Abstract
A numerical model of mantle magmatism in a convecting upper mantle has been developed to study the thermo-chemical evolution of the upper mantle of the early Earth. The solid-state convection in the upper mantle is modeled by a convection of a binary eutectic material with a Newtonian temperature-dependent rheology in a two-dimensional rectangular box placed on a heat bath as a model of the lower mantle. The density depends on the chemical composition and melt-content as well as temperature of the material. The material contains heat-producing elements that are incompatible and exponentially decay with time. Mantle magmatism is modeled by a permeable flow of melt generated by a pressure-release melting induced by the solid-state convection through matrix. The permeable flow is driven by a buoyancy due to the density difference between the melt and the matrix. The thermo-chemical evolution in the box occurs in two stages if the deeper part of the box is not so strongly depleted in heat-producing elements in spite of the upward migration and concentration of heat-producing elements into a crustal layer along the top surface boundary due to magmatism. In the earlier stage, active magmatism occurs because of a strong internal heating due to the heat-producing elements, a chemically stratified structure develops well in the box with dense magmatic products in the deeper part and less dense residual materials in the shallower part, and the temperature distribution becomes strongly superadiabatic over the entire box. The temperature at the base of the box becomes as high as the solidus temperature. The chemically stratified structure is, however, suddenly destroyed by convective mixing and the temperature in the deeper part of the box suddenly drops by several hundred degrees when the internal heat source becomes too weak owing to the decay of heat-producing elements which sustain the active magmatism and hence keep the effect of chemical differentiation due to the magmatism stronger than the effect of convective mixing. In the later stage of the evolution, the box becomes chemically homogeneous and magmatism occurs only mildly. If heat-producing elements are efficiently transported into the crustal layer and the deeper part of the box becomes strongly depleted in heat-producing elements owing to the magmatism, only a mild magmatism occurs even at the beginning, a chemically stratified structure does not develop well, and the temperature in the box rapidly decreases to a stationary value. The regime of hot and chemically stratified upper mantle suggested from the earlier stage of the case with mild depletion of heat-producing elements at depth fits in with many observations of the Archean continental crust.
Published Version
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