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Abstract

Our understanding of rheological properties of the Earth’s interior is largely based on a combination of mineral physics data and direct geophysical observations. Hence seismic velocities and attenuation may be interpreted if we understand how they depend on the mechanical properties of matter. For example, the travel-times and amplitudes of seismic waves propagating through the Earth can be interpreted in terms of mineralogical models when we know the properties of minerals and rocks at depth.

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References

  1. Zener, C. (1948). Elasticity and anelasticity of metals. Chicago: University of Chicago Press.

    Google Scholar 

  2. Hashin, Z., & Shtrikman, S. (1963). A variational approach to the theory of the elastic behaviour of multiphase materials. Journal of the Mechanics and Physics of Solids, 11(2), 127–140.

    Article  Google Scholar 

  3. Jones, A. G., Evans, R. L., & Eaton, D. W. (2009). Velocity-conductivity relationships for mantle mineral assemblages in archean cratonic lithosphere based on a review of laboratory data and hashin-shtrikman extremal bounds. Lithos, 109(1–2), 131–143.

    Article  Google Scholar 

  4. Gist, G. A. (1994). Fluid effects on velocity and attenuation in sandstones. The Journal of the Acoustical Society of America, 96(2), 1158–1173.

    Article  Google Scholar 

  5. James Jr, S. W. (1981). Stress relaxations at low frequencies in fluid-saturated rocks: Attenuation and modulus dispersion. Journal of Geophysical Research, 86(B3), 1803–1812.

    Article  Google Scholar 

  6. Jackson, I., Fitz Gerald, J. D., Faul, U. H., & Tan, B. H. (2002). Grain-size-sensitive seismic wave attenuation in polycrystalline olivine. Journal of Geophysical Research, 107(B12), 2360.

    Article  Google Scholar 

  7. Jackson, I., Faul, U. H., Fitz Gerald, J. D., & Tan, B. H. (2004). Shear wave attenuation and dispersion in melt-bearing olivine polycrystals: 1. specimen fabrication and mechanical testing. Journal of Geophysical Research, 109(B6), B06201.

    Article  Google Scholar 

  8. Dobson, D., Ammann, M., & Tackley, P. (2012). The grain size of the lower mantle. Proceeding of European Mineralogical Conference, Vol. 1, p. 403.

    Google Scholar 

  9. Priestley, K., & McKenzie, D. (2006). The thermal structure of the lithosphere from shear wave velocities. Earth and Planetary Science Letters, 244(1–2), 285–301.

    Article  Google Scholar 

  10. Karato, S.-I., & Jung, H. (1998). Water, partial melting and the origin of the seismic low velocity and high attenuation zone in the upper mantle. Earth and Planetary Science Letters, 157(3—-4), 193–207.

    Article  Google Scholar 

  11. Sato, H., Sacks, I. S., Murase, T., Muncill, G., & Fukuyama, H. (1989). Qp-melting temperature relation in peridotite at high pressure and temperature: attenuation mechanism and implications for the mechanical properties of the upper mantle. Journal of Geophysical Research, 94(B8), 10,661–10,647.

    Article  Google Scholar 

  12. Gribb, T. T., & Cooper, R. F. (1998). Low-frequency shear attenuation in polycrystalline olivine: Grain boundary diffusion and the physical significance of the andrade model for viscoelastic rheology. Journal of Geophysical Research, 103(B11), 27,267–27,279.

    Article  Google Scholar 

  13. White, R. S., Drew, J., Martens, H. R., Key, J., Soosalu, H., & JakobsdĂ³ttir, S. S. (2011). Dynamics of dyke intrusion in the mid-crust of iceland. Earth and Planetary Science Letters, 304(3—-4), 300–312.

    Article  Google Scholar 

  14. HalĂ¡sz, Z., TimĂ¡r, G., & Kun, F. (2010). The effect of disorder on crackling noise in fracture phenomena. Progress of Theoretical Physics Supplement, 184, 385–399.

    Article  Google Scholar 

  15. King, M. S. (1966). Wave velocities in rocks as a function of changes in overburden pressure and pore fluid saturants. Geophysics, 31(1), 50–73.

    Article  Google Scholar 

  16. Nur, A. M., Mavko, G., Dvorkin, J., & Gal, D. (1995). Critical porosity: The key to relating physical properties to porosity in rocks. SEG Technical Program Expanded Abstracts, 14(1), 878–881.

    Article  Google Scholar 

  17. Hooke, R. (1678). de potentia restitutiva. London: John Martyn Printer.

    Google Scholar 

  18. Cowin, S. C. (1989). Properties of the anisotropic elasticity tensor. The Quarterly Journal of Mechanics and Applied Mathematics, 42(2), 249–266.

    Article  Google Scholar 

  19. Lovett, D. R. (1999). Tensor properties of crystals (2nd ed.). Bristol: Institute of Physics Publishing.

    Google Scholar 

  20. Nye, J. (1985). Physical properties of crystals: Their representation by tensors and matrices. New York: Oxford University Press.

    Google Scholar 

  21. Christensen, N. I. (1982). Seismic velocities, volume II (pp. 1–228). Boca Raton: CRC Press.

    Google Scholar 

  22. Crampin, S., & Peacock, S. (2008). A review of the current understanding of seismic shear-wave splitting in the earth’s crust and common fallacies in interpretation. Wave Motion, 45(6), 675–722.

    Article  Google Scholar 

  23. Crampin, S. (1999). Calculable fluid-rock interactions. Journal of the Geological Society, 156(3), 501–514.

    Article  Google Scholar 

  24. Voigt, W. (1892). Ueber innere reibung fester körper, insbesondere der metalle. Annalen der Physik, 283(12), 671–693.

    Article  Google Scholar 

  25. Nowick, A. S., & Berry, B. S. (1972). Anelastic relaxation in crystalline solids. New York: Academic Press.

    Google Scholar 

  26. Schaller, R., Fantozzi, G., & Gremaud, G. (2001). Mechanical spectroscopy \(Q{^{-1}}\) 2001: With applications to materials science. Materials science forum. Switzerland: Trans Tech Publications.

    Google Scholar 

  27. Debye, P. (1912). Einige resultate einer kinetischen theorie der isolatoren. Physikalische Zeitschrift, 13, 97–100.

    Google Scholar 

  28. Landau, L. D., & Lifshitz, E. M. (1985). Statistical physics (3rd ed.). Oxford: Butterworth-Heinemann.

    Google Scholar 

  29. Cole, K. S., & Cole, R. H. (1941). Dispersion and absorption in dielectrics I. Alternating current characteristics. The Journal of Chemical Physics, 9(4), 341–351.

    Article  Google Scholar 

  30. Fuoss, R. M., & Kirkwood, J. G. (1941). Electrical properties of solids. VIII. Dipole moments in polyvinyl chloride-diphenyl systems*. Journal of the American Chemical Society, 63(2), 385–394.

    Article  Google Scholar 

  31. McCrum, N. G., Read, B. E., & Williams, G. (1967). Anelastic and dielectric effects in polymeric solids. New York: Dover Publications Inc.

    Google Scholar 

  32. Schoeck, G., Bisogni, E., & Shyne, J. (1964). The activation energy of high temperature internal friction. Acta Metallurgica, 12(12), 1466–1468.

    Article  Google Scholar 

  33. Terzaghi, K. (1923). Die berechnung der durchlassigkeitsziffer des tones aus dem verlauf der hydrodynamischen spannungserscheinungen. Akademie der Wissenschaften in Wien Mathematisch-naturwissenschaftliche Klasse Abteilung, 132, 105–124.

    Google Scholar 

  34. Rendulic, L. (1936). Porenziffer und porenwasserdrunk in tonen. Der Bauingenieur, 17, 559–564.

    Google Scholar 

  35. Biot, M. A. (1935). Le problème de la consolidation des matières argileuses sous une charge. Annales de la Societe Scientifique de Bruxelles, B55, 110–113.

    Google Scholar 

  36. Biot, M. A. (1941). General theory of three-dimensional consolidation. Journal of Applied Physics, 12(2), 155–164.

    Article  Google Scholar 

  37. Detournay, E. and Cheng, A. H. D. (1993). Fundamentals of poroelasticity, volume II, chapter 5, (pp. 113–171). Oxford: Pergamon Press.

    Google Scholar 

  38. Rice, J. R., & Cleary, M. P. (1976). Some basic stress diffusion solutions for fluid-saturated elastic porous media with compressible constituents. Reviews of Geophysics, 14(2), 227–241.

    Article  Google Scholar 

  39. Skempton, A. W. (1954). The pore-pressure coefficients a and b. Géotechnique, 4(4), 143–147.

    Article  Google Scholar 

  40. Nautiyal, B. D. (2001). Introduction to Structural Analysis. New Delhi: New Age International.

    Google Scholar 

  41. Gassmann, F. (1951a). Elastic waves through a packing of spheres. Geophysics, 16(4), 673–685.

    Article  Google Scholar 

  42. Carroll, M. M., & Katsube, N. (1983). The role of terzaghi effective stress in linearly elastic deformation. Journal of Energy Resources Technology, 105(4), 509–511.

    Article  Google Scholar 

  43. Salje, E. K. H., Koppensteiner, J., Schranz, W., & Fritsch, E. (2010). Elastic instabilities in dry, mesoporous minerals and their relevance to geological applications. Mineralogical Magazine, 74(2), 341–350.

    Article  Google Scholar 

  44. Zimmerman, R. W., Somerton, W. H., & King, M. S. (1986). Compressibility of porous rocks. Journal of Geophysical Research, 91(B12), 12765–12777.

    Article  Google Scholar 

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Correspondence to Su-Ying Chien .

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Chien, SY. (2014). Introduction. In: Rheological and Seismic Properties of Solid-Melt Systems. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-03098-2_1

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