A bifurcation in the coupled magmatism-mantle convection system and its implications for the evolution of the Earth's upper mantle

Abstract

A numerical model is presented for the coupled magmatism-mantle convection system in the upper mantle to study how the coupled system controls the thermochemical state of the upper mantle depending upon the internal or basal heating rate. The solid-state convection in the upper mantle is modeled as a convection of a binary eutectic material with constant viscosity in a two-dimensional rectangular box uniformly heated from the bottom boundary or by an internal heat source. The density of the material depends on the composition and melt-content as well as temperature. Magmatism is modeled as a permeable flow of the melt generated by a pressure-release partial melting of the material; the permeable flow is driven by the buoyancy of the melt. There are two branches in the thermochemical state controlled by the coupled system for both of the basal and internal heating cases. On one branch called the TC-branch, the solid-state convection occurs dominantly as a thermal convection, the box remains chemically homogeneous as a whole, and magmatism occurs only slightly at most. The TC-branch is stable only when the heating rate is lower than a threshold; a bifurcation occurs on the TC-branch at the threshold and the thermochemical state falls on another branch called the CS-branch above the threshold. An episodic magmatism actively occurs, a chemically stratified structure develops well in spite of the homogenizing effect of convective stirring, the temperature becomes as high as the solidus temperature at depth, and the convection is strongly affected by the buoyancy of melt and the chemical buoyancy that accompanies the chemical stratification on the CS-branch. The CS-branch is stable even at heating rates slightly lower than the threshold; a hysteresis in the thermochemical state occurs between the two branches as the heating rate changes around the threshold. The observations of tectosphere suggest that the thermochemical state on the CS-branch occurred in the upper mantle in the Archean and early Proterozoic when the mantle was strongly heated by radioactive elements and that the thermochemical state jumped to the TC-branch at the end of the early Proterozoic.