# Investigation of Microseismic Monitoring of and Precursor Information on Roof Collapse
## 4 Data Analysis and Discussions
### Distribution Characteristics of Crack Clusters  
The different forms of crack clusters can reflect the complexity of crack development in the region. The distribution patterns of the identified crack clusters are relatively diverse and can be divided into three stages. The first stage is that each cluster is independent of the others, and the influence range is not superimposed, as shown in Figure 4a. The boundary contour of the crack cluster is clear and easy to distinguish. In the second stage, there is a small amount of overlap between the clusters, as shown in Figure 4b. The boundary contour of the crack clusters is relatively clear, mostly overlapping at the beginning and end of the ellipsoidal model. The third stage is where there are large overlapping influence areas between each cluster, as shown in Figure 4c. Under the first two conditions, the  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Cluster** & **a** & **b** & **c** & \begin{tabular}{c} **Ellipsoidal** \\ **Volume/m3** \\ \end{tabular} & \
\begin{tabular}{c} **Number of MS** \\ **Events** \\ \end{tabular} &
\begin{tabular}{c} **MS Event Density** \\ **Logarithm** \\ \end{tabular} \\ \hline
1 & 157.51 & 150.49 & 95.61 & 9,488,279.657 & 1006 & \(-\)3.97 \\
2 & 220.87 & 181.01 & 160.11 & 26,799,466.08 & 1616 & \(-\)4.22 \\
3 & 48.27 & 30.72 & 22.19 & 137,760.3372 & 1062 & \(-\)2.11 \\
4 & 82.5 & 27.4 & 21.45 & 203,001.942 & 2310 & \(-\)1.94 \\
5 & 74.54 & 41.91 & 16.32 & 213,449.7195 & 937 & \(-\)2.36 \\
6 & 228.04 & 137.01 & 44.86 & 5,868,011.45 & 458 & \(-\)4.11 \\
7 & 96.21 & 49.29 & 24.89 & 494,165.3772 & 1891 & \(-\)2.42 \\
8 & 88.65 & 60.35 & 19.76 & 442,599.9284 & 980 & \(-\)2.65 \\
9 & 87.89 & 34.45 & 34.45 & 436,703.127 & 1761 & \(-\)2.39 \\
10 & 68 & 57 & 12.13 & 196,839.8176 & 1401 & \(-\)2.15 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Ellipsoidal parameters of a single crack.  
development of crack clusters is relatively independent and has little mutual influence. When a large area of overlap occurs in the crack cluster, the cracks are considered to have penetrated. When new crack clusters appear around the overlapping crack clusters and surround them, the penetrating cracks begin to expand, expanding the scope of influence. Figure 4d shows a comparison between the clustering results and onsite cracks, indicating that obvious cracks have appeared in the roadway and are spreading horizontally.  
The size of the MS event sphere in Figure 3 is positively correlated with its magnitude. The energy of the MS events at both ends of the ellipsoidal model is relatively small, while the central position exhibits relatively large energy. Based on statistical analysis, the energy distribution of the crack cluster follows a Gaussian model and can serve as a criterion for identifying individual cracks. The spatiotemporal correlation between adjacent clusters is stronger, with the long axis \"a\" representing the crack length, the long axis \"b\" representing the crack width, and the long axis \"c\" representing the crack's range of influence. Clusters with a higher MS event density and a concentrated range of influence (shorter \"c\"-axis length) are more prone to macroscopic cracks. The clustering results of MS events demonstrate the dynamic evolution process of the rock mass, including independent development from the nucleation location, mutual influence between adjacent locations, crack growth, and crack propagation.