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On the recovery of core and crustal components of geomagnetic potential fields

Abstract : In Geomagnetism it is of interest to separate the Earth's core magnetic field from the crustal magnetic field. However, measurements by satellites can only sense the sum of the two contributions. In practice, the measured magnetic field is expanded in spherical harmonics and separation into crust and core contribution is achieved empirically, by a sharp cutoff in the spectral domain. In this paper, we derive a mathematical setup in which the two contributions are modeled by harmonic potentials Phi(0) and Phi(1) generated on two different spheres S-R0 (crust) and S-R1 (core) with radii R-1 < R-0. Although it is not possible in general to recover Phi(0) and Phi(1) knowing their superposition Phi(0) + Phi(1) on a sphere S-R2 with radius R-2 > R-0, we show that it becomes possible if the magnetization m generating Phi(0) is localized in a strict subregion of S-R0. Beyond unique recoverability, we show in this case how to numerically reconstruct characteristic features of Phi(0) (e.g., spherical harmonic Fourier coefficients). An alternative way of phrasing the results is that knowledge of m on a nonempty open subset of S-R0 allows one to perform separation.
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https://hal.inrae.fr/hal-02626950
Déposant : Migration Prodinra <>
Soumis le : mardi 26 mai 2020 - 18:31:19
Dernière modification le : dimanche 5 juillet 2020 - 03:09:49

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L. Baratchart, C. Gerhards. On the recovery of core and crustal components of geomagnetic potential fields. SIAM Journal on Applied Mathematics, Society for Industrial and Applied Mathematics, 2017, 77 (5), pp.1756-1780. ⟨10.1137/17M1121640⟩. ⟨hal-02626950⟩

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