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

从2000年到2010年，CHAMP任务在全球范围内提供了大量的地磁数据。其密集的数据覆盖范围使我们能够建立Grimm|GFZ参考内部磁模型|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。我们已经通过将无扩散磁感应方程应用于最新版本的GRIMM来模拟地球外核中的流体流动，发现流动在亚十年的时间尺度上演变，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长达六年的扭转振荡。扭振(TO)是流体磁波的一种，理论上被认为是十年或亚十年内核动力学中最重要的元素。它由刚性流体环空与地幔自转同轴、与地幔和地核动态耦合的相对方位向旋转组成。在以前的工作中，已经通过数值模拟来研究TO系统，或者使用全数值发电机，或者求解理想地代表TO系统的特征值问题。虽然这些研究得出了关于模拟目标的动力学方面的见解，但它们没有直接考虑到对地磁场和地球自转的观测。特别是，目前还没有以观测为基础的研究，以使用卫星磁场数据或模型。在拟议的项目中，我们的目标是在卫星磁观测的基础上揭示地球核-地幔系统的亚十年动力学和能量学。为此，我们将执行四个工作包(1)至(4)，所有这些工作包我们都使用格林。(1)对核心场模型和流动模型进行时间序列分析，对不同纬度的TOS信号进行精细提取。(2)通过对堆芯表面的磁扩散进行参数化，改进了传统的流动模拟方案。这里，在磁感应方程中恢复了扩散项，通过将其与Navier-Stokes方程中的洛伦兹项联系起来，动态地约束了扩散项。(3)提出了一种计算岩心流体环空电磁核幔耦合力矩的方法，从而计算了每个环空由于焦耳加热引起的能量耗散。这一分析将为了解地球的ToS是自由振荡还是强迫振荡提供洞察力。(4)结合(1)到(3)中的物理含义和计算工具，我们最终建立了一个地球TOS和核幔耦合的动力学模型，使它们与GRIMM和地球自转观测结果相一致。这种建模的独特之处在于，在时间域中研究了与ToS有关的力平衡，并且该建模还旨在通过考虑岩心动力学来改进基于观测的岩心流动模型。

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.