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Far Zone Effects for Integral Transformations: Theory and Implementation
Trnka, Petr ; Belinger, Jiří ; Šprlák, Michal ; Pitoňák, Martin ; Novák, Pavel
Integral transformations are a useful mathematical apparatus for modelling the gravitational field and require the formulation of integral estimates including error propagation. For classical integral transformations, this issue has already been studied, but the formulation for all available gravitational observables has not been studied yet. The assumption of integral transformations is global data coverage. In practice, however, data availability is limited, so we divide the 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. The theory is implemented in the form of a precise software. In this paper, we present the basic theory for the evaluation of the far zones. We also investigate properties of integral kernels and truncation error coefficients. In the numerical experiments, we compare calculation of the far zones by numerical integration with truncated spherical harmonic series. One of the outputs of this contribution is a software library for computation of the far zones for integral transformations mutually relating all quantities up to the third derivatives of the gravitational potential.
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