Possibilities of inversion of satellite third-order gravitational tensor onto gravity anomalies: a case study for central Europe

We investigate a numerical performance of four different schemes applied to a regional recovery of the gravity anomalies from the third-order gravitational tensor components (assumed to be observable in the future) synthetized at the satellite altitude of 200 km above the mean sphere. The first approach is based on applying a regional inversion without modelling the far-zone contribution or long-wavelength support. In the second approach we separate integral formulas into two parts, that is, the effects of the third-order disturbing tensor data within near and far zones. Whereas the far-zone contribution is evaluated by using existing global geopotential model (GGM) with spectral weights given by truncation error coefficients, the near-zone contribution is solved by applying a regional inversion. We then extend this approach for a smoothing procedure, in which we remove the gravitational contributions of the topographic-isostatic and atmospheric masses. Finally, we apply the remove-compute-restore (r-c-r) scheme in order to reduce the far-zone contribution by subtracting the reference (long-wavelength) gravity field, which is computed for maximum degree 80. We apply these four numerical schemes to a regional recovery of the gravity anomalies from individual components of the third-order gravitational tensor as well as from their combinations, while applying two different levels of a white noise. We validated our results with respect to gravity anomalies evaluated at the mean sphere from EGM2008 up to the degree 250. Not surprisingly, better fit in terms of standard deviation (STD) was attained using lower level of noise. The worst results were gained applying classical approach, STD values of our solution from T_zzz are 1.705 mGal (noise value with a standard deviation 0.01 × 10⁻¹⁵m⁻¹s⁻²) and 2.005 mGal (noise value with a standard deviation 0.05 × 10⁻¹⁵m⁻¹s⁻²), while the superior from r-c-r up to the degree 80, STD fit of gravity anomalies from T_zzz with respect to the same counterpart from EGM2008 is 0.510 mGal (noise value with a standard deviation 0.01 × 10⁻¹⁵m⁻¹s⁻²) and 1.190 mGal (noise value with a standard deviation 0.05 × 10⁻¹⁵m⁻¹s⁻²).