Abstract: On Intermittent Lower-Mantle Convection​

U. Walzer and R. Maaz. On intermittent lower-mantle convection. In Carey, S.W. (Ed.): Expanding Earth Symposium, Sydney 1981, 329-340, 1983.

On Intermittent Lower-Mantle Convection

U. Walzer and R. Maaz

Abstract

Starting from geochemical results, we assume that the lower mantle has a lower amount of radioactive heat produced per unit volume per unit time than the upper mantle. Consequently, the thermoconvective driving energy in the lower mantle is too weak to permanently maintain convection there. At the same time, however, the lattice and radiative heat conductivities are low there, so that the heat generated is dissipated only to a minor extent. Therefore, temperature increases. As a result, due to the well-known temperature dependence of the effective viscosity, the Rayleigh number increases until the critical Rayleigh number is surpassed and convection starts in the lower mantle, too. Through the currents, heat is dissipated, causing an increase in the permanently existing upper-mantle convection, in magmatism and orogeny as well as earth-wide transgressions. As a result of the heat dissipation, the Rayleigh number again drops beyond the critical value, i.e., due to the low internal heat source density, lower-mantle convection dies down until the next convection interval is started after a long period of heat accumulation. The differential equations of the problem have been reduced to a system of equations with a Hammerstein integral equation and solved numerically. Four convection episodes resulted which agree, in respect of time, with the four highest maxima of Gastil's curve of magmatic activity: These four overturns are found 2820, 3633,4128 and 4496 Ma. after the accretion of the Earth, an age of the Earth of 4600 Ma. being assumed. A comparison of empirical curves showed that these times also correspond to earth-wide transgressions and that the latter are found to lie precisely in the periods in the Phanerozoic in which the geomagnetic dipole field only rarely reversed polarity. The latter most probably has to do with the fact that the lower mantle determines part of the boundary conditions of the hydromagnetic convection in the Earth's outer core.

Key words: mantle convection, lower mantle, Earth, mantle, Hammerstein equation, Hammerstein integral equation, episodicity, magmatism, abundance, transgression, platform, regression, Phanerozoic, Gastil curve, heat flux

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