Probing the Earth's subdecadal core-mantle dynamics based on satellite geomagnetic field models

CHAMP任务从2000年到2010年在全球范围内提供了大量的地磁数据。其密集的数据覆盖使我们能够建立格林| GFZ参考内磁模型|，该模型在空间和时间上都具有有史以来最高的核心场分辨率。我们已经将无扩散磁感应方程应用于最新版本的GRIMM，模拟了地球外核的流体流动，发现流体流动在亚年代际时间尺度上演变，与观测到的地球自转波动有显著的相关性。这些流动模型证实了外核流体中存在六年扭转振荡。扭转振荡（TO）是一种水磁波，理论上被认为是构成年代际或次年代际地核动力学的最重要因素。它由刚性流体环空的相对方位旋转组成，与地幔的旋转同轴，并与地幔和内核动态耦合。在之前的工作中，已经通过数值模拟研究了TO系统，或者用全数值发电机，或者解决理想地表示TO系统的特征值问题。虽然这些研究对模拟TOs的动力学方面有所了解，但它们并没有直接考虑到地磁场和地球自转的观测结果。特别是，没有利用卫星磁数据或模式对赤道进行基于观测的研究。在本项目中，我们的目标是在卫星磁观测的基础上揭示地球核-地幔系统的年代际动力学和能量学。为此，我们将开展四个工作包(1)至(4)，我们都使用GRIMM。(1)对岩心场和流模型进行时间序列分析，仔细提取不同纬度TOs信号。(2)通过参数化岩心表面的磁扩散，改进了传统的流动建模方案。这里，磁感应方程中恢复了扩散项，通过将其与纳维-斯托克斯方程中的洛伦兹项联系起来，对磁感应方程进行了动态约束。(3)提出了一种计算岩心流体环空上的电磁核幔耦合力矩的方法，并在此基础上计算了每个环空由于焦耳加热引起的能量耗散。这一分析将有助于了解地球的TOs是自由振荡还是强迫振荡。(4)结合(1)~(3)的物理意义和计算工具，最终构建了与格林（GRIMM）和地球自转观测相一致的地球TOs和核幔耦合动力学模型。该模型的独特之处在于在时域上研究了与TOs相关的力平衡，并且该模型还旨在通过考虑岩心动力学来改进基于观测的岩心流模型。

The CHAMP mission provided a great amount of geomagnetic data all over the globe from 2000 to 2010. Its dense data coverage has allowed us to build GRIMM | GFZ Reference Internal Magnetic Model | which has the highest ever resolution for the core field in both space and time. We have already modeled the fluid flow in the Earth's outer core by applying the diffusionless magnetic induction equation to the latest version of GRIMM, to find that the flow evolves on subdecadal timescales, with a remarkable correlation to the observed fluctuation of Earth rotation. These flow models corroborated the presence of six-year torsional oscillations in the outer core fluid. Torsional oscillation (TO) is a type of hydromagnetic wave, theoretically considered to form the most important element of decadal or subdecadal core dynamics. It consists of relative azimuthal rotations of rigid fluid annuli coaxial with the mantle's rotation and dynamically coupled with the mantle and inner core. In preceding works, the TOs have been studied by numerical simulations, either with full numerical dynamos, or solving eigenvalue problems ideally representing the TO system. While these studies drew insights about dynamical aspects of the modeled TOs, they did not directly take into account the observations of geomagnetic field and Earth rotation. Particularly, there have been no observation-based studies for the TO using satellite magnetic data or models. In the proposed project, we aim at revealing the subdecadal dynamics and energetics of the Earth's core-mantle system on the basis of satellite magnetic observations. To that end, we will carry out four work packages (1) to (4), for all of which we use GRIMM. (1) We perform time-series analyses of core field and flow models, to carefully extract the signals from TOs at different latitudes. (2) We refine the conventional flow modeling scheme by parameterizing the magnetic diffusion at the core surface. Here, the diffusion term is reinstated in the magnetic induction equation, which is dynamically constrained by relating it to the Lorentz term in the Navier-stokes equation. (3) We develop a method to compute the electromagnetic core-mantle coupling torque on the core fluid annuli, whereby the energy dissipation due to the Joule heating is evaluated for each annulus. This analysis would provide insights on whether the Earth's TOs are free or forced oscillations. (4) Bringing together physical implications and computational tools obtained by (1) to (3), we finally construct a dynamical model for the Earth's TOs and core-mantle coupling such that they are consistent with GRIMM and Earth rotation observation. This modeling is unique in that the force balances concerning the TOs are investigated in time domain, as well as that the modeling also aims at improving the observation-based core flow model by considering the core dynamics.