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Abstract

We present local quasigeoid modelling in Slovakia treated in spatial domain. The finite element method (FEM) is used to solve numerically the fixed gravimetric boundary-value problem (FGBVP) directly on the Earth’s topography discretized with the high horizontal resolution 100 x 100 m. Here the input surface gravity disturbances as the oblique derivative boundary conditions are generated from a detailed map of the complete Bouguer anomalies and detailed digital terrain model. Together with the non-uniform resolution in the radial direction it results in a 3D unstructured mesh of finite elements with 5,287,500,000 unknowns. The FEM numerical solution is fixed to the GO_CONS_GCF_2_DIR_R6 satellite-only geopotential model on the upper boundary at the altitude of 230 km. Large-scale parallel computations are performed on a parallel cluster using 1.5 TB of distributed memory.

The obtained local quasigeoid model (Minarechová et al. 2021) is tested at 403 GNSS-levelling benchmarks. It is also compared with the local model computed in spectral domain using a combination of spherical harmonics, band-limited spherical radial basis functions and the residual terrain model technique (Bucha et al. 2016). Such a comparison clearly shows a low-frequency character of differences up to few cm without a significant correlation with topography. Surprisingly, the GNSS-levelling test indicates that the quasigeoid model computed in spectral domain fits better to the national vertical datum while the FEM soluition to EVRS-2019. Based on these analyses, we aim to discuss pros and cons of both approaches treated in spatial vs. spectral domain.