Mantle convection and evolution with growing continents

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 U-238-Pb-206, U-235-Pb-207, Th-232-Pb-208, and K-40-Ar-40. The pressure- and temperature-dependent viscosity is supplemented by a viscoplastic yield stress, sigma(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-sigma(y) parameter space. We find Earth-like continent distributions in a central part of the Ra-sigma y space we explored. We identified a Ra-sigma(y) region where the calculated total continental volume is very close to the observed value; another Ra-sigma(y) region where the Urey number, Ur, is close to the accepted value; a third Ra-sigma(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-sigma(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, Rat, 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 present-day continents is not generated in a single process at the beginning of the thermal evolution of the Earth but in episodically distributed processes. This is in accord with observation.