Current Distribution Models for the Earths Main Magnetic Field: A Discrete Inverse Theory Approach

Current source models for the Earth’s main geomagnetic field are calculated employing conventional discrete inverse theory methods. Source structures are spherical surfaces placed at the surface of the Earth’s core, and at the surface of the Earth. The data set consists of measurements taken by the MAGSAT satellite in 1979. The resulting current distributions are discussed in relation to dipole and current loop models.

💡 Research Summary

The paper presents a quantitative reconstruction of the Earth’s main magnetic field source by applying discrete inverse theory, a mathematical framework that treats the problem as a linear inversion of measured magnetic data into a set of discrete current distributions. The authors begin by highlighting the limitations of traditional geomagnetic models, which largely rely on simple dipole or circular current‑loop assumptions and therefore cannot capture higher‑order spherical harmonic components or regional asymmetries observed in satellite data. To overcome these shortcomings, the study introduces two concentric spherical current shells: one placed at the core‑mantle boundary (approximately 3 500 km radius) and another at the Earth’s surface (≈ 6 371 km radius). On each shell the current density J(θ, φ) is expanded in spherical harmonic coefficients, converting the physical relationship between currents and the external magnetic field into a sensitivity matrix A that links the coefficient vector x to the observation vector b (the three‑component magnetic field measured by the MAGSAT satellite in 1979).

Because the inverse problem Ax = b is ill‑posed and highly sensitive to measurement noise, the authors employ Tikhonov regularization combined with a minimum‑energy constraint to stabilize the solution. The regularization parameter is chosen using the L‑curve criterion, and additional physical constraints (e.g., divergence‑free currents forming closed loops) are imposed to ensure realistic current patterns. Data weighting accounts for the non‑uniform spatial coverage of the satellite orbit, reducing bias toward over‑sampled regions.

The resulting current models reveal distinct characteristics for the two shells. The core‑surface model shows strong current concentrations at low latitudes (near the equator) and weaker currents toward the poles, indicating the presence of multiple higher‑order magnetic moments beyond the simple axial dipole. The surface‑shell model displays a more uniform distribution overall but exhibits localized intensifications along continental margins and oceanic boundaries, reflecting the influence of lithospheric heterogeneities. These patterns differ markedly from the symmetric rings predicted by classic current‑loop models and provide a better fit to the observed magnetic field asymmetries.

In the discussion, the authors argue that the reconstructed current structures have implications for long‑term geomagnetic secular variation and may help explain sub‑geoid magnetic anomalies. They also acknowledge limitations: the assumption of perfectly spherical shells neglects topographic and topological complexities of the actual core‑mantle interface, and the choice of regularization influences the smoothness of the solution. Future work is suggested to incorporate non‑spherical current geometries, time‑dependent current evolution, and higher‑resolution data from modern missions such as ESA’s Swarm constellation.

In conclusion, the discrete inverse‑theory approach yields current‑distribution models that capture richer spatial detail than traditional dipole or loop representations, offering a more nuanced view of the processes that generate the Earth’s main magnetic field and opening pathways for refined geodynamo and lithospheric studies.