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A new software library for calculation of the far zone effects for spherical integral transformations

Authors

Trnka,  Petr
IUGG 2023, General Assemblies, 1 General, International Union of Geodesy and Geophysics (IUGG), External Organizations;

Belinger,  Jiří
IUGG 2023, General Assemblies, 1 General, International Union of Geodesy and Geophysics (IUGG), External Organizations;

Šprlák,  Michal
IUGG 2023, General Assemblies, 1 General, International Union of Geodesy and Geophysics (IUGG), External Organizations;

Pitoňák,  Martin
IUGG 2023, General Assemblies, 1 General, International Union of Geodesy and Geophysics (IUGG), External Organizations;

Novák,  Pavel
IUGG 2023, General Assemblies, 1 General, International Union of Geodesy and Geophysics (IUGG), External Organizations;

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Citation

Trnka, P., Belinger, J., Šprlák, M., Pitoňák, M., Novák, P. (2023): A new software library for calculation of the far zone effects for spherical integral transformations, XXVIII General Assembly of the International Union of Geodesy and Geophysics (IUGG) (Berlin 2023).
https://doi.org/10.57757/IUGG23-1193


Cite as: https://gfzpublic.gfz-potsdam.de/pubman/item/item_5017414
Abstract
Integral transformations are a useful mathematical apparatus for gravitational field modelling and form the main mathematical basis for the formulation of integral estimates including error propagation. Theoretical and practical aspects of classical integral transformations, such as Poisson’s, Stokes’s, or Hotine’s, have already been studied. On the other hand, theoretical and practical concepts are not known for many other integral formulas including non-isotropic ones. The basic assumption of integral transformations is global data coverage. In practice, however, data availability is limited. Therefore, we divide global integration into the effects of the near and far zones. The computation of distant zones is a non-negligible systematic effect requiring an accurate calculation. In this paper, we introduce a new software library for the evaluation of the far zones. The software library allows the computation of the far zones for integral transformations mutually relating all quantities up to the third derivatives of the gravitational potential. The library includes scripts for the calculation of the integral kernels, error kernels, and truncation error coefficients for a selected set of input parameters. The implementation and subsequent functionality of the library are tested in a closed-loop simulation by using synthetic data.