## 3 Simulated Experiment
### The Influence of Different Layout Forms of Survey Lines on Parameter Inversion  
The standard observation line layout in mining subsidence studies is generally two orthogonal observation lines along the strike main section and the inclination main section \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multicolumn{2}{c}{**Parameter**} & \(\mathbf{q}\) & \(\mathbf{\tan\beta}\) & \(\mathbf{\theta}^{c}\) & \(\mathbf{S_{1}/m}\) & \(\mathbf{S_{2}/m}\) & \(\mathbf{S_{3}/m}\) & \(\mathbf{S_{4}/m}\) & \(\mathbf{RMSE/mm}\) \\ \hline \multirow{3}{*}{\(k=10\)} & Design & \multirow{3}{*}{0.6400} & \multirow{3}{*}{1.5000} & \multirow{3}{*}{86.5000} & \multirow{3}{*}{45.0000} & \multirow{3}{*}{45.0000} & \multirow{3}{*}{45.0000} & \multirow{3}{*}{45.0000} & \multirow{3}{*}{45.0000} \\  & value & & & & & & & \\  & IV & 0.6404 & 1.6268 & 86.0113 & 46.1155 & 45.3005 & 43.8490 & 47.2080 \\  & RE & 0.06\% & 8.45\% & \(-0.56\%\) & 2.48\% & 0.67\% & \(-2.56\%\) & 4.91\% \\  & IV & 0.6444 & 1.5001 & 85.3051 & 44.8297 & 44.3856 & 43.7977 & 47.5408 \\  & RE & 0.69\% & 0.01\% & \(-1.38\%\) & \(-0.38\%\) & \(-1.37\%\) & \(-2.67\%\) & 5.65\% \\  & IV & 0.6405 & 1.4804 & 85.5932 & 45.2301 & 44.8294 & 44.9171 & 47.0725 \\  & RE & 0.09\% & 1.31\% & 1.05\% & 0.51\% & 0.38\% & 0.18\% & 4.61\% \\  & IV & 0.6390 & 1.5257 & 85.2503 & 43.8192 & 45.1534 & 46.4601 & 46.0842 \\  & RE & \(-0.15\%\) & 1.71\% & \(-1.44\%\) & \(-2.62\%\) & 0.34\% & 3.24\% & 2.41\% \\  & IV & 0.6368 & 1.5205 & 85.6139 & 43.0816 & 46.2739 & 47.1941 & 44.4129 \\  & RE & \(-0.50\%\) & 1.37\% & \(-1.02\%\) & \(-4.26\%\) & 2.83\% & 4.88\% & \(-1.30\%\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Results and accuracy of inversion probability integral parameters (Plan 2). \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multicolumn{2}{c}{**Parameter**} & \(\mathbf{q}\) & \(\mathbf{\tan\beta}\) & \(\mathbf{\theta}^{c}\) & \(\mathbf{S_{1}/m}\) & \(\mathbf{S_{2}/m}\) & \(\mathbf{S_{3}/m}\) & \(\mathbf{S_{4}/m}\) & \(\mathbf{RMSE/mm}\) \\ \hline \multirow{3}{*}{\(k=10\)} & Design & \multirow{3}{*}{0.6400} & \multirow{3}{*}{1.5000} & \multirow{3}{*}{86.5000} & \multirow{3}{*}{45.0000} & \multirow{3}{*}{45.0000} & \multirow{3}{*}{45.0000} & \multirow{3}{*}{45.0000} & \multirow{3}{*}{45.0000} \\  & value & & & & & & & \\  & IV & 0.6505 & 1.5557 & 85.7074 & 42.4913 & 45.6933 & 44.8361 & 44.8234 \\  & RE & 1.64\% & 3.72\% & \(-0.92\%\) & \(-5.57\%\) & 1.54\% & \(-0.36\%\) & \(-0.39\%\) \\  & IV & 0.6427 & 1.5000 & 85.4679 & 43.9696 & 46.1892 & 46.7253 & 45.0778 \\  & RE & 0.42\% & 0.00\% & \(-1.19\%\) & \(-2.29\%\) & 2.64\% & 3.83\% & 0.17\% \\  & IV & 0.6400 & 1.5000 & 85.9763 & 44.8008 & 45.1991 & 45.5575 & 45.4753 \\  & RE & 0.00\% & 0.00\% & 0.61\% & 0.44\% & 0.44\% & 1.24\% & 1.06\% \\  & IV & 0.6407 & 1.5314 & 86.1272 & 44.4732 & 46.4933 & 43.4665 & 46.6973 \\  & RE & 0.11\% & 2.09\% & \(-0.43\%\) & \(-1.17\%\) & 3.32\% & \(-3.41\%\) & 3.77\% \\  & IV & 0.6399 & 1.5000 & 85.1070 & 44.6436 & 45.1770 & 45.0159 & 46.3817 \\  & RE & \(-0.01\%\) & 0.00\% & \(-1.61\%\) & \(-0.79\%\) & 0.39\% & 0.04\% & 3.07\% \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Results and accuracy of inversion probability integral parameters (Plan 3). of the coal seam. However, the actual layout of observation lines is often restricted by conditions such as terrain and buildings, and cannot be arranged into a standard observation line layout form. In the experimental analysis of the influence of different survey lines on the proposed method, the layout schemes of six different line layout patterns are presented in this study, as shown in Figure 9.  
Figure 9: Schematic diagram of different line layout schemes.