A Numerical Model of a Coupled Magmatism—Mantle Convection System in Venus and the Earth's Mantle beneath Archean Continental Crusts

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A numerical model of a coupled magmatism-mantle convection system has been developed to study how a surface-temperature T srfc of a terrestrial planet influences the thermal state and the chemical structure of its mantle. Mantle convection is modeled by a convection of a binary eutectic material A ζB 1-ζ in an internally heated two-dimensional rectangular box; A stands for olivine, B stands for a mixture of pyroxene and garnet, and the eutectic composition (ζ = 0.1) corresponds to a basaltic composition. Initially, the box is chemically homogeneous with ζ = 0.64. The theology of the material is Newtonian with a strongly temperature-dependent viscosity. The density of the material decreases linearly with increasing ζ, temperature, and melt content except in a thin crustal layer at the top of the box. Mantle magmatism (i.e., an upward migration of magma generated at depth in the mantle) is modeled by an extraction of the end member B-rich melt generated at depth by a pressure-release partial melting and the deposit of the extracted melt in the crustal layer at the top of the box. (a) When T srfc is 447°C, a layer of high-ζ, low-density material produced as a residue of melt develops in the upper part of the box and a layer of a dense low-ζ material, which is a mixture of the undifferentiated material and a magmatic product, develops in the lower part of the box. A sharp chemical discontinuity develops between the two layers and the convection occurs us a layered convection. The temperature in the upper layer is significantly lower than expected from the high surface temperature because of the chemical layering. (b) When T srfc is 27°C, a layer of high-ζ material develops in the upper part of the box and a layer of dense low-ζ material develops in the lower part of the box only at the beginning when the temperature is sufficiently high at depth and an active magmatism occurs to produce a large amount of new additions of residue and magmatic product. As time goes, the temperature at depth decreases, the magmatism becomes less active, and the box becomes more and more chemically homogeneous because of the mixing due to convection. Layered convection is unstable and chemical discontinuity does not develop well when T srfc is 27°C. A further calculation at T srfc = 447°C with higher viscosity at the surface reveals that whether or not a chemical discontinuity develops well and a layered convection occurs stably is controlled by the viscosity at the surface, which depends strongly on T srfc. The surface temperature of a terrestrial planet controls the chemical structure of its mantle indirectly through the strong temperature-dependence of the viscosity of mantle material. The qualitative feature of the coupled magmatism-mantle convection system is consistent with many observations of Venus and the Earth's Archean continental crusts.