Studies of Mantle Dynamics and Evolution

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This work will investigate the relationship between plate tectonics and the evolution of the Earth throughout its history. We will study the effects of radioactive heat sources and the viscosity of the Earth's mantle on the speed of tectonic plates and the rate of melting and heat loss at mid-ocean ridges. Our recently developed theory of mantle convection with plates on the surface has predicted different styles of plate tectonics, and we will determine how this may have influenced the thermal evolution of the Earth, the cooling of the Earth's core (which controls the magnetic field) and the rate of the formation and recycling of the continents and the ocean over Earth history. The results will help determine the amount of radioactive heat sources within the Earth, and the rate of recycling the water in the oceans back into the solid Earth, as well as the temporal variability of convection and plate tectonics on the Earth, and estimate how similar the present state is to previous conditions over Earth history.The new model of boundary layer convection includes strong plates on the surface as well as viscosity layering in the mantle, which allows a much more realistic treatment of the Earth's thermal evolution than previous uniform-mantle models. The model is based on conservation of mechanical energy for the lithosphere and the upper and lower mantles, which results in an analytical formulation for heat transport, plate and convection speeds as functions of the Rayleigh number and other parameters. The dependence of the results on parameters in the model is apparent from the analytic formulation and results, unlike the case for numerical simulations. The solutions can be evaluated in seconds, compared to hours (or days) for fully numerical models. The main determinant of plate behavior is the ratio of viscous stress on the lithosphere from mantle flow to the strength of the lithosphere. Mantle stresses depend on mantle viscosity, which depends strongly on temperature and water content, and the upper and lower mantle may have different dependencies. The model allows these to be investigated efficiently, for the first time. Preliminary results already indicate that the model may resolve a longstanding discordance between geochemical estimates of mantle radioactive heating and inferences from geophysical thermal evolution models (the Urey ratio), which is a central issue related to current studies and debates about the precise composition of the Earth. The incorporation of the effects of water on rheology together with models of recycling the oceans through the mantle will contribute to investigations of variation of ocean volume over geologic time, as well as more general problems of geochemical recycling. Lastly, the general analytic formulation and realization of the model will allow its application to other planets, both within the solar system and as exoplanets around other stars.