Three-Dimensional Rotational Dynamics and Coupling of the Core-Mantle System

对地球深处的性质和动力学的研究必然依赖于间接观测。地震学研究提供了关于地球深部及其边界的物理性质的信息，在某些情况下，重复观测可以揭示地球深部的动力学；例如，观测到的固体内核的“超旋转”。地磁长期变化的研究提供了对流体核表面流体流动性质的深入了解，以及对地球深部物理性质的间接信息。行星的旋转动力学提供了关于地球深层内部的额外信息来源，并且发展对行星旋转动力学的更完整的理解是这个项目的目标。地球自转的变化既涉及自转速率的变化（观测到的是白昼长度的变化，与所谓的流体核心的扭转振荡流动有关），也涉及旋转轴相对于天体参照系的方向的变化（由与太阳、月球和行星的引力相互作用引起的周期性波动称为章动）。日长变化和章动都涉及到地幔、外核和内核之间的角动量交换。这些区域之间耦合的强度取决于地球的物理性质，如地核内磁场的强度和几何形状、地核和下地幔的电导率以及内外核的粘度。尽管日长变化和章动都涉及类似的动态效应，并提供了关于地球深部性质的补充证据，但以前的工作倾向于分别分析这些现象。该项目的第一个目标是完善和协调章动模型和日长变化模型中对核-地幔耦合的理论描述。在这样做的过程中，我们将利用已经出现的理论进步来改进一种模型，但尚未应用于另一种模型。例如，章动模型中的粘性耦合理论比日长模型中的理论发展得更充分。另一方面，最近的工作改进了对日长模型中磁场几何形状的描述，并认识到一个通常被忽视的效应的重要性，该效应会增加核-幔边界的欧姆耗散。利用更新的模型，我们将重新分析现有的旋转数据集，以获得对地球深部物理特性的改进估计。在这个项目的最后阶段，我们将开发一个单一的模型，可以自一致地描述章动和扭转振荡。这将允许对独立数据集进行联合反演，进一步改善对地球深部物理特性的限制。联合模型将用于研究系统内交叉耦合的动力学，包括扭转振荡激发被称为马科维茨摆动的旋转轴方向观测到的十年周期变化的可能性，以及提出的钱德勒摆动（周期为433天）的相位跳跃时间与所谓的地磁跳变（也与扭转振荡有关）之间的相关性。我们获得的有关地球核-地幔系统的物理性质和短时间尺度动力学的新信息，将有助于测试地球动力过程的数值模型，而地球动力过程是产生地球磁场的原因。

Investigation of the properties and dynamics of the deep interior of the Earth necessarily relies on indirect observations. Seismological studies provide information on the physical properties of the deep Earth and its boundaries and in some cases repeat observations can reveal the dynamics of the deep Earth; for example, the observed 'super-rotation' of the solid inner core. Study of geomagnetic secular variation provides insight on the nature of fluid flow at the surface of the fluid core, and indirect information on the physical properties of the deep Earth. The planet's rotational dynamics provide an additional source of information on the Earth's deep interior and developing a more complete understanding of planetary rotational dynamics is the goal of this project. Variation in the Earth's rotation involves changes in both the rate of rotation (observed as a change in the length of day and correlated with so-called torsional oscillation flow in the fluid core) and the orientation of the rotation axis with respect to the celestial reference frame (periodic fluctuations arising from gravitational interaction with the sun, moon and planets are referred to as nutations). Both length-of-day variations and nutations involve angular momentum exchange between the mantle, outer core and inner core. The strength of the coupling between these regions depends on physical properties of the Earth such as the strength and geometry of the magnetic field within the core, the electrical conductivity of the core and lower mantle, and the viscosities of the outer and inner cores. Although both length-of-day variations and nutations involve similar dynamic effects and provide complementary evidence on the nature of the deep Earth, previous work has tended to analyse these phenomena separately. The first goal of this project is to refine and harmonise the theoretical descriptions of core-mantle coupling in models of nutation and of length-of-day variation. In so doing, we will take advantage of theoretical advances that have occurred to improve one of the types of model, but that have not yet been applied to the other. For example, the theory of viscous coupling in nutation models is more fully developed than that in models of length-of-day. On the other hand, recent work has led to improved descriptions of the geometry of the magnetic field in length-of-day models, and an appreciation for the importance of a commonly neglected effect that adds to ohmic dissipation at the core-mantle boundary. Using the updated models we will reanalyse the existing rotation data sets to obtain improved estimates of the physical properties of the deep Earth. In the final stage of this project we will develop a single model that can self-consistently describe both nutations and torsional oscillations. This would allow for joint inversion of the independent data sets, providing further improvements in the constraints on the physical properties of the deep Earth. The joint model will be used to investigate the dynamics of cross-coupling within the system, including the possibility that torsional oscillations excite an observed decadal-period variation in the orientation of the rotation axis known as the Markowitz Wobble, and a proposed correlation between the timing of phase jumps in the Chandler Wobble (which has a period of 433 days) and so-called geomagnetic jerks (which have also been linked to torsional oscillations). The new information that we gain concerning the physical properties and short time scale dynamics of the Earth's core-mantle system will be useful for testing numerical models of the geodynamo process that is responsible for generation of the Earth's magnetic field.