On the thermal state of the Earth's mantle
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An apparent paradox is discussed, arising from the contrast between an inferred constant mantle viscosity profile and theoretical and experimental rheological flow laws, which predict a mantle viscosity function varying strongly as a function of both temperature and pressure. One can explain the paradox by a particular choice of material parameters, but then mantle temperatures (computed adiabatically) are too low; increasing the temperature by inserting compensatory thermal boundary layers is considered to be dynamically unfeasible, again because of the flow law. We consider this an impasse, and to resolve it, we suggest that old dogmas concerning boundary layers and adiabats need to be critically re-examined, to understand their basis. When this is done, we find that the observed constant viscosity is, in effect, demanded by the interplay of the rheology with the convective process, the mantle temperature is not necessarily adiabatic, and some form of layering effect may be expected, although the ideas presented here are virtually independent of the precise dynamical style of the convective motion. A consequence of these results is that explanations and extrapolations taken from constant-viscosity convection models are, a priori, unjvstifiable. (Specifically, a constant viscosity mantle is a fundamental consequence of the state of flow together with the fluid parameters and rheology: it is not a passive coincidence, which may then be used to deduce the flow state, etc.)
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Anderson, D.L (1982b) Isotopic evolution of the mantle: a model. Earth Planet. Sci. Lett. 57, 13-24
Anderson, O.L., Sumino, Y. (1980) The thermodynamic properties of the Earth's lower mantle. Phys. Earth. Planet. Int. 23, 314-331
Bullen, K.E. (1975) The earth's density. New York: Wiley
Cathles, L.M. (1975) The viscosity of the Earth's mantle. Princeton, N.J.: Princeton University Press
Christensen, U. (1982) Phase boundaries in finite-amplitude convection. Geophys. J. R. Astron. Soc. 68, 487-497
Daly, S.F. (1980) The vagaries of variable-viscosity convection. Geophys. Res. Lett. 7, 841-844
Davies, G.F. (1977) Whole mantle convection and plate tectonics. Geophys. J. R. Astron. Soc. 49, 459-486
De Paolo, D.J. (1981) Nd isotopic studies: some new perspectives on earth structure and evolution. EOS, Trans. Am. Geophys. Union 62, 137-140
Dziewonski A.M., Anderson, D.L. (1981) Preliminary reference Earth model. Phys. Earth Planet. Int. 25, 297-356
Elsasser, W.H., Olson, P., Marsh, B.D. (1979) The depth of mantle convection. J. Geophys. Res. 84, 147-155
Fowler, A.C. (1982a) The depth of convection in a fluid with strongly temperature and pressure dependent viscosity. Geophys. Res. Lett. 9, 816-819
Fowler, A.C. (1982b) Implications of scaling and nondimensionalisation for the convection of the Earth's mantle. Preprint
Goetze, C. (1978) The mechanisms of creep in olivine. Phil. Trans. R. Soc. Lond. A288, 99-119
Goetze, C., Brace, W.F. (1972) Laboratory observations of hightemperature rheology of rocks. Tectonophys. 13, 583-600
Hewitt, J.M., McKenzie, D.P., Weiss, N.O. (1981) Large aspect ratio cells in two-dimensional thermal convection. Earth Planet. Sci. Lett. 51, 370-380
Howard, L.N. (1966) Convection at high Rayleigh number. In: Proc. 11th Int. Cong. Appl. Mech., Munich 1964, H. Gortler, ed.: pp. 1109-1115, Berlin: Springer
Ivins, E.R., Unti, T.W.J., Phillips, R.J. (1982) Large Prandtl number finite-amplitude thermal convection with Maxwell viscoelasticity. Geophys. Astrophys. Fluid Dynamics 22, 103-132
Jaoul, 0., Poumellec, M., Froidevaux, C., Havette, A. (1981) Silicon diffusion in forsterite: a new constraint for understanding mantle deformation. In: Anelasticity in the Earth, F.D. Stacey, M.S. Paterson, A. Nicholas, eds.: pp. 95-100, Geodynamics Series No.4. Washington, D.C.: A.G.U.
Jarvis, G.T., Peltier, W.R. (1982) Mantle convection as a boundary layer phenomenon. Geophys. J. R. Astron. Soc. 68, 389-427
Jeanloz, R., Richter, F.M. (1979) Convection, composition, and the thermal state of the lower mantle. J. Geophys. Res. 84, 5497-5504
Karato, S. (1981) Rheology of the lower mantle. Phys. Earth Planet. Int. 24, 1-14
Kevorkian, J., Cole, J.D. (1981) Perturbation methods in applied mathematics. New York: Springer
Kopitzke, U. (1979) Finite-element convection models: comparison of shallow and deep mantle convection, and temperatures in the mantle. J. Geophys. 46, 97-121
McKenzie, D.P., Roberts, J.M., Weiss, N.O. (1974) Convection in the Earth's mantle: towards a numerical simulation. J. Fluid. Mech. 62, 465-538
Morris, S. (1980) An asymptotic method for determining the transport of heat and matter by creeping flows with strongly variable viscosity; fluid dynamic problems motivated by island arc volcanism. Ph.D. thesis, Johns Hopkins University, Baltimore
Nataf, H.C., Richter, F.M. (1982) Convection experiments in fluids with highly temperature-dependent viscosity and the thermal evolution of the planets. Phys. Earth Planet. Int. 29, 320-329
O'Connell, R.J. (1977) On the scale of mantle convection. Tectonophys. 38, 119-136
O'Connell, R.J., Hager, B. H. (1980) On the thermal state of the earth. In: Physics of the earth's interior, A.M. Dziewonski and E. Boschi, eds. Proc. Int. School of Physics, 'Enrico Fermi', Course LXXVII, 270-317. Amsterdam: NorthHolland
Olson, P.M., Corcos, G.M. (1980) A boundary layer model for mantle convection with surface plates. Geophys. J. R. Astron. Soc. 62, 195-219
Parmentier, E.M., Turcotte, D.L. (1978) Two-dimensional mantle flow beneath a rigid accreting lithosphere. Phys. Earth Planet. Int. 17, 281-289
Peltier, W.R. (1980) Mantle convection and viscosity. In: Physics of the Earth's interior, A.M. Dziewonski and E. Boschi, eds. Proc. Int. School of Physics 'Enrico Fermi', Course LXXVII, 361-431. Amsterdam: North-Holland
Peltier, W.R. (1981) Surface plates and thermal plumes: separate scales of the mantle convective circulation. In: Evolution of the Earth, R.J. O'Connell and W.S. Fyfe, eds.: pp. 229-248. Geodynamics Ser. Vol. 5; Washington, D.C.: A.G.U.
Peltier, W.R., Yuen, D.A., Wu, P. (1980) Postglacial rebound and transient rheology. Geophys. Res. Lett. 7, 733-736
Sammis, C.G., Smith, J.C., Schubert, G., Yuen, D.A. (1977) Viscosity-depth profile of the earth's mantle: effects of polymorphic phase transitrons. J. Geophys. Res. 82, 3747-3761
Schmeling, H. (1980) Numerische Konvektionsrechnungen unter Annahme verschiedener Viskositiitsverteilungen und Rheologien im Mantel. Berichte des Instituts ftir Meteorologie und Geophysik der Universitat Frankfurt am Main, Feldbergstrasse 47
Schmeling, H., Jacoby, W. (1981) On modelling the lithosphere in mantle convection with non-linear rheology. J. Geophys. 50, 89-100
Schubert, G., Spohn, T. (1981) Two-layer mantle convection and the depletion of radioactive elements in the lower mantle. Geophys. Res. Lett. 8, 951-954
Schubert, G., Turcotte, D.L., Oxburgh, E.R. (1969) Stability of planetary interiors. Geophys. J. R. Astron. Soc. 18, 441-460
Stacey, F.D. (1977) A thermal model of the earth. Phys. Earth Planet. Int. 15, 341-348
Stocker, R.L., Ashby, M.F. (1973) On the rheology of the upper mantle. Rev. Geophys. Space Phys. 11, 391-426
Tozer, D.C. (1967) Towards a theory of thermal convection in the mantle. In: The Earth's mantle, Gaskell, T.F. ed.: pp. 325-353. London: Academic Press
Tozer, D.C. (1972) The present thermal state of the terrestrial planets. Phys. Earth Planet. Int. 6, 182-197
Tozer, D.C. (1977) The thermal state and evolution of the Earth and terrestrial planets. Sci. Pro g. 64, 1-28
Turcotte, D.L., Haxby, W.F., Ockendon, J.R. (1977) Lithospheric instabilities. In: Island Arcs, Deep Sea Trenches, and Back-Arc Basins, M. Talwani and W.C. Pitman III, eds.: pp. 63-69. Washington, D.C.: A.G.U.
Turcotte, D.L., Oxburgh, E.R. (1967) Finite amplitude convective cells and continental drift. J. Fluid Mech. 28, 29-42
Weertman, J. (1978) Creep laws for the mantle of the Earth. Phil. Trans. R. Soc. A288, 9-26
Yuen, D.A., Sabadini, R., Boschi, E.V. (1982) The viscosity of the lower mantle as inferred from rotational data. J. Geophys. Res., 87, 10745-10762