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Error bounds for the spectral approximation of the potential of a homogeneous almost spherical body

Studia Geophysica et Geodaetica volume 65, pages 235–260 (2021)Cite this article

Abstract

Several kinds of approximation of the gravitational potential of a homogeneous body by truncated spherical harmonics series are in use in physical geodesy. However, only one of them is capable of a representation converging to the true potential in the whole layer between the Brillouin sphere and the Bjerhammar sphere of the body. We aim at providing various majorizations, namely upper bounds, of the error with the double purpose of proving explicitly the convergence in the sense of different norms and of giving computable bounds, that might be used in numerical studies. The first aim is reached for all the norms. For the second, however, it turns out that among the bounds, when applied to the example of the terrain correction of the Earth, only those referring to the mean absolute error and the mean squared error at the level of Brillouin sphere of minimum radius give significant and useful results. In order to make the computation an easy exercise, a simple approximate formula has been developed requiring only the use of the distribution function of the heights of the surface of the body with respect to the Bjerhammar sphere.

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Authors and Affiliations

  1. Department of Theoretical Geodesy and Geoinformatics, Slovak University of Technology, Radlinského 11, 81005, Bratislava, Slovakia

    Blažej Bucha

  2. Department of Civil and Environmental Engineering, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133, Milan, Italy

    Lorenzo Rossi & Fernando Sansò

Authors
  1. Blažej Bucha
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  2. Lorenzo Rossi
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  3. Fernando Sansò
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Correspondence to Lorenzo Rossi.

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Bucha, B., Rossi, L. & Sansò, F. Error bounds for the spectral approximation of the potential of a homogeneous almost spherical body. Stud Geophys Geod 65, 235–260 (2021). https://doi.org/10.1007/s11200-021-0730-4

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  • DOI: https://doi.org/10.1007/s11200-021-0730-4

Keywords

  • homogeneous bodies
  • gravity field
  • spectral approximation
  • convergence theory
  • numerical bounds