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Article

Segeth, Karel
Spherical RBF interpolation employing particular geodesic metrics and trend functions. (English). In: Chleboun, J., Papež, J., Segeth, K., Šístek, J. and Vejchodský, T. (eds.): Programs and Algorithms of Numerical Mathematics. Proceedings of Seminar. Hejnice, June 23-28, 2024. , Prague, 2025. pp. 149-158
MSC: 65D05, 65D12, 65Z05 | DOI: 10.21136/panm.2024.14
Keywords:
radial basis function; spherical interpolation; spherical radial basis function; geodesic metric; trend; multiquadric; magnetic susceptibility
Summary:
The paper is concerned with spherical radial basis function (SRBF) interpolation. We introduce particular SRBF interpolants employing several different geodesic metrics and a single trend function. Interpolation on a sphere is an important tool serving to processing data measured on the Earth's surface by satellites. Nevertheless, our model physical quantity is the magnetic susceptibility of rock measured in different directions. We construct a general SRBF formula and prove conditions sufficient for its existence. Particular formulae with specified geodesic metrics, trend and SRBFs are then constructed and tested on a series of magnetic susceptibility examples. The results show that this interpolation is sufficiently robust in general.
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