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.
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