On the Recovery of Core and Crustal Components of Geomagnetic Potential Fields

In geomagnetism it is of interest to separate 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 contributions 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, ${\mathbb{S}}_{R_0}$ (crust) and ${\mathbb{S}}_{R_1}$ (core), with radii $R_1 R_0$, we show that it becomes possible if the magnetization $\mathbf{m}$ generating $\Phi_0$ is localized in a strict subregion of ${\mathbb{S}}_{R_0}$. Beyond unique recoverability, we show in this case how to ...