Whole-Mantle Convection, Continent Generation, and Preservation of Geochemical Heterogeneity

The focus of this paper is numerical modeling of crust-mantle differentiation. We begin by surveying the observational constraints of this process. The present-time distribution of incompatible elements are described and discussed. The mentioned differentiation causes formation and growth of continents and, as a complement, the generation and increase of the depleted MORB mantle (DMM). Here, we present a solution of this problem by an integrated theory that also includes the thermal solid-state convection in a 3-D compressible spherical-shell mantle heated from within and slightly from below. The conservation of mass, momentum, energy, angular momentum, and of four sums of the number of atoms of the pairs

238

U-

206

Pb,

235

U-

207

Pb,

232

Th-

208

Pb,

40

K-

40

Ar is guaranteed by the used equations. The pressure- and temperature-dependent viscosity is supplemented by a viscoplastic yield stress, σ

y

. No restrictions are supposed regarding number, size, form and distribution of continents. Only oceanic plateaus touching a continent have to be united with this continent. This mimics the accretion of terranes. The numerical results are an episodic growth of the total mass of the continents and acceptable courses of the curves of the laterally averaged surface heat flow, qob, the Urey number,

Ur

, and the Rayleigh number, Ra. In spite of more than 4500 Ma of solid-state mantle convection, we typically obtain separate, although not simply connected geochemical mantle reservoirs. None of the reservoirs is free of mixing. This is a big step towards a reconciliation of the stirring problem. As expected, DMM strongly predominates immediately beneath the continents and the oceanic lithosphere. Apart from that, the result is a marble-cake mantle but DMM prevails in the upper half of the mantle. We find Earth-like continent distributions in a central part of Ra-σy plot obtained by a comprehensive variation of parameters. There are also Ra-σy areas with small deviations of the calculated total continental volume from the observed value, with acceptable values of Ur and with realistic surface heat flow. It is remarkable that all of these different acceptable Ra-σy regions share a common overlap area. We compare the observed present-time topography spectrum and the theoretical flow spectrum

n

1/2

× (

n

+ 1)1/2 × (

v

2

n,pol

).