## 3 Results
### Stochastic Evaluation of Results  
For clearer outputs of the FEA, the results are processed in the form of statistical histograms. Anthill software [44; 45] is used to plot the histograms, which give the total displacements at each node over the whole analyzed time. Thus, sufficiently accurate statistical records of the data are obtained. Statistical processing of the stresses was carried out in [9]. All Monte Carlo calculations were performed for \(2\times 10^{6}\) pseudo-random simulations. Figures 13-15 show examples of histograms and distribution functions of radial and tangential displacement components for nodes '1', '7094', and '12,044' on the outer surface (labelled according to Figure 11). Tables 2 and 3 show a statistical evaluation of the tangential and radial displacements of the Earth's crustal surface. Figure 16 shows the tangential schematic displacement histograms for all nodes on the outer surface according to Figure 11, i.e., with angular divisions of \(7.5^{\circ}\) (48 histograms). Radial displacements, which are not presented in this article, can also be evaluated in a similar way [9]. The findings of Table 2 show that the thermally induced displacements on the Earth's surface can be as large as the interval \(\langle-29.332;40.070\rangle\) m for tangential displacement over two years, an interesting finding that is not generally inconsistent with crustal motion. Some places on Earth move less and some move more, e.g., in areas of tectonic plate contact or faulting. Figure 13: Histograms and distribution functions for node ‘1’ (**a**) tangential components of crustal surface displacement, (**b**) radial components of crustal surface displacement (sw MSC.Marc Mentat and Anthill). Figure 14: Histograms and distribution functions for node ‘7094’ (**a**) tangential components of crustal surface displacement, (**b**) radial components of crustal surface displacement (sw MSC.Marc Mentat and Anthill). Figure 15: Histograms and distribution functions for node ‘12,044’ (**a**) tangential components of crustal surface displacement, (**b**) radial components of crustal surface displacement (sw MSC.Marc Mentat and Anthill). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Node** & **Angle \(\phi\) / deg/** & **Min /m/** & **Mean /m/** & **Median /m/** & **Max /m/** \\ \hline
13017 & \(307.5\) & \(-2.130202\) & \(0.200543\) & \(0.266355\) & \(1.685076\) \\ \hline
13116 & \(315.0\) & \(-9.207633\) & \(1.157171\) & \(1.258941\) & \(8.282640\) \\ \hline
13259 & \(322.5\) & \(-3.271788\) & \(0.624200\) & \(0.663308\) & \(3.667678\) \\ \hline
13384 & \(330.0\) & \(-12.221221\) & \(2.082060\) & \(2.173141\) & \(12.821112\) \\ \hline
13569 & \(337.5\) & \(-2.657303\) & \(-0.430821\) & \(-0.459640\) & \(2.697734\) \\ \hline
10258 & \(345.0\) & \(-23.800367\) & \(-4.473265\) & \(-4.585868\) & \(18.998453\) \\ \hline
10135 & \(352.5\) & \(-8.195234\) & \(-1.552937\) & \(-1.599643\) & \(6.756131\) \\ \hline TOTAL & & \(-29.331777\) & \(0.063933\) & \(0.055363\) & \(40.070023\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: _Cont._  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Node** & **Angle \(\phi\) / deg/** & **Min /m/** & **Mean /m/** & **Median /m/** & **Max /m/** \\ \hline
1 & \(0.0\) & \(-0.247709\) & \(0.045662\) & \(0.048070\) & \(0.264486\) \\ \hline
7646 & \(7.5\) & \(-1.069984\) & \(-0.220166\) & \(-0.225239\) & \(0.744611\) \\ \hline
7094 & \(15.0\) & \(-0.225554\) & \(0.050253\) & \(0.052106\) & \(0.273853\) \\ \hline
51 & \(22.5\) & \(-2.949429\) & \(-0.597693\) & \(-0.609791\) & \(2.074209\) \\ \hline
3 & \(30.0\) & \(-2.840615\) & \(-0.575473\) & \(-0.589606\) & \(1.996382\) \\ \hline
53 & \(37.5\) & \(-2.451921\) & \(-0.498885\) & \(-0.509240\) & \(1.719541\) \\ \hline
4 & \(45.0\) & \(-2.948489\) & \(-0.593957\) & \(-0.604933\) & \(2.117883\) \\ \hline
55 & \(52.5\) & \(-3.122978\) & \(-0.632979 The findings in Table 3 show that the displacement at the Earth's surface can be as large as \(\langle-3.992;2.817\rangle\) m for radial displacement over two years.