A lithospheric magnetic field model to spherical harmonic degree 1300

Detailed mapping of the Earth's magnetic field brings key constraints on the composition, dynamics, and history of the crust. Satellite and near-surface measurements detect different length scales and are complementary. However, direct global inversion of a design matrix built with magnetic field measurements locations of near surface and satellite data is numerically intractable at high spatial resolutions.

We apply a procedure developed during the Swarm mission satellite preparation phase to bypass this severe computing issue. We first select the magnetic field measurements during magnetically quiet days of the German CHAMP satellite up to year 2010 and of the ESA Swarm satellites from January 2014 to 31^st August 2022. We then build a a complete dataset by combining the selected satellite measurements with the second version of the World Magnetic Anomaly Map; the most globally complete grid of airborne and marine data.

We follow a regional approach for the modelling of the full vector, scalar and gradient dataset. We compute a series of spherical cap harmonic models within 700 overlapping spherical caps tiling the Earth’s sphere. This regional strategy allows us to perform linear inverse problems in parallel using robust procedures, to deal with the Backus effect in equatorial regions, and to assess independently each regional model. The complete procedure is described in Thébault, Erwan, et al. "A Spherical Harmonic Model of Earth's Lithospheric Magnetic Field up to Degree 1050." Geophysical Research Letters 48.21 (2021): e2021GL095147).  We finally transform the series of regional models into a unique set of spherical harmonic (SH) Gauss coefficients. This produces the first global model to SH degree 1300. The new model agrees with previous satellite-based models at large wavelengths and fits the CHAMP and Swarm satellite data down to expected noise levels. Further assessment in the geographical and spectral domains show that the model is stable when downward continued to the Earth's surface.