FarZone4IT: A new software for the calculation of far–zone effects for spherical integral

Integral transformations are a useful mathematical apparatus for modelling the gravitational field. They represent the mathematical basis for the formulation of integral estimators of gravity field values, including error propagation. The theoretical and practical aspects of integral transformations traditionally used for the calculation of geoid/quasi-geoid heights in geodesy, such as Stokes’ and Hotine’s integral transformations, have already been studied. However, theoretical and practical concepts regarding other integral transformations, including non-isotropic (azimuth-dependent) transformations, have not yet been explored. One of the basic assumptions of integral transformations is global data coverage. However, the availability of ground measurements is frequently limited. In practice, the global integral is divided into two complementary regions, namely the near and far zones. Non-negligible systematic effects of data in the far zone require accurate evaluation. For this purpose, a new software library entitled FarZone4IT is being created in the MATLAB environment to calculate far-zone effects in integral transformations for gravitational potential gradients up to the third order. The library contains scripts for the calculation of integral kernels, error kernels, truncation error coefficients, and far zone effects for a selected set of input parameters. This contribution concerns the implementation of theoretical equations defining far zone effects and the subsequent numerical testing of the library functionality. Closed-loop tests were carried out using gravitational potential functionals generated from a synthetic model of the Earth's gravity field.