Broadband a priori temporal cross-covariances for the geomagnetic inverse problem: application to the satellite era

Abstract We present COV-SAT, a magnetic field model covering the era of continuous satellite monitoring from space, constrained by ground-based and virtual observatory data. It incorporates as a priori information temporal cross-covariances associated with auto-regressive processes of order 3. These are derived analytically, and rely on a small number of free parameters (variances and time-scales) deduced from spectral properties extracted from long magnetic records and geodynamo simulations. The new a priori information proposed here encompasses power spectra stemming from paleomagnetic, observatory and satellite records, statistically replicating magnetic variations over a broad range of time-scales. It, furthermore, allows the cutoff in the spectral density expected for periods shorter than $$\approx 2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>≈</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:math> years, the Alfvén time in Earth’s core, to be mimicked. Field model coefficients are projected in time based on the a priori cross-correlation functions, avoiding the use of arbitrary temporal basis functions. This formalism is exploited to forecast the field evolution, and to provide uncertainties for the estimated main field and its secular variation over the upcoming 5 years. Graphical Abstract