# Investigation of Microseismic Monitoring of and Precursor Information on Roof Collapse
## 5 Discussion  
### Cluster Analysis of Roof Collapse MS Events  
A machine learning method was employed to analyze the MS events, and the results are presented in Figure 6. The MS events at the caving through the roof are identified as Cluster 6, represented by the red shadow. The identification results align with the field observations, validating the practical application of this analysis method. Cluster 6 is spatially surrounded by surface Clusters 1 and 2, indicating that it is the outcome of further crack propagation and penetration under its influence. In the elevation range of 450-530 m, MS events continue to gather, and the emergence of Cluster 5 indicates a strengthening connection between the mining area and the surface fractures.  
Figure 5: Spatial distribution of MS events in the roof of the surface and overlying goat. (**a**) Distribution of MS events in May; (**b**) distribution of MS events in May to June; (**c**) distribution of MS events in May to July; (**d**) distribution of MS events in May to August; (**e**) evolution trend of MS events.  
Variance analysis was used to assess the differences between different clusters [31; 32; 33; 34; 35]. Pairwise comparisons between different clusters were conducted using \(t\)-tests, and the results are presented in Table 2. In the data comparisons, the t-statistic values are all relatively large, and the \(p\)-values are all close to 0, indicating that these differences are statistically significant. The \(p\)-value for the comparison between Cluster 2 and Cluster 6 is 0.2252, suggesting nonsignificance, likely because Clusters 2 and 6 overlap spatially. Based on the field measurements, it can be concluded that the grouping of these two components is reasonable.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Comparison** & **t-Statistic** & \(p\)**-Value** & **Significant Difference** \\ \hline cluster1 and cluster 2 & \(-\)40.8732 & 0 & Yes \\ cluster 1 and cluster 3 & \(-\)16.0652 & 0 & Yes \\ cluster 1 and cluster 4 & 18.4766 & 0 & Yes \\ cluster 1 and cluster 5 & 32.0344 & 0 & Yes \\ cluster 1 and cluster 6 & \(-\)13.2928 & 0 & Yes \\ cluster 2 and cluster 3 & \(-\)4.9693 & 0 & Yes \\ cluster 2 and cluster 4 & \(-\)59.092 & 0 & Yes \\ cluster 2 and cluster 5 & 76.7093 & 0 & Yes \\ cluster 2 and cluster 6 & 1.2132 & 0.2252 & No \\ cluster 3 and cluster 4 & \(-\)15.863 & 0 & Yes \\ cluster 3 and cluster 5 & 16.9806 & 0 & Yes \\ cluster 3 and cluster 6 & 1.9937 & 0.0465 & Yes \\ cluster 4 and cluster 5 & 15.1011 & 0 & Yes \\ cluster 4 and cluster 6 & \(-\)19.3877 & 0 & Yes \\ cluster 5 and cluster 6 & 25.1445 & 0 & Yes \\ \hline \hline \end{tabular}
\end{table}
Table 2: Analysis of variance by cluster.  
Figure 6: 3D spatial clustering results of MS events in 2019. (**a**) MS event data; (**b**) cluster results; (**c**) cluster influence range; (**d**) projection results.  
As shown in Figure 7, after July, the number of MS events detected at positions 2# (490-450 m) and 3# (450-250 m) also slightly increased due to the influence of crack Cluster 6. The trend for the MS events in the three regions becomes more consistent after August, indicating the downward extension of the crack's influence range. Prior to the penetration of roof cracks in early May and late June, there was a slight increase in the number of MS events within the range of 1# (980-490 m). Based on the distribution characteristics of the MS events in Cluster 6, it can be observed that the energy of the events is greater in the middle and lower parts. Therefore, it can be inferred that crack Cluster 6 will continue to have a downward impact, leading to the occurrence of small energy MS events.