## 4 Research Results
### Designation of the CBA and the Distance Between the Geoid and Quasigeoid  
With the developed GGI model using density of the gravity points 2.4 \(\frac{\text{km}^{2}}{1\ point}\), the UNB_TopoDens model as a reference density of topography model, DEM with resolution of \(0.1\times 0.1\) km, and assuming zones of constant density equal \(4\times 4\) km, the complete Bouguer anomalies were determined according to \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Prediction Version** & 2.4 \(\frac{\text{km}^{2}}{1\ point}\) & 4.9 \(\frac{\text{km}^{2}}{1\ point}\) & 9.7 \(\frac{\text{km}^{2}}{1\ point}\) & 19.4 \(\frac{\text{km}^{2}}{1\ point}\) \\ \hline GGI\({}_{2200}\) & 1.03 & 1.38 & 1.86 & 2.50 \\ CBA\({}_{2200}\)_Kriging_ & 1.56 & 1.86 & 2.21 & 2.68 \\ Pratt\({}_{2200}\)_Kriging_ & 1.52 & 1.81 & 2.16 & 2.65 \\ GGI\({}_{2670}\) & 1.06 & 1.13 & 1.26 & 1.56 \\ CBA\({}_{2670}\)/_Kriging_ & 0.94 & 1.00 & 1.15 & 1.43 \\ Pratt\({}_{2670}\)/_Kriging_ & 0.96 & 1.02 & 1.17 & 1.45 \\ GGI\({}_{\text{LIN}}\) & 1.06 & 1.23 & 1.57 & 2.21 \\ CBA\({}_{\text{LINB}}\)/_Kriging_ & 1.65 & 2.02 & 2.56 & 3.19 \\ Pratt\({}_{\text{LINB}}\)/_Kriging_ & 1.63 & 1.99 & 2.53 & 3.17 \\ FA/_Kriging_ & 9.47 & 10.95 & 12.46 & 14.18 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Standard deviations of \(\Delta\)g values in mGal determined for different versions indicated in Table 4 and for different densities of known gravity points for the Slovak part. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Prediction Version** & 2.4 \(\frac{\text{km}^{2}}{1\ point}\) & 4.9 \(\frac{\text{km}^{2}}{1\ point}\) & 9.7 \(\frac{\text{km}^{2}}{1\ point}\) & 19.4 \(\frac{\text{km}^{2}}{1\ point}\) \\ \hline GGI\({}_{2200}\) & 0.96 & 1.19 & 1.50 & 1.89 \\ CBA\({}_{2200}\)_Kriging_ & 1.04 & 1.18 & 1.42 & 1.70 \\ Pratt\({}_{2200}\)_Kriging_ & 1.03 & 1.17 & 1.42 & 1.71 \\ GGI\({}_{2670}\) & 0.98 & 1.05 & 1.17 & 1.40 \\ CBA\({}_{2670}\)_Kriging_ & 0.92 & 1.00 & 1.09 & 1.28 \\ Pratt\({}_{2670}\)/_Kriging_ & 0.92 & 1.01 & 1.10 & 1.29 \\ GGI\({}_{\text{LINB}}\) & 1.00 & 1.11 & 1.33 & 1.67 \\ CBA\({}_{\text{LINB}}\)/_Kriging_ & 1.13 & 1.32 & 1.51 & 1.77 \\ Pratt\({}_{\text{LINB}}\)/_Kriging_ & 1.13 & 1.32 & 1.51 & 1.76 \\ FA/_Kriging_ & 5.47 & 6.29 & 7.23 & 7.95 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Standard deviations of \(\Delta\)g values in mGal determined for different versions indicated in Table 4 and for different densities of known gravity points for the Polish part. Equation (17) while the differences between the geoid undulations and the height anomalies were determined according to Equation (18). These quantities will hereinafter be designated as \(\text{CBA}_{GGI}\) and \((N-\zeta)_{GGI}\). The values calculated from the GGI model were compared with the classical approach using the UNB_TopoDens model and DEM with resolution of \(0.1\times 0.1\) km for a square with side of 10.500 km, in the centre of which there was a gravity point and \(0.5\times 0.5\) km within a radius up to 167 km. The CBA values were calculated according to Equation (10). We also use Poincare and Prey reduction (according to the procedure presented in Section 2.2.4, using full topographic reduction and normal gravity gradient) to calculate the values of \(\overline{g}\) that are required in Equation (18). These classically determined quantities are hereinafter marked as \(\text{CBA}_{UNB}\) and \((N-\zeta)_{UNB}\). In addition, the following differences were also calculated: \(\delta\text{CBA}=\text{CBA}_{UNB}-\text{CBA}_{GGI}\) and \(\delta(N-\zeta)=(N-\zeta)_{UNB}-(N-\zeta)_{GGI}\). The basic statistics of the aforementioned values are presented in Table 7.  
Figures 5-7 show the maps of individual quantities (Figure 5--CBA\({}_{UNB}\) and \(\text{CBA}_{GGI}\), Figure 6--\((N-\zeta)_{UNB}\) and \((N-\zeta)_{GGI}\); Figure 7--\(\delta\)CBA and \(\delta(N-\zeta)\)).