Modeling petrological geodynamics in the Earth's mantle

Abstract

We have developed an approach that combines principles of fluid dynamics and chemical thermodynamics into a fully coupled scheme to model geodynamic and petrological evolution of the Earth's mantle. Transport equations involving pressure, temperature, velocities, and bulk chemical composition are solved for one or more dynamic phases and interfaced with the thermodynamic solutions for equilibrium mineralogical assemblages and compositions. The mineralogical assemblage and composition are computed on a space‐time grid, assuming that local thermodynamic equilibrium is effectively achieved. This approach allows us to simultaneously compute geophysical, geochemical, and petrological properties that can be compared with a large mass of observational data to gain insights into a variety of solid Earth problems and melting phenomena. We describe the salient features of our numerical scheme and the underlying mathematical principles and discuss a few selected applications to petrological and geophysical problems. First, it is shown that during the initial stage of passive spreading of plates, the composition of the melt near Earth's surface is in reasonable agreement with the average major element composition of worldwide flood basalts. Only the silica content from our model is slightly higher that in observational data. The amount of melt produced is somewhat lower than the estimated volumes for extrusive and upper crustal intrusive igneous rocks from large igneous provinces suggesting that an active upwelling of a larger mantle region should be considered in the process. Second, we have modeled a plume upwelling under a moving plate incorporating the effects of mineralogy on the density structure and viscous dissipation on the heat transport equation. The results show how these effects promote mantle instability at the base of the lithosphere. Third, we have considered a mantle convection model with viscosity and density directly related to the local equilibrium mineralogical assemblage. Interesting lateral variations and significant differences in the viscosity structure of the upper and lower mantle are revealed from our model results. The averaged viscosity variations with depth retrieved from our numerical simulations seem to reproduce the main features of the mantle viscosity structure under the Pacific ocean obtained from recent studies based on inversion of seismic data.