CMG Research: Constraints on the Earth's thermal history and probing the geomagnetic field beneath the core-mantle boundary using nonlinear inversions

目前关于地球热史的思想以内核的年龄和是否需要核放射性加热来维持磁场的显著争议为标志。这种平衡的一个关键因素是驱动地球发电机所需的能量，它以热量的形式在内部消散。目前的估计主要是基于远离相关参数范围的数值发电机模拟，差异很大。该项目的目的是通过寻找当前场耗散的严格下限来约束地球的热历史。建立在基于观测约束和地球章动模型的现有约束的基础上，提议添加的泰勒约束将施加一个长期以来已知的适用于核心场的重要动力学约束。如果得到的范围足够大，那么对于没有放射性加热的内核寿命的有争议的情景就可以很好地排除。此外，这种变分公式暴露了一些有趣的数学问题，这些问题与将地球发电机视为一个动力系统的考虑密切相关。所得到的最佳场将是三维的和时间相关的，因此第一次提供了证据，证明最近大规模地表特征的大量观测结果是否真的代表了内部场。大规模计算机模拟从根本上改变了科学研究的方式。然而，尽管取得了诸多进步，但在地球物理流体动力学领域，许多最苛刻的计算要求将关键属性，特别是粘度（流体“厚度”）人为设置为较高的值。这种调整对数值结果的影响还不太清楚，而且仍然缺乏比目前预期的任何更好的湍流理论。本提案中概述的所谓变分方法将对地球发电机的数值模拟进行补充和批判。结果不依赖于人为的参数化，它们的解释提供了发电机过程产生的热量的界限，因此是完全严格的。这项工作的关键将是合作努力，将广泛的长期观测数据与数学上适当和数值上易于处理的问题公式联系起来。

Current thinking on the Earth's thermal history is marked by notable controversies on the age of the inner core and whether core radiogenic heating is required in order to maintain the magnetic field. A key factor in this balance is the power required to drive the geodynamo, dissipated internally as heat. Present estimates, primarily based on numerical dynamo simulations operating far from the relevant parameter range, vary significantly. The aim of this project is to constrain the Earth's thermal history by finding rigorous lower bounds for the dissipation of the present field. Building on an existing bound based on constraints from observation and models for the Earth's nutation, the proposed addition of the Taylor constraint will impose a significant dynamical restriction long known to be appropriate for the core field. If the resulting bound is sufficiently increased, then contentious scenarios for the lifetime of the inner core without radiogenic heating may well be excluded. Further, this variational formulation exposes some intriguing mathematical issues germane to consideration of the geodynamo as a dynamical system. The optimal fields resulting will be both three-dimensional and time-dependent and thus for the first time give evidence of whether or not the large body of recent observationally-derived findings of large-scale surface features are really representative of the internal field.Large scale computer simulation has fundamentally altered the way in which science is done. Yet for all the numerous advances, many of the most demanding computations in the area of geophysical fluid dynamics require that key properties, notably viscosity (the fluid "thickness"), be set to artificially high values. The effects of this adjustment on the numerical results are poorly understood and will remain so short of a better theory of turbulence than any presently in prospect. The so-called variational methods outlined in this proposal will both complement and critique numerical simulations of the Earth's dynamo. The results do not rely on artificial parameterizations and their interpretation as providing a bound on heat generated by the dynamo process is thus entirely rigorous. Key to this work will be a collaborative effort to link extensive long term observational data with a mathematically appropriate and numerically tractable formulation of the problem.