John R. Baumgardner

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 238U- 206Pb, 235U-207Pb, 232Th-208Pb, 40K-40Ar 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 ).

Plateness of the Oceanic Lithosphere and the Thermal Evolution of the Earth’s Mantle

Compared to [33], the model of the thermal evolution of the Earth’s mantle is considerably improved. The temporal development of the radial viscosity profile due to cooling of the Earth could substantially be taken into account by numerical progress using a new variant of the temperature- and pressure-dependence of the shear viscosity of the mantle, namely Eq (5). The laterally averaged heat flow, the Urey number, the Rayleigh number and the volume-averaged temperature as a function of time come up to the expectations that stem from the parameterized evolution models. The mentioned evolution parameters of the present paper better approximate the observational data. Contrary to the parameterized curves, these quantities show temporal variations. This seems to be more realistic for geological reasons. Due to the activation enthalpy, the presented viscosity profile has a highly viscous transition layer (TL) with steep viscosity gradients at the phase boundaries. A low-viscosity zone is situated above and below the TL, each. The lithosphere moves piecewise en bloc. Thin cold sheet-like downwellings have an Earth-like distribution.

Continental Growth and Thermal Convection in the Earth’s Mantle

The main subject of this paper is the numerical simulation of the chemical differentiation of the Earth’s mantle. This differentiation induces the generation and growth of the continents and, as a complement, the formation and augmentation of the depleted MORB mantle. Here, we present for the first time a solution of this problem by an integrated theory in common with the problem of thermal convection in a 3-D compressible spherical-shell mantle. The whole coupled thermal and chemical evolution of mantle plus crust was calculated starting with the formation of the solid-state primordial silicate mantle. No restricting assumptions have been made regarding number, size and form of the continents. It was, however, implemented that moving oceanic plateaus touching a continent are to be accreted to this continent at the corresponding place. The model contains a mantle-viscosity profile with a usual asthenosphere beneath a lithosphere, a highly viscous transition zone and a second low-viscosity layer below the 660-km mineral phase boundary. The central part of the lower mantle is highly viscous. This explains the fact that there are, regarding the incompatible elements, chemically different mantle reservoirs in spite of perpetual stirring during more than 4.49×109 a. The highly viscous central part of the lower mantle also explains the relatively slow lateral movements of CMB-based plumes, slow in comparison with the lateral movements of the lithospheric plates. The temperature- and pressure-dependent viscosity of the model is complemented by a viscoplastic yield stress, σ y. The paper includes a comprehensive variation of parameters, especially the variation of the viscosity-level parameter, r n, the yield stress, σ y, and the temporal average of the Rayleigh number. In the r n−σ y plot, a central area shows runs with realistic distributions and sizes of continents. This area is partly overlapping with the r n−σ y areas of piecewise plate-like movements of the lithosphere and of realistic values of the surface heat flow and Urey number. Numerical problems are discussed in Sect. 3.

Mantle dynamics - A case study

Solid state convection in the rocky mantles is a key to understanding the thermochemical evolution and tectonics of terrestrial planets and moons. It is driven by internal heat and can be described by a system of coupled partial differential equations. There are no analytic solutions for realistic configurations and numerical models are an indispensable tool for researching mantle convection. After a brief general introduction, we introduce the basic equations that govern mantle convection and discuss some common approximations. The following case study is a contribution towards a self-consistent thermochemical evolution model of the Earth. A crude approximation for crustal differentiation is coupled to numerical models of global mantle convection, focussing on geometrical effects and the influence of rheology on stirring. We review Earth-specific geochemical and geophysical constraints, proposals for their reconciliation, and discuss the implications of our models for scenarios of the Earth’s evolution. Specific aspects of this study include the use of passive Lagrangian tracers, highly variable viscosity in 3-d spherical geometry, phase boundaries in the mantle and a parameterised model of the core as boundary condition at the bottom of the mantle.