## 4 Research Results
### Assessment of the Accuracy of the Gravity Values and height Anomalies Determined from the GGI Model
The analyses were carried out for DEM with resolution of \(0.1\times 0.1\) km and constant density zones dimension \(4\times 4\) km. The research was supplemented with the classical methods of gravity data interpolation, using CBA and Pratt-Hayford topographic-isostatic anomalies (hereinafter referred as Pratt anomalies and marked as \(\Delta g_{Pratt}\)). In the classical approach, the calculations were made according to the scheme further marked as CBA/Kriging and Pratt/Kriging:  
1. CBA and Pratt anomalies calculations at known (CBA\({}_{Kuemu}\); \(\Delta g_{PrattKnown}\) and test points (CBA\({}_{Test}\); \(\Delta g_{PrattTest}\)). 2. Based on CBA\({}_{Known}\) and \(\Delta g_{PrattKnown}\), we build a dense grid of these anomalies using the Kriging method (we used for this step the Surfer 16, Golden Software). 3. Using the grid specified in the previous point, we interpolate the CBA and Pratt anomalies at test points (CBA\({}_{int}\); \(\Delta g_{Prattint}\)). 4. We compare the interpolated and computed anomalies at test points (\(\Delta\)g = CBA\({}_{Test}-\)CBA\({}_{int}\)\(\Delta\)g = \(\Delta g_{PrattTest}-\Delta g_{Prattint}\), and then determine the accuracy indicators. Figure 4: Constant density zones dimensions taken for calculations in various versions. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Constant Density Zones Dimension** & \(\mathbf{8\times 8}\)**km** & \(\mathbf{6\times 6}\)**km** & \(\mathbf{4\times 4}\)**km** & \(\mathbf{3\times 3}\)**km** \\ \hline \multicolumn{5}{c}{Polish part} \\ \hline Stdev(\(\Delta\zeta\)) [cm] & 2.19 & 2.20 & 2.19 & 2.14 \\ Stdev(\(\Delta\)g) [mGal] & 1.30 & 1.14 & 0.98 & 0.96 \\ \hline \multicolumn{5}{c}{Slovak part} \\ \hline Stdev(\(\Delta\zeta\)) [cm] & 0.89 & 0.91 & 0.97 & 0.99 \\ Stdev(\(\Delta\)g) [mGal] & 1.42 & 1.23 & 1.06 & 1.00 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Standard deviations of differences \(\Delta\zeta\) and \(\Delta\)g depending on the constant density zones dimensions. In the analyses, CBA has been calculated on the basis of Equation (10), whereas Pratt anomalies were defined as [4]:  
\[\Delta g_{Pratt}=\Delta g_{FA}-\delta g_{Top}+\delta g_{[PERSON]}=g_{o}-\gamma_{e}- \delta g_{Top}+\delta g_{Pratt} \tag{22}\]  
where \(\delta g_{[PERSON]}\) is compensation attraction according to Pratt-Hayford system:  
\[\delta g_{Pratt}=G\iint\limits_{\mu}\int\limits_{z=-D}^{z=0}\frac{(z-H_{P})} {l^{3}}\Delta pdzd\mu \tag{23}\]  
where D is depth of compensation level and \(\Delta\rho\) is the density difference between the constant density \(\rho_{o}\) and the actual density of the compensation model. In the calculations, we adopted a compensation model using the constant density \(\rho_{o}\) of topographic masses used for Bouguer reduction, for which the mass equality has the form [4]:  
\[(\rho_{o}-\Delta\rho)D+\rho_{o}H=\rho_{o}D \tag{24}\]  
Hence:  
\[\Delta\rho=\frac{H}{D}\rho_{o} \tag{25}\]  
It is worth noting that in the GGI model, the initial density model (\(\delta_{o}\)) of the volume \(\kappa\) is determined from an analogous relationship (see Section 3). This means that in the modelling process, after taking into account the initial density model (\(\rho_{o}\) and \(\delta_{o}\)), we use a kind of topographic-isostatic gravity disturbance and the component \(-\frac{\partial T_{E}}{\partial H}\) represents the topographic-isostatic gravity disturbances after optimization of the densities (\(\rho\) and \(\delta\)) with respect to the measured data. Both, CBA and Pratt anomalies were calculated using normal gravity gradient in free-air reduction, and an integration radius of 167 km was used for topographic and isostatic reductions. For isostatic reductions, the standard depth of the compensation level \(D\) = 100 km was also assumed. The calculations used a DEM with a 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 for the rest of the area.