Spectral analysis of regional main field and secular variation in CHAOS-4 using spherical Slepian functions

Magnetic models such as CHAOS-4 represent the global field using Spherical Harmonic (SH) functions weighted by a set of numbers known as Gauss coefficients. This representation allows values of the field to be calculated at any location and altitude above the core-mantle boundary, but has limitations when attempting to isolate the contribution to the field from specific areas or regions. Spherical Slepian functions provide an alternative mathematical basis to represent the field [Ref. 1]. They have the advantage of allowing an area of interest to be optimally described in a spatio-spectral sense. In addition, spherical Slepian functions can also be used to separate and decompose the Gauss coefficients from a SH magnetic field model into the components that represent the contribution to the model from individual regions of the globe [Ref. 2]. We investigate the spectral and spatial changes of the main magnetic field of CHAOS-4q [Ref. 3] at the Earth's surface between spherical harmonic degrees 12-35 in eight different regions across the globe: the Americas; Africa; Australia; Eurasia; Antarctica; the Pacific Ocean; the Atlantic Ocean and the Indian Ocean between 1997 and 2011.