Dissertation, Univ. Alberta, Alberta, 1996.Google Scholar
  36. 36.
    Spravochnik (kadastr) fizicheskikh svoistv gornykh porod (Reference Book (Cadaster) of Physical Properties of Rocks), Moscow: Nedra, 1975.Google Scholar
  37. 37.
    Struktura, svoistva, sostoyanie porod i geodinamika v geoprostranstve Kol’skoi sverkhglubokoi skvazhiny (SG-3) (Structure, Properties, State of the Rocks and Geodynamics in Geospace of the Kola Superdeep Borehole (SG-3)), Gorbatsevich, F.F., Ed., St. Petersburg: Nauka, 2015.Google Scholar
  38. 38.
    Takanashi, M., Nishizawa, O., Kanagawa, K., and Yasunaga, K., Laboratory measurements of elastic anisotropy parameters for the exposed crustal rocks from the Hidaka Metamorphic Belt, Central Hokkaido, Japan, Geophys. J. Int., 2000, vol. 145, pp. 33–47.CrossRefGoogle Scholar
  39. 39.
    Thomsen, L., Week elastic anisotropy, Geophysics, 1986, vol. 51, no. 10, pp. 1–37.CrossRefGoogle Scholar
  40. 40.
    Tsvankin, I., Anisotropic parameters and P-wave velocity for orthorhombic media: Geophysics, 1997, vol. 62, pp. 1292–1309.CrossRefGoogle Scholar

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© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.Geological Institute, Kola Science Center, Russian Academy of SciencesApatityRussia

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