A Viscosity Model for the Mantle Based on Diffusion in Minerals and Constrained by the Thermal History and Melting of the Mantle

Viscosity of the mantle is traditionally inferred from geophysical data. However the geophysical approach provides only a spatially averaged information. At high temperature, viscosity is mainly controlled by the diffusivity of the slowest species in the minerals forming the rock assemblage (diffusion creep regime). Therefore to characterize the viscosity of the mantle, one can take a direct approach using the available experimental diffusion data in the most common mantle minerals. In this way the viscosity is expressed as a function of pressure, temperature and mineralogical assemblage. One problem with this method is that the uncertainty (experimental error) can have a significant effect on the characterization of the viscosity model. Here we present our simplified model for the viscosity of the mantle based on the diffusion data in olivine (alpha, beta, gamma) magnesio-wüstite and perovskite. In the upper mantle viscosity is assumed to be controlled by the most abundant mineral (olivine) and by the fastest diffusion process between grain boundary and volume diffusion of silicon, which is considered to be the slowest diffusing species. In the lower mantle the viscosity of the mantle assemblage is determined by a weighted average of the properties in magnesio-wüstite and perovskite. The initial model has been applied to study the thermal history of the mantle and the CMB temperature using a parametrized mantle convection model combined with a thermodynamic formulation, and then refined based on the results of the thermal model. In particular the thermal evolution model must satisfy certain criteria that define the melting temperature requirement in the upper mantle in the past (Archean) and more recent times. Some diffusion parameters have been adjusted within the experimental uncertainty and we have opted for the homogeneous stress model to construct the viscosity of the lower mantle. Our results show a steady increase of viscosity vs depth in the lower mantle and a viscosity drop by ~ an order of magnitude from the transition zone to the top of the lower mantle. The latter result is in contrast to the viscosity jump inferred from geophysical observations. This conclusion applies for the present day most relevant thermal conditions retrieved from the thermal history model. However it is possible that using a multiphase model for the rock assemblage in the transition zone the mineralogical and geophysical models may be in better agreement. As it would be shown here, the viscosity model (and the thermal state of the CMB) combined with a thermodynamic formulation allows us to study the geodynamics of mantle plumes with a considerably smaller number of assumptions than in previous studies. The thermal evolution of the plume in the upper mantle is then applied to model the petrological evolution of melting in hot spots using a coupled thermodynamic and two phase flow model (session DI03, contribution entitled: Present Day Hot Spot Melting Inferred from Geodynamics and Thermodynamics Modeling and the Thermal History of the Mantle).