## 4 Research Results
### Designation of the CBA and the Distance Between the Geoid and Quasigeoid
Analyzing the maps shown in Figure 5, it should be pointed out that, in their general course, the determined \(\text{CBA}_{GGI}\) correspond to \(\text{CBA}_{UNB}\) values and also correspond to CBA determined in other studies for this area [30; 31; 32]. Unfortunately, the imperfections of the GGI approach in terms of CBA determination are also very clearly visible. Apart from the differences in the values of the determined CBA, which are shown in detail in Figure 7A, the basic problem of the \(\text{CBA}_{GGI}\) values concerns its resolution. The \(\text{CBA}_{GGI}\) values were calculated according to the Equation (17), in which this value depends primarily on the \(T_{\kappa}\) potential, defined by the volume \(\kappa\), the resolution of which is defined by constant density zones (in this case \(4\times 4\) km). Therefore, increasing the resolution of the \(\text{CBA}_{GGI}\) requires a significant increase in the resolution of the volume \(\kappa\). In its current form, the CBA calculated by the GGI model may only be use in little detailed considerations. The map of differences \((N-\zeta)_{GGI}\) is significantly better. Even small structures are clearly visible. The course of the determined values \((N-\zeta)_{GGI}\) corresponds to the values \((N-\zeta)_{UNB}\), however the differences are also visible. Referring to the values included in Table 7, note that the statistics are very similar for the couples \(\text{CBA}_{UNB}\leftrightarrow\text{CBA}_{GGI}\) and \((N-\zeta)_{UNB}\leftrightarrow(N-\zeta)_{GGI}\). However, the statistics of differences \(\delta\text{CBA}\) and \(\delta(N-\zeta)\) indicate that in the whole sets there are points of significant divergence. Let us add that the average values of the absolute values of the differences \(\delta\text{CBA}\) and \(\delta(N-\zeta)\) are 3.18 mGal and 0.32 cm, respectively, and are relatively small and acceptable. However, the extreme values of these differences are already very large. In Figure 6, representing the spatial decomposition of these differences, it can  
Figure 6: Maps of \((N-\zeta)_{UNB}\) (**A**) and \((N-\zeta)_{GGI}\) (**B**). be seen that the highest values occur in the area of the eastern part of the Tatra Mountain and in the higher mountain parts of Slovakia. Estimation of the Formal Errors of the Complete Bouguer Anomalies and the \((N-\zeta)\) Differences Resulting from Errors of Density Estimation. We will now consider the differences (\(\delta\)CBA and \(\delta(N-\zeta)\)) that were presented in the previous Section while taking into account the density distribution of topographic masses from the UNB_TopoDens model (\(\rho_{\text{UNB}}\)) and the standard deviations of these densities \(\left(\sigma_{\rho_{\text{UNB}}}\right)\) (which are part of the UNB_TopoDens model). These data make it possible to determine, on the basis of the low of covariance propagation, the formal errors of both the CBA (\(\sigma_{CBA_{\rho}}\)) and the \((N-\zeta)\) differences (\(\sigma_{N-\zeta_{\rho}}\)), which result from errors of density estimation; however, these are not the only factor affecting the accuracy of the Bouguer anomalies and the \((N-\zeta)\) differences. The maps of this values are presented in Figure 8 (\(\rho_{\text{UNB}}\) and \(\sigma_{\rho_{\text{UNB}}}\)) and Figure 9 (\(\sigma_{CBA_{\rho}}\) and \(\sigma_{N-\zeta_{\rho}}\)). The errors \(\sigma_{CBA_{\rho}}\) and \(\sigma_{N-\zeta_{\rho}}\) may be determined on the basis of topographic reduction (13). First, let us express this reduction in the form of the executable equation.