Building time dependent magnetic field models satisfying the frozen-flux radial induction equation

一般来说，从磁场的角度研究地核时，要依次考虑以下两个问题：计算磁场模型，在此基础上计算流动模型。然而，很明显，原则上这些模型是相互联系的，应该同时分析。事实上，流动本身是核心磁场的来源，因此从流动中导出的物理约束可以提高磁场建模的质量。因此，我们建议通过拟合卫星和天文台数据来建立磁场模型，这些模型满足冻结通量径向感应方程的要求，其中流动本身被约束到物理上可接受的空间和时间形态和行为。这种模型的建立和实现对流动的参数化和反问题的正则化提出了一些数学上的挑战。

In general, the following two problems are considered sequentially when investigating theEarth’s core from a magnetic point of view:computing a magnetic field model,computing a flow model based on this modelHowever, it is obvious that in principle these models are connected and should be analyzedsimultaneously. Indeed, the flow itself is the source of the core magnetic field and thereforephysical constraints derived from the flow may enhance the quality of magnetic fieldmodeling. We therefore propose to build models of the magnetic field by fitting satelliteand observatory data, under the requirement that these models satisfy the frozen-flux radialinduction equation, where the flow itself is constrained to physically acceptable morphologiesand behavior in space and time. The construction and the implementation of suchmodels sets some mathematical challenge concerning the parameterization of the flow andthe regularization of the inverse problem.