Investigation of regional variation in core flow models using spherical Slepian functions

By assuming that changes in the magnetic field in the Earth's outer core are advection-dominated on short timescales, models of the core surface flow can be deduced from secular variation. Such models are known to be under-determined and thus require other assumptions to produce feasible flows. There are regions where poor knowledge of the core flow dynamics gives rise to further uncertainty, such as within the tangent cylinder, and assumptions about the nature of the flow may lead to ambiguous patches, such as if it is assumed to be strongly tangentially geostrophic. We use spherical Slepian functions to spatially and spectrally separate core flow models, confining the flow to either inside or outside these regions of interest. In each region we examine the properties of the flow and analyze its contribution to the overall model. We use three forms of flow model: (a) synthetic models from randomly generated coefficients with blue, red and white energy spectra, (b) a snapshot of a numerical geodynamo simulation and (c) a model inverted from satellite magnetic field measurements. We find that the Slepian decomposition generates unwanted spatial leakage which partially obscures flow in the region of interest, particularly along the boundaries. Possible reasons for this include the use of spherical Slepian functions to decompose a scalar quantity that is then differentiated to give the vector function of interest, and the spectral frequency content of the models. These results will guide subsequent investigation of flow within localized regions, including applying vector Slepian decomposition methods.