Localized crustal magnetic field inversion using inner- and outer-source altitude vector Slepian functions

Abstract:

When inverting for a planetary magnetic potential from vector-valued satellite magnetic field data we need to take into account that the recorded data also contain fields not stemming from the planet but from outer sources in space. In classical global spherical-harmonic analysis this is done by fitting, in addition to the inner sources potential field, a linear combination of outer-source spherical harmonics to the data. This approach has been successfully applied to data with global homogeneous coverage and quality but is not suited for purely regional data. In many situations a local method would be beneficial to take full advantage of data with regionally varying quality or coverage, or to avoid ringing artifacts from sharp intensity contrasts. Here we present a local method that allows such a magnetic source separation. We simultaneously create inner-source and outer-source altitude vector Slepian functions by solving an optimization problem that considers the satellite altitude, the upper radial limit of the satellite trajectory, and the maximum spherical-harmonic degree we want to resolve. This new dual-source altitude vector Slepian system allows to invert for both inner-source and outer-source magnetic potential fields from regional data in a computationally efficient manner, as we show with a series of examples for Earth, the Moon, and terrestrial planets.