Abstract: Convection and the Formation of the Principal Reservoirs of the Earth's Silicate Mantle​

U. Walzer and R. Hendel. Convection and the formation of the principal reservoirs of the Earth's silicate mantle. EOS, 80, no. 46, F1171, 2000.

1999 Fall Meeting

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V41E-01

Convection and the Formation of the Principal Reservoirs of the Earth's Silicate Mantle

* Walzer, U.
uwe@kokopelli.lanl.gov
Inst.Geowiss., Univ.Jena, Burgweg 11, Jena, 07749 Germany
Hendel, R.
hdl@kokopelli.lanl.gov
Inst.Geowiss., Univ.Jena, Burgweg 11, Jena, 07749 Germany

Mantle convection tends to diminish and to annihilate chemical reservoirs by blend. However, the chemical differentiation generates new geochemical reservoirs. It takes place in partially molten areas of the asthenosphere. If this partially molten regions are rich in incompatible elements,i.e., if this region is fed by plumes from deeper parts of the mantle, oceanic plateaus develop which will be carried by the normal oceanic lithosphere up to the continent where they will be accreted. The solved main problem is to show by computation, why we observe two spatially divided chemical main reservoirs of the mantle, i.e., a depleted upper part of the mantle and a lower part rich in incompatible elements, in spite of the mantle convection that is active since more than 4.49 billion years. The problem has been solved by computation of a convection-fractionation model that differs from the published model K2A [Walzer,U., Hendel,R., PEPI 112 (1999) 211-256]pdf, 13 mb · en in a new viscosity model. The principal idea is to compute the relative viscosity variations as a function of depth from observable quantities. We developed a self-consistent theory using the Helmholtz free energy, the Ullmann-Pan'kov equation of state,the free-volume Grueneisen parameter and Lindemann's law. In order to get the relative variations of the radial factor of the viscosity, we insert the pressure P, the bulk modulus K, and ∂K / ∂P from PREM. For calibration, the standard postglacial-uplift viscosity under continental lithosphere was used. Moreover, we took into account the dependence of the viscosity on temperature and on the degree of depletion of volatiles. The convection-fractionation mechanism is based on the solution of the differential equations of a 2D-FD thermal Oberbeck-Boussinesq convection and of the chemical segregation and fractionation. For the latter one, we use a tracer mechanism. The conservation of the four numbers of atoms of the radionuclides ²³⁸U, ²³⁵U, ²³²Th, ⁴⁰K plus the corresponding daughter nuclides is guaranteed. Oceanic plateaus develop leaving behind depleted parts of the mantle. Although our model mantle is essentially heated from within, we assume additionally a 20 mW/m² heat flow at the CMB. This is necessary because of the dynamo theory of the outer core. The concentrations of the heating radionuclides and the viscosity are functions of the location and time. Although the viscosity distribution is crucial for the convection patterns, we included also the phase boundaries using conventional values of the Clapeyron slope, the density contrast and the transition width of the olivine-spinel transition and of the spinel-perovskite transition. The evolving inhomogeneity of the heat source concentrations in the mantle and the lateral movability of the growing continent generate a non-steady state. The frequency distribution of the fluctuations of juvenile continent material addition and surface heat flow is similar to the observed world-wide time distribution of mineral dates and the tectonic episodicity. We obtained realistic values for the lateral velocity of the continent, the continental growth rate, the surface heat flow and for the distributions of temperature, viscosity and mantle flow velocity as a function of time, especially for the present time. The following result is insensitive even to strong variations of the Rayleigh number: We arrive at a predominantly depleted upper part of the mantle and at a lower part of the mantle which is rich in incompatible elements, yet. This bipartition corresponds to geochemical expectations.

Key words: Earth, mantle, convection, mantle convection, geochemical reservoirs.