Studies of Mantle Dynamics and Evolution

这项工作将调查板块构造和地球整个历史演变之间的关系。我们将研究放射性热源和地幔粘度对构造板块的速度以及大洋中脊的融化和热损失率的影响。我们最近发展的地幔对流和表面板块的理论预测了不同类型的板块构造，我们将确定这可能如何影响地球的热演化，地核的冷却（控制磁场）以及地球历史上大陆和海洋的形成和再循环的速度。这些结果将有助于确定地球内部放射性热源的数量，海洋中的水再循环回固体地球的速度，以及地球上对流和板块构造的时间变化，并估计地球历史上当前状态与以前条件的相似程度。边界层对流的新模型包括表面上的强板块以及地幔中的黏性分层，这使得对地球热演化的处理比以前的均匀地幔模型更加真实。该模型以岩石圈和上下地幔的机械能守恒为基础，得到了热传递、板块速度和对流速度随瑞利数和其他参数的函数的解析表达式。与数值模拟的情况不同，从解析公式和结果可以明显看出模型中参数对结果的依赖性。与全数值模型的数小时（或数天）相比，可以在几秒钟内评估解决方案。板块行为的主要决定因素是地幔流对岩石圈的粘性应力与岩石圈强度的比值。地幔应力依赖于地幔黏度，而黏度又强烈依赖于温度和含水量，上下地幔可能具有不同的依赖关系。该模型首次允许对这些问题进行有效的调查。初步结果已经表明，该模型可以解决地球化学对地幔放射性加热的估计与地球物理热演化模型（Urey比率）的推断之间长期存在的不一致，这是当前关于地球精确组成的研究和争论的核心问题。将水对流变学的影响与海洋通过地幔循环的模型结合起来，将有助于研究海洋体积随地质时间的变化，以及更普遍的地球化学循环问题。最后，该模型的一般解析公式和实现将允许其应用于其他行星，无论是太阳系内的行星还是其他恒星周围的系外行星。

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.