The influence of microstructure on seismic wave speed anisotropy in the crust: Computational analysis of quartz-muscovite rocks

Geophysical Journal International

Volumn 185, Issue 2, 2011, Pages 609-621

  Naus Thijssen, Félice M J ^a   Goupee, Andrew J ^b   Vel, Senthil S ^b   Johnson, Scott E ^a  

^a UNIVERSITY OF MAINE   (United States)

^b University of Maine   (United States)

Author keywords

Crustal structure; Elasticity and anelasticity; Mechanics, theory and modelling; Microstructures; Numerical approximations and analysis; Seismic anisotropy

Indexed keywords

ASYMPTOTIC EXPANSION HOMOGENIZATION; BULK ELASTIC PROPERTIES; CHRISTOFFEL EQUATION; COMPUTATIONAL ANALYSIS; CRUSTAL ROCKS; CRUSTAL STRUCTURE; ELASTICITY AND ANELASTICITY; FINITE ELEMENT MODELLING; INCIDENCE ANGLES; MICROSTRUCTURAL VARIABLES; MUSCOVITE GRAINS; NUMERICAL APPROXIMATIONS; ORIENTATION DISTRIBUTIONS; QUARTZ GRAINS; ROCK SAMPLE; SEISMIC ANISOTROPY; STIFFNESS TENSOR; WAVE SPEED; WAVE VELOCITY;

ANISOTROPY; ASYMPTOTIC ANALYSIS; ELASTICITY; FINITE ELEMENT METHOD; HOMOGENIZATION METHOD; MICA; MICROSTRUCTURE; QUARTZ; ROCKS; SEISMOLOGY; SILICATES; SPEED; STIFFNESS; TENSORS;

SEISMIC WAVES;

CRUSTAL STRUCTURE; ELASTICITY; FINITE ELEMENT METHOD; MICROSTRUCTURE; MUSCOVITE; NUMERICAL METHOD; SEISMIC ANISOTROPY; WAVE VELOCITY;

EID: 79954585762     PISSN: 0956540X     EISSN: 1365246X     Source Type: Journal    
DOI: 10.1111/j.1365-246X.2011.04978.x     Document Type: Article

References (71)

1. Auld, B.A., 1990. Acoustic Fields and Waves in Solids, 2nd edn, Vol 2, Robert E Krieger Publishing Co, Malabar, FL, 432 pp.
2. Backus, G.E., 1962. Long-wave elastic anisotropy produced by horizontal layering, J. geophys. Res., 67, 4427-4441.
3. Bascou, J., Barroul, G., Vauchez, A. & Mainprice, D., 2001. EBSD-measured lattice preferred orientations and seismic properties of eclogites, Tectonophysics, 342, 61-80.
4. Bensoussan, A., Lions, J.L. & Papanicolaou, G., 1978. Asymptotic Analysis for Periodic Structures, North-Holland Publishing Co., Amsterdam, 724 pp.
5. Birch, F., 1960. The velocity of compressional waves in rocks to 10 kilobars, part 1, J. geophys. Res., 65, 1083-1102.
6. Birch, F., 1961. The velocity of compressional waves in rocks to 10 kilobars, part 2, J. geophys. Res., 66, 2199-2224.
7. Bond, W.L., 1943. The mathematics of the physical properties of crystals, Bell Sys. Tech. J., 22, 1-72.
8. Bruner, W.M., 1976. Comments on "Seismic velocities in dry and saturated cracked solids", J. geophys. Res., 81, 2573-2576.
9. Bunge, H.J., Kiewel, R., Reinert, T. & Fritsche, L., 2000. Elastic properties of polycrystals: influence of texture and stereology, J. Mech. Phys. Solids, 48, 29-66.
10. Champion, M.E., White, N.J., Jones, S.M. & Priestley, K.F., 2006. Crustal velocity structure of the British Isles: a comparison of receiver functions and wide-angle seismic data, Geophys. J. Int., 166, 795-813.
11. Christensen, N.I., 1965. Compressional wave velocities in metamorphic rocks at pressures to 10 kilobars, J. geophys. Res., 70, 6147-6164.
12. Christensen, N.I., 1966. Shear wave velocities in metamorphic rocks at pressures to 10 kilobars, J. geophys. Res., 71, 3549-3556.
13. Christoffel, E.B., 1877. Ueber die Fortpflanzung von Stössen durch elastische feste Körper, Ann. Mat. Purö Appl., 8, 193-243.
14. Cook, R.D., Malkus, D.S., Plesha, M.E. & Witt, R.J., 2002. Concepts and Applications of Finite Element Analysis, 4th edn, John Wiley & Sons, Inc., Hoboken, NJ, 784 pp.
15. Crampin, S., 1981. A review of wave motion in anisotropic and cracked elastic-media, Wave Motion, 3, 343-391.
16. Fish, J. & Wagiman, A., 1992. Multiscale finite element method for a periodic and nonperiodic heterogeneous medium, Adaptive, Multilevel, and Hierarchical Computational Strategies, ASME AMD, 157, 95-117.
17. Godfrey, N.J., Christensen, N.I. & Okaya, D.A., 2000. Anisotropy of schists: contribution of crustal anisotropy to active source seismic experiments and shear wave splitting observations, J. geophys. Res., 105, 27 991-28 007.
18. Goupee, A.J. & Vel, S.S., 2010. Multiscale thermoelastic analysis of random heterogeneous materials, Part II: direct micromechanical failure analysis and multiscale simulations, Comput. Mater. Sci., 48, 39-53.
19. Guedes, J.M. & Kikuchi, N., 1990. Preprocessing and postprocessing for materials based on the homogenization method with adaptive finite element methods, Comput. Meth. Appl. Mech. Eng., 83, 143-198.
20. Hearmon, R.F.S., 1979. The elastic constants of crystals and other anisotropic materials, in Landolt-Börnstein Tables, III/181-244, eds, Hellwege, K.H. & Hellwege, A.M., Springer-Verlag, Berlin .
21. Higham, N.J., 2008. Functions of Matrices: Theory and computation, Society for Industrial & Applied Mathematics, Philadelphia, PA, 445 pp.
22. Hill, R., 1952. The elastic behaviour of a crystalline aggregate, Proc. Phys. Soc. Lond., A65, 349-354.
23. Hill, R., 1965. A self consistent mechanics of composite materials, J. Mech. Phys. Solids, 13, 213-222.
24. Hughes, T.J.R., 2000. The Finite Element Method: Linear Static and Dynamic Finite Element Analysis, Dover Publications, Mineola, 672 pp.
25. Ji, S., Wang, Q. & Xia, B., 2002. Handbook of Seismic Properties of Minerals, Rocks and Ores, Polytechnic International Press, Canada, 630 pp.
26. Ji, S., Wang, Q., Xia, B. & Marcotte, D., 2004. Mechanical properties of multiphase materials and rocks: a phenomenological approach using generalized means, J. Struct. Geol., 26, 1377-1390.
27. Johnson, S.E., Vernon, R.H. & Upton, P., 2004. Foliation development and progressive strain-rate partitioning in the crystallizing carapace of a tonalite pluton: microstructural evidence and numerical modeling, J. Struct. Geol., 26, 1845-1865.
28. Johnston, J.E. & Christensen, N.I., 1995. Seismic anisotropy of shales, J. geophys. Res., 100, 5991-6003.
29. Kaneshima, S., Ando, M. & Kimura, S., 1988. Evidence from shear-wave splitting for the restriction of seismic anisotropy to the upper crust, Nature, 335, 627-629.
30. Karato, S., 1987. Seismic anisotropy due to lattice preferred orientation of minerals: kinematic or dynamic? In High-Pressure Research in Mineral Physics455-471, Manghnani, M.H. & Syono, Y., eds, American Geophysical Union, Washington, D.C.
31. Karato S., 2008. Deformation of Earth Materials: An Introduction to the Rheology of Solid Earth, Cambridge University Press, Cambridge, 463 pp.
32. Karato, S., Jung, H., Katayama, I. & Skemer, P., 2008. Geodynamic significance of seismic anisotropy in the upper mantle: new insights from laboratory studies, Annu. Rev. Earth planet. Sci., 36, 59-95. doi:.
33. Lloyd, G.E. & Kendall, J-M., 2005. Petrofabric derived seismic properties of a mylonitic quartz simple shear zone: implications for seismic reflection profiling, in Petrophysical Properties of Crystalline Rocks, 24075-94, Harvey, P.K., Brewer, T., Pezard, P.A. & Petrov, V.A., eds, Sp. Publ. Geol. Soc. Lond.
34. Lloyd, G.E., Butler, R.W.H., Casey, M. & Mainprice, D., 2009. Mica, deformation fabrics and the seismic properties of the continental crust, Earth planet. Sci. Lett., 288, 320-328.
35. Mahan, K., 2006. Retrograde mica in deep crustal granulites: implications for crustal seismic anisotropy, Geophys. Res. Lett., 33, L24301, doi:.
36. Mainprice, D., 1997. Modelling anisotropic seismic properties of partially molten rocks found at mid-ocean ridges, Tectonophysics, 279, 161-179.
37. Mainprice, D., 2007. Seismic anisotropy of the deep Earth from a mineral and rock physics perspective, in Treatise in Geophysics, 2437-492, Schubert, G., ed., Elsevier, Oxford .
38. Mainprice, D. & Humbert, M., 1994. Methods of calculating petrophysical properties from lattice preferred orientation data, Surv. Geophys., 15, 575-592.
39. Mainprice, D. & Nicolas, A., 1989. Development of shape and lattice preferred orientations: application to the seismic anisotropy of the lower crust, J. Struct. Geol., 11, 175-189.
40. Mainprice, D., Barruol, G. & Ben Ismaïl, W., 2000. The anisotropy of the Earth's mantle: from single crystal to polycrystal, in Mineral Physics and Seismic Tomography from the Atomic to the Global Scale, Geophys. Monograph Ser. 117237-264, eds Karato, S.-I., Stixrude, L., Liebermann, R., Masters, G. & Forte, A., AGU, Washington, D.C.
41. Matthies, S. & Humbert, M., 1993. The realization of the concept of a geometric mean for calculating physical constants of polycrystalline materials, Phys. Status Solidi B-Basic Solid State Phys., 177, K47-K50.
42. Mauler, A., Burlini, L., Kunze, K., Phillippot, P. & Burg, J.-P., 2000. P-wave anisotropy in eclogites and relationship to the omphacite crystallographic fabric, Phys. Chem. Earth (A), 25, 119-126.
43. Montagner, J.-P. & Guillot, L., 2002. Seismic anisotropy and global geodynamics, in Plastic Deformation of Minerals and Rocks353-385, eds Karato, S. & Wenk, H.-R., MSA, Washington, D.C .
44. Naus-Thijssen, F.M.J., Johnson, S.E. & Koons, P.O., 2010. Modeling crenulation cleavage: a polymineralic approach, J. Struct. Geol., 32, 330-341.
45. Nicolas, A. & Christensen, N.I., 1987. Formation of anisotropy in upper mantle peridotite: a review, in Composition, Structure and Dynamics of the Lithosphere-Asthenosphere System111-123, eds Fuchs, K. & Froidevaux, C., AGU, Washington, D.C .
46. Nye J.F., 1985. Physical Properties of Crystals: Their Representation by Tensors and Matrices, Oxford University Press, Oxford, 352 pp.
47. Okaya, D.A. & Christensen, N.I., 2002. Anisotropic effects of non-axial seismic wave propagation in foliated crustal rocks, Geophys. Res. Lett., 29, 1507. doi:.
48. Okaya, D.A. & McEvilly, T.V., 2003. Elastic wave propagation in anisotropic crustal material possessing arbitrary internal tilt, Geophys. J. Int., 153, 344-358.
49. Okaya, D.A., Christensen, N., Stanley, D. & Stern, T., 1995. Crustal anisotropy in the vicinity of the Alpine Fault Zone, South Island, N. Z. J. Geol. Geophys., 38, 579-583.
50. Ozacar, A.A. & Zandt, G., 2004. Crustal seismic anisotropy in central Tibet: implications fordeformation style and flow in the crust, Geophys. Res. Lett., 31, L23601, doi:.
51. Readman, P.W., Hauser, F., O'Reilly, B.M. & Do, V.C., 2009. Crustal anisotropy in southwest Ireland from analysis of controlled source shear-wave data, Tectonophysics, 474, 571-583.
52. Reuss, A., 1929. Berechnung der Flieβgrenze von Mischkristallen auf grund der Plastizitätsbedingung für Einkristalle, Z. Angew. Math. Mech., 9, 49-58.
53. Sanchez-Palencia, E., 1981. Nonhomogeneous media and vibration theory, J. acoust. Soc. Am., 69, 884.
54. Sanchez-Palencia, E., 1983. Homogenization method for the study of composite media, Asymptotic Anal. II, 985, 192-214.
55. Savage, M.K., 1999. Seismic anisotropy and mantle deformation: what have we learned from shear wave splitting?, Rev. Geophys., 37, 65-106.
56. Shapiro, N.M., Ritzwoller, M.H., Molnar, P. & Levin, V., 2004. Thinning and flow of Tibetan crust constrained by seismic anisotropy, Science, 305, 233-236.
57. Sherrington, H.F., Zandt, G. & Fredriksen, A., 2004. Crustal fabric in the Tibetan Plateau based on waveform inversions for seismic anisotropy parameters, J. geophys. Res., 109, B02312, doi:.
58. Silver, P.G., 1996. Seismic anisotropy beneath the continents: probing the depths of geology, Annu. Rev. Earth planet. Sci., 24, 385-432.
59. Simmons, G., 1964. Velocity of shear waves in rocks to 10 kilobars, J. geophys. Res., 69, 1123-1130.
60. Tatham, D.J., Lloyd, G.E., Butler, R.W.H. & Casey, M., 2008. Amphibole and lower crustal seismic properties, Earth planet. Sci. Lett., 267, 118-128.
61. Terada, K., Hori, M., Kyoya, T. & Kikuchi, N., 2000. Simulation of the multi-scale convergence in computational homogenization approaches, Int. J. Solids Struct., 37, 2285-2311.
62. Tommasi, A., Mainprice, D., Canova, G. & Chastel, Y., 2000. Viscoplastic self-consistent and equilibrium-based modeling of olivine lattice preferred orientations: implications for the upper mantle seismic anisotropy, J. geophys. Res., 105, 7893-7908.
63. Tullis, T.E., Horowitz, F.G. & Tullis, J., 1991. Flow laws of polyphase aggregates from end-member flow laws, J. geophys. Res., 96, 8081-8096.
64. Valcke, S.L.A., Casey, M., Lloyd, G.E., Kendall, J.M. & Fisher, Q.J., 2006. Lattice preferred orientation and seismic anisotropy in sedimentary rocks, Geophys. J. Int., 166, 652-666.
65. Vaughan, M.T. & Guggenheim, S., 1986. Elasticity of muscovite and its relationship to crystal structure, J. geophys. Res., 91, 4657-4664.
66. Vel, S.S. & Goupee, A.J., 2010. Multiscale thermoelastic analysis of random heterogeneous materials, Part I: microstructure characterization and homogenization of material properties, Comput. Mater. Sci., 48, 22-38.
67. Vergne, J., Wittlinger, G., Farra, V. & Su, H., 2003. Evidence for upper crustal anisotropy in the Songpan-Ganze (northeastern Tibet) terrane, Geophys. Res. Lett., 30, 1552, doi:.
68. Voigt W., 1928. Lehrbuch der Kristallphysik. B.G. Teubners Lehrbücher, Leipzig .
69. Weiss, T., Siegesmund, S., Rabbel, W., Bohlen, T. & Pohl, M., 1999. Seismic velocities and anisotropy of the lower continental crust: A review, Pure appl. Geophys., 156, 97-122.
70. Willis, J.R., 1977. Bounds and self-consistent estimates for the overall properties of anisotropic composites, J. Mech. Phys. Solids, 25, 185-202.
71. Xu, Y., Li, Z. & Roecker, S.W., 2007. Uppermost mantle structure and its relation with seismic activity in the central Tien Shan, Geophys. Res. Lett., 34, L10304, doi:.