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The Microphysical Approach to Mantle Rheology

  • G. Ranalli
Chapter
Part of the NATO ASI Series book series (ASIC, volume 334)

Abstract

The rheology of the mantle can be estimated from geophysical observables related to the Earth’s response to changes in surface load and lateral density differences, and from theoretical and experimental knowledge on creep mechanisms in polycrystalline silicates (microphysical approach). We review the latter here, with particular emphasis on steady-state creep but including an assessment of the possible relevance of transient creep, and stressing the methodological importance of systematics, via deformation maps and isomechanical groups. Geophysical and rheological estimates converge in the assessment of mantle viscosity (a factor of 10–100 higher in the lower than in the upper mantle), and in the conclusion that glacioisostatic rebound may sample the transient rheology of the lower mantle. Microphysics, however, leads to the conclusion that the transition stress between power-law (dislocation climb) and linear (diffusional and Harper-Dora) creep is of the order of 1 MPa (± one order of magnitude) for grain sizes in the range 0.1 – 10 mm. Conditions in the mantle are close to this transition stress, and it is possible that high-stress regions have a nonlinear rheology while low-stress regions are linear.

Keywords

Creep Rate Lower Mantle Transition Stress Mantle Convection Creep Mechanism 
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References

  1. Anderson, D.L. (1989) Theory of the Earth, Blackwell Scientific Publications, Boston, 366 p.Google Scholar
  2. Ashby, M.F. and Verrali, R.A. (1978) ‘Micromechanisms of flow and fracture, and their relevance to the rheology of the upper mantle’, Phil. Trans. R. Soc. London, A 288, 59–95.Google Scholar
  3. Banerdt, W.B. and Sammis, C.G. (1985) ‘Low stress high temperature creep in single crystal NaCl’, Phys. Earth Planet. Inter. 41, 108–124.CrossRefGoogle Scholar
  4. Beauchesne, S. and Poirier, J.P. (1989) ‘Creep of barium titanate perovskite: a contribution to a systematic approach to the viscosity of the lower mantle’, Phys. Earth Planet. Inter. 55, 187–199.CrossRefGoogle Scholar
  5. Borch, R.S. and Green, H.W., II (1987) ‘Dependence of creep in olivine on homologous temperature and its implications for flow in the mantle’, Nature 330, 345–348.CrossRefGoogle Scholar
  6. Borch, R.S. and Green, H.W., II (1989) ‘Deformation of peridotite at high pressure in a new molten salt cell: comparison of traditional and homologous temperature treatments’, Phys. Earth Planet. Inter. 55, 269–276.CrossRefGoogle Scholar
  7. Caputo, M. (1986) ‘Linear and nonlinear inverse rheologies of rocks’, Tectonophysics 122, 53–71.CrossRefGoogle Scholar
  8. Carter, N.L. and Kirby, S.H. (1978) ‘Transient creep and semibrittle behaviour of crystalline rocks’, Pure & Appl. Geophys. 116, 807–839.CrossRefGoogle Scholar
  9. Carter, N.L., Anderson, D.A., Hansen, F.D., and Kranz, R.L. (1981) ‘Creep and creep rupture of granitic rocks’, Am. Geophys. Union, Geophys. Mon. 24, 61–82.Google Scholar
  10. Chopra, P.N. (1986) ‘The plasticity of some fine-grained aggregates of olivine at high pressure and temperature’, Am. Geophys. Union., Geophys. Mon. 36, 25–33.Google Scholar
  11. Christensen, U.R. (1987) ‘Some geodynamical effects of anisotropic viscosity’, Geophys. J. R. Astr. Soc. 91, 711–736.CrossRefGoogle Scholar
  12. Christensen, U.R. (1989) ‘Mixing by time-dependent convection’, Earth Planet. Sci. Lett. 95, 382–394.CrossRefGoogle Scholar
  13. Christensen, U.R. and Yuen, D.A. (1989) ‘Time-dependent convection with non-Newtonian viscosity’, J. Geophys. Res. 94, 814–820.CrossRefGoogle Scholar
  14. Davies, G.F. (1984) ‘Geophysical and isotopic constraints on mantle convection: an interim synthesis’, J. Geophys. Res. 89, 6017–6040.CrossRefGoogle Scholar
  15. Dziewonski, A.M. and Anderson, D.L. (1981) ‘Preliminary reference Earth model’, Phys. Earth Planet. Inter. 25, 297–356.CrossRefGoogle Scholar
  16. Ellsworth, K., Schubert, G., and Sammis, C.G. (1985) ‘Viscosity profile of the lower mantle’, Geophys. J.R. Astr. Soc. 83, 199–214.CrossRefGoogle Scholar
  17. Freeman, B. and Ferguson, C.C. (1986) ‘Deformation mechanism maps and micromechanics of rocks with distributed grain sizes’, J. Geophys. Res. 91, 3949–3960.CrossRefGoogle Scholar
  18. Frost, H.J. and Ashby, M.F. (1982) Deformation-Mechanism Maps, Pergamon Press, Oxford, 166 p.Google Scholar
  19. Gasperini, P., Yuen, D.A. and Sabadini, R. (1990) ‘Effects of lateral viscosity variations on postglacial rebound: implications for recent sea-level trends’, Geophys. Res. Lett. 17, 5–8.CrossRefGoogle Scholar
  20. Gérard, O. and Jaoul, O. (1989) ‘Oxygen diffusion in San Carlos olivine’, J. Geophys. Res. 94, 4119–4128.CrossRefGoogle Scholar
  21. Gordon, R.S. (1985) ‘Diffusional creep phenomena in polycrystalline oxides’, Am. Geophys. Union, Geophys. Mon. 31, 132–140.Google Scholar
  22. Gurnis, M. (1988) ‘Large-scale mantle convection and the aggregation and dispersal of supercontinents’, Nature 332, 695–699.CrossRefGoogle Scholar
  23. Gurnis, M. and Hager, B.H. (1988) ‘Controls of the structure of subducted slabs’, Nature 335, 317–321.CrossRefGoogle Scholar
  24. Hager, B.H. (1984) ‘Subducted slabs and the geoid: constraints on mantle rheology and flow’, J. Geophys. Res. 89, 6003–6015.CrossRefGoogle Scholar
  25. Heinz, D.L. and Jeanloz, R. (1987) ‘Measurement of the melting curve of Mg0.9Fe0.1SiO3 at lower mantle conditions and its geophysical implications’, J. Geophys. Res. 92, 11437–11444.CrossRefGoogle Scholar
  26. Houlier, B., Jaoul, O., Abel, F. and Liebermann, R.C. (1988) ‘Oxygen and silicon self-diffusion in natural olivine at T = 1300°C’, Phys. Earth Planet. Inter. 50, 240–250.CrossRefGoogle Scholar
  27. Ito, E. and Takahashi, E. (1987) ‘Melting of peridotite at uppermost lower-mantle conditions’, Nature 328, 514–517.CrossRefGoogle Scholar
  28. Ito, E. and Katsura, T. (1989) ‘A temperature profile of the mantle transition zone’, Geophys. Res. Lett. 16, 425–428.CrossRefGoogle Scholar
  29. Jeanloz, R. and Knittle, E. (1989) ‘Density and composition of the lower mantle’, Phil. Trans. R. Soc. London, A 328, 377–389.Google Scholar
  30. Kampfmann, W. and Berckhemer, H. (1985) ‘High temperature experiments on the elastic and anelastic behaviour of magmatic rocks’, Phys. Earth Planet. Inter. 40, 223–247.CrossRefGoogle Scholar
  31. Karato, S. (1988) ‘The role of recrystallization in the preferred orientation of olivine’, Phys. Earth Planet. Inter. 51, 107–122.CrossRefGoogle Scholar
  32. Karato, S. (1989a) ‘Defects and plastic deformation in olivine’, in S. Karato and M. Toriumi (eds.), Rheology of Solids and of the Earth, Oxford University Press, Oxford, pp. 176–208.Google Scholar
  33. Karato, S. (1989b) ‘Plasticity-crystal structure systematics in dense oxides and its implications for the creep strength of the Earth’s deep interior: a preliminary result’, Phys. Earth Planet. Inter. 55, 234–240.CrossRefGoogle Scholar
  34. Karato, S., Paterson, M.S., and FitzGerald, J.D. (1986) ‘Rheology of synthetic olivine aggregates: influence of grain size and water’, J. Geophys. Res. 91, 8151–8176.CrossRefGoogle Scholar
  35. Karato, S., Fujino, K. and Ito, E. (1990) ‘Plasticity of MgSiO3 perovskite: the results of microhardness tests on single crystals’, Geophys. Res. Lett. 17, 13–16.CrossRefGoogle Scholar
  36. Kirby, S.H. and Kronenberg, A.K. (1987) ‘Rheology of the lithosphere: selected topics’, Rev. Geophys. 25, 1219–1244.CrossRefGoogle Scholar
  37. Knittle, E. and Jeanloz, R. (1989) ‘Melting curve of (Mg,Fe)SiO3 perovksite to 96 GPa: evidence for a structural transition in lower mantle melts’, Geophys. Res. Lett. 16, 421–424.CrossRefGoogle Scholar
  38. Körnig, M. and Müller, G. (1989) ‘Rheological models and interpretation of postglacial uplift’, Geophys. J. Int. 98, 243–253.CrossRefGoogle Scholar
  39. Langdon, T.G. (1985) ‘Regimes of plastic deformation’, in H.-R. Wenk (ed.), Preferred Orientation in Deformed Metals and Rocks: An Introduction to Modern Texture Analysis, Academic Press, Orlando, pp. 219–232.Google Scholar
  40. Langdon, T.G. and Yavari, P. (1982) ‘An investigation of Harper-Dorn creep — II. The flow process’, Acta Metall. 30, 881–887.CrossRefGoogle Scholar
  41. Langdon, T.G., Dehghan, A., and Sammis, C.G. (1982) ‘Deformation of olivine, and the application to lunar and planetary interiors’, in R.C. Gifkins (ed.), Strength of Materials and Alloys, Pergamon Press, New York, pp. 757–762.Google Scholar
  42. Leitch, A.M. and Yuen, D.A. (1989) ‘Internal heating and thermal constraints on the mantle’, Geophys. Res. Lett. 16, 1407–1410.CrossRefGoogle Scholar
  43. Liu, L-G. (1989) ‘Silicate perovskites: a review’, Surv. Geophys. 10, 63–81.CrossRefGoogle Scholar
  44. Mackwell, S.J., Kohlstedt, D.L. and Paterson, M.S. (1985) ‘The role of water in the deformation of olivine single crystals’, J. Geophys. Res. 90, 11319–11333.CrossRefGoogle Scholar
  45. Mackwell, S.J., Bai, Q. and Kohlstedt, D.L. (1990) ‘Rheology of olivine and the strength of the lithosphere’, Geophys. Res. Lett. 17, 9–12.CrossRefGoogle Scholar
  46. Melosh, H.J. (1980) ‘Rheology of the Earth: theory and observation’, in A.M. Dziewonski and E. Boschi (eds.), Physics of the Earth’s Interior, North-Holland, Amsterdam, pp. 318–336.Google Scholar
  47. Minster, J.B. and Anderson, D.L. (1981) ‘A model of dislocation-controlled rheology for the mantle’, Phil. Trans. R. Soc. London, A 299, 319–356.Google Scholar
  48. Müller, G. (1986) ‘Generalized Maxwell bodies and estimates of mantle viscosity’, Geophys. J.R. Astr. Soc. 87, 1113–1141.CrossRefGoogle Scholar
  49. Nakada, M. and Lambeck, K. (1987) ‘Glacial rebound and relative sea-level variations: a new appraisal’, Geophys. J.R. Astr. Soc. 90, 171–224.CrossRefGoogle Scholar
  50. Nakada, M. and Lambeck, K. (1989) ‘Late Pleistocene and Holocene sea-level change in the Australian region and mantle rheology’, Geophys. J. 96, 497–517.CrossRefGoogle Scholar
  51. O’Connell, R.J. (1977) ‘On the scale of mantle convection’, Tectonophysics 38, 119–136.CrossRefGoogle Scholar
  52. Officer, C.B., Newman, W.S., Sullivan, J.M. and Lynch, D.R. (1988) ‘Glacial isostatic adjustment and mantle viscosity’, J. Geophys. Res. 93, 6397–6409.CrossRefGoogle Scholar
  53. Olson, P., Silver, P.G. and Carlson, R.W. (1990) ‘The large-scale structure of convection in the Earth’s mantle’, Nature 344, 209–215.CrossRefGoogle Scholar
  54. Oxburgh, E.R. (1980) ‘Mantle mineralogy and dynamics’ in A.M. Dziewonski and E. Boschi (eds.), Physics of the Earth’s Interior, North-Holland, Amsterdam, pp. 247–269.Google Scholar
  55. Paterson, M.S. (1987) ‘Problems in the extrapolation of laboratory rheological data’, Tectonophysics 133, 33–43.CrossRefGoogle Scholar
  56. Peltier, W.R. (1985a) ‘Mantle convection and viscoelasticity’, Ann. Rev. Fluid Mech. 17, 561–608.CrossRefGoogle Scholar
  57. Peltier, W.R. (1985b) ‘New constraints on transient lower mantle rheology and internal mantle buoyancy from glacial rebound data’, Nature 318, 614–617.CrossRefGoogle Scholar
  58. Peltier, W.R., Wu, P. and Yuen, D.A. (1981) ‘The viscosities of the Earth’s mantle’, Am. Geophys Union, Geodynamics Series 4, 59–77.CrossRefGoogle Scholar
  59. Peltier, W.R., Drummond, R.A. and Tushingham, A.M. (1986) ‘Post-glacial rebound and transient lower mantle rheology’, Geophys. J.R. Astr. Soc. 87, 79–116.CrossRefGoogle Scholar
  60. Poirier, J.P. (1985) Creep of Crystals, Cambridge University Press, Cambridge, 260 p.CrossRefGoogle Scholar
  61. Poirier, J.P. (1988) ‘The rheological approach to the viscosity of planetary mantles: a critical assessment’, in S.K. Runcorn (ed.), The Physics of the Planets, Wiley, Chichester, pp. 161–171.Google Scholar
  62. Poirier, J.P. and Liebermann, R.C. (1984) ‘On the activation volume for creep and its variation with depth in the Earth’s lower mantle’, Phys. Earth Planet. Inter. 35, 283–293.CrossRefGoogle Scholar
  63. Poirier, J.P., Peyronneau, J. Gesland, J.Y. and Brebec, G. (1983) ‘Viscosity and conductivity of the lower mantle: an experimental study on a MgSiO3 perovskite analogue, KZnF3’, Phys. Earth Planet. Inter. 32, 273–287.CrossRefGoogle Scholar
  64. Quareni, F. and Yuen, D.A. (1988) ‘Mean-field methods in mantle convection’, in N.J. Vlaar, G. Nolet, M.J.R. Wortel and S.A.P.L. Cloetingh (eds.), Mathematical Geophysics, Reidel, Amsterdam, pp. 227–264.CrossRefGoogle Scholar
  65. Quareni, F. and Mulargia, F. (1989) ‘The Grüneisen parameter and adiabatic gradient in the Earth’s interior’, Phys. Earth Planet. Inter. 55, 221–233.CrossRefGoogle Scholar
  66. Quareni, F., Yuen, D.A. and Saari, M.R. (1986) ‘Adiabaticity and viscosity in deep mantle convection’, Geophys. Res. Lett. 13, 38–41.CrossRefGoogle Scholar
  67. Ranalli, G. (1980) ‘Regional models of the steady-state rheology of the upper mantle’, in N.-A. Mörner (ed.), Earth Rheology, Isostasy and Eustasy, Wiley, Chichester, pp. 111–123.Google Scholar
  68. Ranalli, G. (1982) ‘Deformation maps in grain size-stress space as a tool to investigate mantle rheology’, Phys. Earth Planet. Inter. 29, 42–50.CrossRefGoogle Scholar
  69. Ranalli, G. (1984) ‘On the possibility of Newtonian flow in the upper mantle’, Tectonophysics 108, 179–192.CrossRefGoogle Scholar
  70. Ranalli, G. (1987) Rheology of the Earth, Allen & Unwin, London, 366 p.Google Scholar
  71. Ranalli, G. and Fischer, B. (1984) ‘Diffusion creep, dislocation creep, and mantle rheology’, Phys. Earth Planet Inter. 34, 77–84.CrossRefGoogle Scholar
  72. Ranalli, G. and Schloessin, H.H. (1989) ‘Role of episodic creep in global mantle deformation’, Am. Geophys. Union, Geophys. Mon. 49, 55–63.Google Scholar
  73. Ricoult, D.L. and Kohlstedt, D.L. (1985) ‘Experimental evidence for the effect of chemical environment upon the creep rate of olivine’, Am. Geophys. Union, Geophys. Mon. 31, 171–184.Google Scholar
  74. Ryerson, F.J., Durham, W.B., Cherniak, D.J. and Lanford, W.A. (1989) ‘Oxygen diffusion in olivine: effect of oxygen fugacity and implications for creep’, J. Geophys. Res. 94, 4105–4118.CrossRefGoogle Scholar
  75. Sabadini, R. and Gasperini, P. (1989) ‘Glacial isostasy and the interplay between upper and lower mantle lateral viscosity heterogeneities’, Geophys. Res. Lett. 16, 429–432.CrossRefGoogle Scholar
  76. Sabadini, R. and Yuen, D.A. (1989) ‘Mantle stratification and long-term polar wander’, Nature 339, 373–375.CrossRefGoogle Scholar
  77. Sabadini, R., Yuen, D.A. and Gasperini, P. (1985) ‘The effects of transient rheology on the interpretation of lower mantle viscosity’, Geophys. Res. Lett. 12, 361–364.CrossRefGoogle Scholar
  78. Sabadini, R., Yuen, D.A. and Portney, M. (1986) ‘The effects of upper-mantle lateral heterogeneities on postglacial rebound’, Geophys. Res. Lett. 13, 337–340.CrossRefGoogle Scholar
  79. Sabadini, R., Smith, B.K., and Yuen, D.A. (1987) ‘Consequences of experimental transient rheology’, Geophys. Res Lett. 14, 816–819.CrossRefGoogle Scholar
  80. Sammis, C.G., Smith, J.C., Schubert, G., and Yuen, D.A. (1977) ‘Viscosity-depth profile of the Earth’s mantle: effect of polymorphic phase transitions’, J. Geophys. Res. 82, 3747–3761.CrossRefGoogle Scholar
  81. Sammis, C.G., Smith, J.C. and Schubert, G. (1981) ‘A critical assessment of estimation methods for activation volume’, J. Geophys. Res. 86, 10707–10718.CrossRefGoogle Scholar
  82. Schmeling, H. (1987) ‘On the interaction between small and large-scale convection and postglacial rebound flow in a power-law mantle’, Earth Planet. Sci. Lett. 84, 254–262.CrossRefGoogle Scholar
  83. Schubert, G., Olson, P., Anderson, C., and Goldman, P. (1989) ‘Solitary waves in mantle plumes’, J. Geophys. Res. 94, 9523–9532.CrossRefGoogle Scholar
  84. Smith, B.K. and Carpenter, F.O. (1987) ‘Transient creep in orthosilicates’, Phys. Earth Planet. Inter. 49, 314–324.CrossRefGoogle Scholar
  85. Stacey, F.D. and Loper, D.E. (1988) ‘Thermal history of the Earth: a corollary concerning non-linear mantle rheology’, Phys. Earth Planet. Inter. 53, 167–174.CrossRefGoogle Scholar
  86. Stacey, F.D., Rong-Shan, F. and Spiliopoulos, S. (1989) ‘Viscosity structure implied by mantle convection’, Phys. Earth Planet. Inter. 55, 1–9.CrossRefGoogle Scholar
  87. Twiss, R.J. (1986) ‘Variable sensitivity piezometric equations for dislocation density and subgrain diameter and their relevance to olivine and quartz’, Am. Geophys. Union, Geophys. Mon. 36, 247–261.Google Scholar
  88. Urai, J.L., Means, W.D., and Lister, G.S. (1986) ‘Dynamic recrystallization of minerals’, Am. Geophys. Union, Geophys. Mon. 36, 161–199.Google Scholar
  89. Walcott, R.I. (1980) ‘Rheological models and observational data of glacioisostatic rebound’, in N.-A. Mörner (ed.), Earth Rheology, Isostasy and Eustasy, Wiley, Chichester, pp. 3–10.Google Scholar
  90. Weertman, J. (1978) ‘Creep laws for the mantle of the Earth’, Phil. Trans. R. Soc. London, A 288, 9–26.CrossRefGoogle Scholar
  91. Wortel, M.J.R. and Vlaar, N.J. (1988) ‘Subduction zone seismicity and the thermo-mechanical evolution of downgoing lithosphere’, Pure Appl. Geophys. 128, 625–659.CrossRefGoogle Scholar
  92. Yuen, D.A., Sabadini, R. and Boschi, E. (1982) ‘Mantle rheology from a geodynamical standpoint’, Riv. Nuovo Cimento 5 (8), 1–35.CrossRefGoogle Scholar
  93. Yuen, D.A., Sabadini, R.C.A., Gasperini, P., and Boschi, E. (1986) ‘On transient rheology and glacial isostasy’, J. Geophys. Res. 91, 11420–11438.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1991

Authors and Affiliations

  • G. Ranalli
    • 1
    • 2
  1. 1.Department of Earth Sciences and Ottawa-Carleton Geoscience CentreCarleton UniversityOttawaCanada
  2. 2.Institut für Mineralogie und PetrographieETH-ZentrumZürichSwitzerland

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