Abstract Spherical elementary current systems (SECS) have become a widely used tool to model vector fields on spherical surfaces in ionospheric data analysis. The systems were originally formulated using point sources for the divergence and curl of the fields. In this paper we present a flexible alternative formulation, showing how continuous functions can be used as the basis of the SECS, eliminating the singularities of the original formulation arising from the point source assumption. In addition, we show that the geophysically interesting variables, such as currents and magnetic fields, have closed form expressions if the basis of the SECS is the Poisson kernel. Typically, SECS lead to an ill‐posed linear inverse problem that requires additional numerical regularization. We present a way to adopt a statistical, Bayesian, framework for the regularization, allowing the use of physically interpretable priors in the resulting inverse problem. We verify our approach with a synthetic test data based on the geometry of an existing Fennoscandian magnetometer network, and demonstrate how different prior assumptions influence the inferred currents. We then validate our findings by comparing them with those of a previous case study on the same network. The proposed differentiable and adjustable formulation of SECS, combined with Bayesian inversion, offers a robust alternative for ionospheric data analysis. It provides discretization‐invariant regularization grounded in physical prior knowledge and transparently reveals how these priors shape the interpretation of the results.
Käki et al. (Sun,) studied this question.