Finite element convection models: comparison of shallow and deep mantle convection, and temperatures in the mantle

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U. Kopitzke


A Finite Element Method for solving the convection problem in a fluid with position-dependent Newtonian viscosity is developed, using bicubic and biquadratic spline functions on a rectangular grid. Introducing weak (less viscous) zones at the active margins of the lithosphere, dynamical mantle convection models are established which have a nearly uniform surface (plate) velocity and a satisfactory heat flux profile. A comparison of upper and deep mantle convection shows:
— a moderate increase of viscosity with depth cannot confine the flow to the upper mantle;
— in shallow depth convection models the temperature is too low inside the cell, but deep mantle convection models yield satisfactory temperatures for the upper mantle.
For that reason deep (or whole) mantle convection should be the favored hypothesis.

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Kopitzke, U. (1979). Finite element convection models: comparison of shallow and deep mantle convection, and temperatures in the mantle. Journal of Geophysics, 46(1), 97-121. Retrieved from
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Andrews, D.J. (1972) Numerical simulation of sea-floor spreading. J. Geophys. Res. 77:6470-6481

Bickle, M.J. (1978) Heat loss from the earth: a constraint on Archean tectonics from the relation between geothermal gradients and the rate of plate production. Earth Planet. Sci. Lett. 40:301-315

Davies, G.F. (1977) Whole-mantle convection and plate tectonics. Geophys. J. R. Astron. Soc. 49:459-486

DeBremaecker, J.-Cl. (1977a) Convection in the earth's mantle. Tectonophysics 41:195-208

DeBremaecker, J.-Cl. (1977b) Is the oceanic lithosphere elastic or viscous? J. Geo phys. Res. 82:2001-2004

Dickinson, W.R., Luth, W.C. (1971) A model for plate tectonic evolution of mantle layers. Science 174:400-404

Elsasser, W.M., Olson, P., Marsh, B.D. (1979) The Depth of Mantle Convection. J. Geophys. Res. 84:147-155

Fusijawa, H. (1968) Temperature and discontinuities in the transition layer within the earth's mantle: geophysical application of the olivine-spinel transition in the Mg2SiO4-Fe2SiO4 system. J. Geophys. Res. 73:3281-3294

Garfunkel, Z. (1975) Growth, shrinking, and long-term evolution of plates and their implications for the flow pattern in the mantle. J. Geophys. Res. 80:4425-4432

Gebrande, H. (1975) Ein Beitrag zur Theorie thermischer Konvektion im Erdman tel mit besonderer Berucksichtigung der Moglichkeit eines Nachweises mit Methoden der Seismologie. University of Munich, Diss. Inst. for General and Applied Geophysics

Graham, E.K. (1970) Elasticity and composition of the upper mantle. Geophys. J. R. Astron. Soc. 20:285-302

Graham, E.K., Dobrzykowski, D. (1976) Temperatures in the mantle as inferred from simple compositional models. Am. Mineral. 61:549-559

Higgins, G., Kennedy, G.C. (1971) The adiabatic gradient and the melting point gradient in the core of the earth. J. Geophys. Res. 76:1870-1878

Houston, M.H., DeBremaecker, J.-Cl. (1975) Numerical models of convection in the upper mantle. J. Geophys. Res. 80:742-751

Jones, G.M. (1977) Thermal interaction of the core and the mantle and long-term behaviour of the geomagnetic field. J. Geo phys. Res. 82:1703-1709

Jordan, T.H. (1977) Lithospheric slab penetration into the lower mantle beneath the Sea of Okhotsk. J. Geophys. 43:473-496

Kanamori, H., Fujii, N., Mizutani, H. (1968) Thermal diffusivity measurements of rock-forming minerals from 300° to 1100° K. J. Geophys. Res. 73:595-605

Leppaluoto, D.A. (1972) Melting of iron by significant structure theory. Phys. Earth Planet. Inter. 6:175-181

McGregor, I.D., Basu, A.R. (1974) Thermal structure of the lithosphere: a petrological model. Science 185:1007-1011

McKenzie, D.P., Roberts, J.M. (1974) Convection in the earth's mantle: towards a numerical simulation. J. Fluid Mech. 62:465-538

Mercier, J.-Cl., Carter, N.L. (1975) Pyroxene geotherms. J. Geophys. Res. 80:3349-3362

O'Connell, R.J. (1977) On the scale of mantle convection. Tectonophysics 38:119-136

Parsons, B., McKenzie, D. (1978) Mantle convection and the thermal structure of plates. J. Geophys. Res. 83:4419-4430

Prenter, P.M. (1975) Splines and variational methods. John Wiley and Sons, New York

Richter, F.M. (1973) Convection and large scale circulation of the mantle. J. Geophys. Res. 78:8735-8745

Richter, F.M., McKenzie, D. (1978) Simple plate models of mantle convection. J. Geophys. 44:441-471

Richter, F.M., Parsons, B. (1975) On the interaction of two scales of convection in the mantle. J. Geophys. Res. 80:2529-2541

Ringwood, A.E. (1975) Composition and petrology of the earth's mantle. McGraw-Hill, New York

Sammis, C.G., Smith, J.C., Schubert, G., Yuen, D.A. (1977) Viscosity-depth profile of the earth's mantle: effects of polymorphic phase transitions. J. Geophys. Res. 82:3747-3761

Sato, A., Thompson, E.G. (1976) Finite element models for creeping convection. J. Comput. Phys. 22:229-244

Schatz, J.F., Simmons, G. (1972) Thermal conductivity of earth materials at high temperatures. J. Geophys. Res. 77:6966-6983

Schubert, G., Froidevaux, C., Yuen, D.A. (1976) Oceanic lithosphere and asthenosphere: thermal and mechanical structure. J. Geophys. Res. 81:3525-3540

Sclater, J.G., Crowe, J. (1976) On the reliability of oceanic heat flow averages. J. Geophys. Res. 81:2997-3006

Stacey, F.D. (1977) A thermal model of the earth. Phys. Earth Planet. Inter. 15:341-348

Tolland, H.G. (1974) Thermal regime of the earth's core and lower mantle. Phys. Earth Planet. Inter. 8:282-286

Torrance, K.E., Turcotte, D.L., Hsui, A.T. (1973) Convection in the earth's mantle. In: Bolt, B.A. (Ed.) Methods in computational physics, Vol. 13, pp. 431-454. Academic Press, New York, London

Tozer, D.C. (1970) Temperature, conductivity, composition and heat flow. J. Geomagn. Geoelectr. 22:35-51

Walcott, R.I. (1970) Flexural rigidity, thickness, and viscosity of the lithosphere. J. Geophys. Res. 75:3941-3954

Wang, C.Y. (1972) Temperature in the lower mantle. Geophys. J. R. Astron. Soc. 27:29-36

Watt, J.P., O'Connell, R.J. (1978) Mixed-oxide and perovskite-structure model mantles from 700-1200 km. Geophys. J. R. Astron. Soc. 54:601-630

Zienkiewicz, O.C. (1977) The finite element method, 3rd edn. McGraw-Hill, London