Searching for models of thermo-chemical convection that explain probabilistic tomography. II—Influence of physical and compositional parameters

Abstract

We continue the exploration of the model space of thermo-chemical convection that we started in a previous study [Deschamps, F., Tackley, P.J., 2008. Exploring the model space of thermo-chemical convection. I—Principles and influence of the rheological parameters. Phys. Earth Planet. Inter. 171, 357–373]. In this second part, we study the influence of the Rayleigh number, the internal heating, the Clapeyron slope of the 660-km transition, the chemical density contrast between dense and regular materials (buoyancy ratio), and the volume fraction of dense material. We apply the same analysis and test the chemical and thermal density distributions predicted by various thermo-chemical models against those predicted by probabilistic tomography. Varying the reference Rayleigh number within a reasonable range of values for the Earth's mantle, we find significant differences in the flow pattern and efficiency of mixing. A Rayleigh number equal to 1/3 only of the standard value (10 8) helps to maintain compositional anomalies throughout the system during a long period of time. The internal heating has no or very little influence on the flow pattern and the efficiency of mixing. An endothermic phase transition with a (non-)dimensional Clapeyron slope lower than −1.0 MPa/K strongly inhibits the mass exchange and thus the efficiency of mixing. It provides a convenient way to maintain strong compositional anomalies in the lower mantle during a long period of time. The stability of the layer of dense material is mainly controlled by the buoyancy ratio, and the influence of the volume fraction of dense material is only of second order. These experiments, together with those performed in our previous study, suggest that four ingredients may enter a successful thermo-chemical model of convection for the Earth's mantle: (1) A buoyancy ratio between 0.15 and 0.25, which is equivalent to a chemical density contrast in the range 90–150 kg/m 3; (2) a large (≥10 4), thermal viscosity contrast, which creates and maintains pools of dense material at the bottom of the mantle; (3) a viscosity contrast at d = 660 km around 30; and (4) a Clapeyron slope of the phase transition at d = 660 km of about −3.0 to −1.5 MPa/K. In addition, pools of dense material can be generated and maintained for a large range of values of the chemical viscosity contrast, but the detailed structure of the pools significantly depends on this parameter.