The proposed research addresses one of the central problems in understanding the evolution and current state of the solid Earth: Whether the Earth?s mantle convects as a whole, or whether it is composed of separately convecting layers. This determines the extent of communication of material from the Earth?s deepest interior to the surface. Evidence from geochemistry, seismology and geodynamics has so far produced contradictory conclusions, and an important consideration involves the high viscosity of the deeper mantle.
This proposal is to develop and investigate models of convection and the thermal evolution of the Earth and its dependence on viscosity layering in the mantle, as well as on some aspects of plate tectonics. The results will include estimates of the heat and mass transport from the lower mantle over Earth history, as well as its dependence of various parameters of the model. This will be compared with estimates from geochemical models based on noble gas isotopic measurements that constrain the lower mantle mass flux. The models will be based on parameterized treatments of mass and energy conservation, and will be verified against numerical calculations. They will allow the results of more detailed numerical calculations to be understood in the context of uncertainties in the governing parameters and features such as variable plate geometry. The model will also address some effects that arise from the three dimensional nature of convection and plate tectonics on the Earth.
The expected results of the models will contribute to the understanding of the evolution of the Earth and its internal state, and questions such as whether or not there is a need for undiscovered or hidden layers deep in the mantle. It will also help to understand the temporal variability of convection and plate tectonics on the Earth, and estimate how representative the present state is of the longer term evolution of the Earth.
On the Dynamics of Plate Tectonics: Multiple Solutions, the Influence of Water, and Thermal Evolution An analytic boundary layer model for thermal convection with a finite-strength plate and depth-dependent viscosity is developed. The model includes a An analytic boundary layer model for thermal convection with a finite-strength plate and depth-dependent viscosity is developed. The model includes a specific energy balance for the lithosphere and accounts for coupling between the plate and underlying mantle. Multiple solutions are possible with three solution branches representing three distinct modes of thermal convection. One branch corresponds to the classic boundary layer solution for active lid plate tectonics while two new branches represent solutions for sluggish lid convec- tion. The model is compared to numerical simulations with highly temperature dependent viscosity and is able to predict both the type of convection (active, sluggish, or stagnant lid) as well as the presence of single and multiple solution regimes. The existence of multiple solutions suggests that the mode of planetary convection may be history dependent. The dependence of mantle viscosity on temperature and water concentration is found to introduce a strong dynamic feedback with plate tectonics. A dimensionless parameter is defined to quantitatively evaluate the relative strength of this feedback and demonstrates that water and heat transport may be equally important in controlling present day plate-mantle dynamics for the Earth. A simple parameterized evolution model illustrates the feedback and agrees well with our analytic results. This suggests that a simple relationship may exist between the rate of change of water concentration and the rate of change of temperature in the mantle. The results indicate that a planet can progress through different stages of evolution, with different plate tectonic exxpressions. The planet may start with a sluggish plate, for example, and then move into a regime with mobile plate tectonics (as on the present Earth). The transitions can be abrupt, and there is hysteresis between transitions in different directions. It is possible that such transitions have occured during the Earth's evolution, and and the model results provide a guide for searching for their effects in the geologic record.
