On the thermal state of the Earth's mantle

Main Article Content

A.C. Fowler

Abstract

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.)


Google Scholar         ARK:/88439/y014655


 

Article Details

How to Cite
Fowler, A.C. 1983. “On the Thermal State of the Earth’s Mantle”. Journal of Geophysics 53 (1), 42-51. https://journal.geophysicsjournal.com/JofG/article/view/17.
Bookmark and Share

References

Anderson, D.L. (1982a) Isotopic evolution of the mantle: the role of magma mixing. Earth Planet. Sci. Lett. 57, 1-12

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