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[1] We present a three-dimensional spherical shell numerical model for chemical differentiation and redistribution of incompatible elements in a convective Earth's mantle heated mostly from within by U, Th, and K and slightly from below. The evolution-model equations guarantee conservation of mass, momentum, energy, angular momentum, and four sums of the number of atoms of the pairs 238 U-206 Pb, 235 U-207 Pb, 232 Th-208 Pb, and 40 K-40 Ar. The pressure-and temperature-dependent viscosity is supplemented by a viscoplastic yield stress, s y . The lithospheric viscosity is partly imposed to mimic its increase by dehydration of oceanic lithosphere and other effects. Also, the asthenosphere is generated not only by the distribution of temperature and melting temperature, but essentially by the profiles of water solubility and water abundance. Therefore we introduced a radial viscosity profile factor describing that behavior. However, the focus of this paper is the episodic growth of continents and oceanic plateaus. As a complement, the differentiation generates the depleted MORB mantle (DMM) which predominates immediately beneath the lithosphere. Our continents are not artificially imposed on the surface of the spherical shell, but instead they evolve by the interplay between chemical differentiation and convection/mixing. No restrictions are imposed regarding number, size, form, and distribution of continents. However, oceanic plateaus that impinge upon a continent have to be united with it. This mimics the accretion of terranes. The numerical results show an episodic growth of the total mass of the continents and display a plausible time history for the laterally averaged surface heat flow, qob, and the Rayleigh number, Ra. We use our model to explore a moderate region of Ra-s y parameter space. We find Earth-like continent distributions in a central part of the Ra-s y space we explored. We identified a Ra-s y region where the calculated total continental volume is very close to the observed value; another Ra-s y region where the Urey number, Ur, is close to the accepted value; a third Ra-s y area where surface heat flow is very close to the present-day observed mean global heat flow using typical abundances of the heat-producing elements. It is remarkable that these different acceptable Ra-s y regions share a common overlap area, where Earth-like behavior is simultaneously fulfilled.Although the convective flow patterns and the chemical differentiation of oceanic plateaus are coupled, the evolution of time-dependent Rayleigh number, Ra t , is relatively well predictable and the stochastic parts of the Ra t (t) curves are small. Regarding the time distribution of juvenile growth rates of the total mass of the continents, predictions are possible only in the first epoch of the evolution, presumed that the initial conditions are given. Later on, the distribution of the continental growth episodes is increasingly stochastic. Independent of the varying individual runs, our model shows that the total mass of the presen...

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[1] We investigate whether the observed zircon age distribution of continental crust (CC) is produced by real crustal growth episodes or is only an artifact of preservation. In connection with the second alternative of this question, other authors proposed that there was little episodicity in the production of new CC and that modeling corroborates this opinion. We conclude that a combination of the two answers might be possible. In matters of modeling, however, we ascertain that a dynamic modeling of the convection-differentiation system of the mantle reveals the high probability of magmatic episodes. We solve the full set of balance equations in a 3-D spherical-shell mantle. The heat-producing elements are redistributed by chemical differentiation. A realistic solidus model of mantle peridotite is essential for an applicable model. The solidus depends not only on depth but also on the volatile concentration. Furthermore, we introduced realistic profiles of Grüneisen parameter, viscosity, adiabatic temperature, thermal expansivity, and specific heat. Our model automatically produces lithospheric plates and growing continents. Regarding number, size, form, distribution, and surface velocity of the continents, no constraints have been prescribed. Regions of the input parameter space (Ra, y , k, f 3 ) that are favorable with respect to geophysical quantities show simultaneously not only episodicity of CC growth but also a reproduction of the observed zircon-age maxima referring to the instants of time. We also obtain Archean events for ages greater than 3000 Ma that are not or scarcely visible in the observed zircon ages. Sinusoidal parts of the evolution curve of qob, Ur, and E kin are superposed with a monotonous decrease. The volumetrically averaged mantle temperature, T mean , however, decreases smoothly and slowly, nearly without pronounced variations. Therefore, we can dismiss catastrophic mechanisms that simultaneously incorporate the whole mantle.