Spheroidal spline interpolation and its application in geodesy

    Mostafa Kiani   Affiliation
    ; Nabi Chegini   Affiliation
    ; Abdolreza Safari Affiliation
    ; Borzoo Nazari   Affiliation


The aim of this paper is to study the spline interpolation problem in spheroidal geometry. We follow the minimization of the norm of the iterated Beltrami-Laplace and consecutive iterated Helmholtz operators for all functions belonging to an appropriate Hilbert space defined on the spheroid. By exploiting surface Green’s functions, reproducing kernels for discrete Dirichlet and Neumann conditions are constructed in the spheroidal geometry. According to a complete system of surface spheroidal harmonics, generalized Green’s functions are also defined. Based on the minimization problem and corresponding reproducing kernel, spline interpolant which minimizes the desired norm and satisfies the given discrete conditions is defined on the spheroidal surface. The application of the results in Geodesy is explained in the gravity data interpolation over the globe.

Keyword : spheroid, discrete Dirichlet and Neumann conditions, norm minization, spline interpolation, Green’s function, gravity data interpolation

How to Cite
Kiani, M., Chegini, N., Safari, A., & Nazari, B. (2020). Spheroidal spline interpolation and its application in geodesy. Geodesy and Cartography, 46(3), 123-135.
Published in Issue
Oct 12, 2020
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