Reconstruction of 3-D core flows using magnetic data from Swarm and MSS-1

The dynamics of Earth’s liquid outer core are essential for understanding geomagnetic field variations. Conventional kinematic inversion methods are typically limited to recovering flow structures near the core–mantle boundary. In contrast, dynamic inversion approaches such as geomagnetic data assimilation have the potential to resolve flow structures at greater depths. However, the practical application of dynamic inversion remains challenging due to observational limitations and computational constraints. In this study, we propose an inversion method that lies between the kinematic and dynamic approaches. It is based on the full vector form of the magnetic induction equation under the frozen flux assumption combined with an inertial mode representation of the flow. This method leverages the expected rotation-dominated structure of the flow together with observational constraints, enabling the recovery of both core-surface flows and some deeper flow structures. The inversion process is realized through physics-informed neural networks. Synthetic dynamo simulations demonstrate that our inversion framework is able to capture large-scale 3-D core flow patterns. Moreover, by utilizing high-precision magnetic data from the Swarm constellation and the Macau Science Satellite-1, we reconstruct a 3-D core flow model within Earth’s outer core over the past decade. Our 3-D core flow model reveals a dominant planetary gyre in the Atlantic hemisphere and pronounced shear-induced helical flow structures in the Pacific hemisphere, characterized by significant downwelling beneath Latin America and upwelling beneath the Indian Ocean. • A new inversion framework is developed to reconstruct 3-D core flows from satellite magnetic observations. • The core flow is expressed as an expansion of quasi-geostrophic inertial modes. • The inversion leverages the vector magnetic induction equation, implemented via physics-informed neural networks. • A 3-D core flow model from 2014–2024 is derived from a core field model using Swarm and MSS-1 data. • The model reveals a planetary-scale gyre in the Atlantic hemisphere and shear-driven helical flows in the Pacific hemisphere.