Numerical experiments on coupled magmatism‐mantle convection system: Implications for mantle evolution and Archean Continental Crusts
Authors: Ogawa Masaki 
Published: February 2008

Numerical experiments on the simple models of coupled mantle magmatism‐mantle convection system were made to study the thermal and chemical evolution of the Earth's mantle. Mantle convection is modeled by the convection of a two‐component Newtonian constant‐viscosity fluid in an internally heated two‐dimensional rectangular region. The density of the convecting fluid is assumed to depend on its chemical composition as well as its temperature. The two components of the convecting fluid are assumed to constitute an eutectic system. Mantle magmatism (i.e., magma segregation in the mantle) is modeled by differentiation of the eutectic mixture from the convecting fluid. This chemical differentiation is assumed to occur when the temperature T increases to the solidus temperature Ts (assumed to increase linearly with depth) owing to convective heat transport. Taking into account the change in density distribution due to this chemical differentiation, we solve the basic equations for convection numerically as an initial value problem. We find that how the mantle evolves depends strongly on two quantities: H (internal heating rate) and r* ≡(ρm − ρε)/Δρ(ρm is the density of undifferentiated mantle material at 0°C, ρe is the density of the eutectic mixture at 0°C, and Δ ρ(> 0) is a measure of density change in the mantle due to thermal expansion); r* represents the magnitude of the dependence of density on chemical composition. (1) When −4 ≲r*≲ −2 and H < Hc (a threshold), the temperature in deep mantle Tav decreases with time. Mantle magmatism occurs owing to high temperatures Tav during the early stage of mantle evolution. The residue of magma produced by this early mantle magmatism occupies the uppermost part of mantle. As Tav decreases, however, mantle magmatism subsides, and the residue of magma produced by earlier mantle magmatism is mixed with undifferentiated materials in the deep mantle owing to convection. This chemical evolution keeps the heat flow at the surface q nearly constant in spite of decreasing Tav. (2) When −4 ≲r*≲ −2 and H> Hc, Tav increases with time, while q continues to be nearly constant. Magmatism occurs to produce a residue, which occupies the uppermost part of mantle, throughout the evolutionary history of the mantle. (3) When −1 < r* < 1, the mantle continues to be chemically homogeneous throughout its evolutionary history in spite of the presence of mantle magmatism because of mixing due to mantle convection, while q and Tav change with time in a manner predicted in the earlier studies on the thermal history of mantle. (When −2≲r*≲ −1, a transitional type of evolution that falls between the type 1 or 2 and the type 3 occurs.) (4) When r*> 1 and H>Hc*, Tav increases with time, while q decreases with time. Mantle magmatism occurs to produce a residue, which accumulates at the bottom of mantle, throughout the evolutionary history of the mantle. We also find that mantle magmatism occurs episodically when r* > 1 and r* ≲ −2, while mantle magmatism occurs continuously when −1 < r* < 1. From an estimate of r* appropriate for the Earth's mantle and known features of the Archean continental crusts, we conclude that the type 1 mantle evolution occurs beneath the continental crusts; many features of the Archean continental crusts fit in with the framework of the type 1 mantle evolution.