## 4 Discussion
The reasons for this state of affairs should be sought primarily in the measurement technology used to determine the subsidence in observation points. For this purpose, the results of RTN-GNSS measurements were used (see Section 2.2), which are characterized by a much larger error in determining the height (m\({}_{\rm H}<\pm\) 0.05) compared to the heights determined based on geometric levelling (m\({}_{\rm H}\leq\) 0.015 m). Figure 10: Comparison of the observed and simulated tilts—25 November 2021 (**left**) and 4 August 2022 (**right**). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **28 September 2021** & **25 November 2021** & **11 March 2022** & **12 May 2022** & **4 August 2022** \\ \hline ME [mm/m] & 0.00 & 0.00 & 0.00 & \(-\)0.01 & \(-\)0.04 \\ MAE [mm/m] & 0.03 & 0.06 & 0.23 & 0.38 & 0.97 \\ RMSE [mm/m] & 0.04 & 0.07 & 0.38 & 0.56 & 1.21 \\ \(\mu_{\rm{{}_{base}}}\) [\%] & \(-\)10.2 & \(-\)3.2 & \(-\)14.6 & \(-\)13.8 & 29.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Modeling tilt errors with the numerical method for subsequent face advances. The mechanical parameters, particularly the ratio E1/E3, played a crucial role in the accuracy of the numerical models. This ratio, which compares the horizontal Young's modulus (E1) to the vertical Young's modulus (E3), is essential in determining the anisotropic behavior of rock layers. Anisotropy in rock mechanics refers to the directional dependence of rock properties, and the E1/E3 ratio is a key indicator of this behavior. It is also responsible for the change in the slope within the subsidence trough, while Young's modulus (E3) influences the value of land surface subsidence. Poisson's number causing a slight change in subsidence trough course [72]. Recent studies have highlighted the impact of anisotropy on rock deformation and subsidence predictions. For example, [PERSON]'s theory on anisotropic elasticity provides a foundation for understanding how the different directional moduli influence stress distribution and deformation in rock masses. In particular, research has shown that the elastic stiffness parameters, including Young's modulus, exhibit strong correlations that significantly affect the rock's response to loading conditions [73]. Additionally, the variation in the E1/E3 ratio influences the deformation characteristics during mining activities. By incorporating the E1/E3 ratio into our numerical models, we achieved high consistency in deformation indicators, which aligns with empirical observations and enhances the reliability of our predictions. This adjustment is crucial for accurately modelling the complex behavior of rock layers under mining-induced stress. It is noteworthy that high accuracy was also achieved in the case where a full subsidence trough did not form, i.e., for the LW501 panel. As the surface measurements conducted from June 2021 to November 2021 showed, the first panel led to slight surface deformation along the observation line, with a maximum subsidence indicator of 38 mm. The maximum estimated subsidence value was 433 mm in the central part of panel LW501. This most likely means that the extraction of this panel did not lead to the fracture (or breaking) of the thick and strong sandstone layer located directly above the mined seam, which has a thickness of up to 100 m. This assumption is supported by reports on the registration of mining tremors recorded on the surface in the area of Ledziny city ([[https://grss.gig.eu/en/seismic-map/](https://grss.gig.eu/en/seismic-map/)]([https://grss.gig.eu/en/seismic-map/](https://grss.gig.eu/en/seismic-map/)), accessed on 9 July 2024). From June 2021 to the end of 2022, monitoring stations recorded tremors mainly in the energy magnitude range of \(1\cdot 10^{5}\) according to the GSIS-2017 scale by PGVH\({}_{\text{max}}\)[74], with the intensity of these tremors classified as the lowest category, i.e., 0. As is known from engineering experience and the literature on the subject, longwall panels can be classified as sub-critical, critical, and supercritical [75; 76].