## 3 Characteristics of the Data and the Area of Elaboration  
The area of study included part of the Western Carpathians, which is located on the border of Poland and Slovakia. In our calculations, for definition of the \(\Omega\) volume, four versions of DEM resolution were used: 0.1 \(\times\) 0.1 km, 0.25 \(\times\) 0.25 km, 0.5 \(\times\) 0.5 km, and 1 \(\times\) 1 km. All DEM grids were determined based on the Shuttle Radar Topography Mission (SRTM) model, which was shared by the _CGIAR-CSI Consortium for Spatial Information_ ([[http://srtm.csi.cgiar.org/contact-us/](http://srtm.csi.cgiar.org/contact-us/)]([http://srtm.csi.cgiar.org/contact-us/](http://srtm.csi.cgiar.org/contact-us/))) with a resolution of \(3^{\prime\prime}\times 3^{\prime\prime}\). Horizontal range of digital terrain model used in the calculations is shown in Figure 3. In all calculations where the DEM model with resolution \(0.1\times 0.1\) km was used, two DEM models were used in order to reduce the computational effort. The \(0.1\times 0.1\) km model was used for a square with side of 10.500 km, in the center of which there was a determined point and \(0.5\times 0.5\) km was used for the rest of the area. Volume \(\kappa\) was defined based on the Moho depth model for the European plate [24]. In the calculations, two constant density values were assumed as the reference density model for the volume \(\Omega\): \(\rho_{0}=2670\) kg/m\({}^{3}\) and \(\rho_{0}=2200\) kg/m\({}^{3}\) (this value is close to the mean density of topographic masses for lowland areas of Poland [25]) as well as the global topographic mass density model UNB_TopoDens [26]. The reference density model for the volume \(\kappa\) (\(\delta_{0}\)) was adopted as \"negative density\", which balanced the topographical masses of the volume \(\Omega\). The density of a separate block of volume \(\kappa\) was calculated based on the equation \(\delta_{j}^{0}=-\frac{H_{i}\rho_{i}^{0}}{h_{j}}\), where \(H_{i}\)\(\rho_{i}^{0}\) are mean height and reference density of zone \(i\) of the \(\Omega\) volume, which are situated directly above block \(j\) of volume \(\kappa\); and \(h_{j}\) is the height of block \(j\).  
Based on the quasigeoid models, PL-geoid-2011 [27] for the area of Poland and the model GMSQ03C [28] for the area of Slovakia, a regular grid of points with known height anomalies has been designated. These points were divided into two sets: The first was used to build the GGI model and consisted of 95 points (about 1 point for 200 km\({}^{2}\)); while the second set consisted of 81 test points and was used for assessment of the accuracy of the quasigeoid model. In the calculations, we also used a  
Figure 3: Relief map of the topography used for the GGI method. Solid white line: The border between Poland and Slovak Republic. Dashed white line: Border of the gravity data used.  
set of gravity points that were divided into two sets: A set of 10,532 known points and a set of 10,513 test points (the approximate density of the data and test points was about 1 point for 2.4 km\({}^{2}\)). For the Polish part of the elaboration area, the gravity points were made available by the Polish Geological Institute National Research Institute (_PGI-NRI_). For the Slovak part, they were made available by Geofyzika, a.s. Brno, CGS--Geofond. Both groups of data points (height anomalies and gravity points) evenly cover the entire study area.  
Taking into account the various datasets from the Slovak and Polish areas (various quasigeoid models and various gravity datasets), it was decided to use the GGI model that separated the Polish (\(T_{Pol}\)) and Slovak (\(T_{S}\)) parts:  
\[\left\{\begin{array}{c}T_{Pol}\\ T_{S}\end{array}\right\}=T_{\Omega}+T_{\kappa}+\left\{\begin{array}{c}T_{ EPol}\\ T_{ES}\end{array}\right\} \tag{21}\]  
Both parts (\(T_{Pol}\) and \(T_{S}\)) share parts \(T_{\Omega}\) and \(T_{\kappa}\), and have independent part \(T_{E}\). This separation is caused by the assumption that the differences in the used data are the trend type.