## 3 Methodology
### Method for High-Energy Seismic Events Discrimination  
Seismic energy has emerged as the primary indicator for identifying high-energy events, yet it remains the sole criterion. This method reflects only the energy magnitude radiated from the seismic source's rupture and does not adequately describe the seismic source medium's perturbation scale or the stress adjustment at the rupture surface. Moreover, it overlooks the impact of other SSPs on dynamic hazard assessment. Thus, while the seismic energy-based criterion is relatively reliable, it serves merely as a sufficient condition for identifying hazardous high-energy events. This evaluation approach also risks overlooking potentially hazardous events and cannot precisely differentiate the relative hazards of mining seismic events with comparable seismic energy levels. This section, predicated on the energy conditions for identifying hazardous high-energy events, examines the correlation between SSPs, selects appropriate evaluation parameters for these events, computes the fitting functions and influence weights for evaluation parameters and seismic energy, and formulates identification criteria based on the seismic energy and SSPs correlation. Consequently, hazardous high-energy events can be assessed accurately and judiciously. Furthermore, in light of the current criteria for evaluating the energy of hazardous high-energy events (referenced in Table 3), a comprehensive energy index (_CEI_) is formulated, as outlined in Table 4, incorporating various SSPs. \begin{table}
\begin{tabular}{c c} \hline \hline
**Scale** & **Meaning** \\ \hline
1 & Indicates that the two factors are of equal importance compared to each other \\
3 & Indicates that one factor is slightly more important than the other when comparing two factors \\
5 & Indicates that one factor is significantly more important than the other when comparing two factors \\
7 & Indicates that one factor is more strongly important than the other when comparing two factors \\
9 & Indicates the extreme importance of one factor over the other when comparing two factors \\
2, 4, 6, 8 & The median level of influence represented by the two neighboring scales above \\ Multiplicative inverse & \(a_{ij}\) of factor \(i\) compared to \(j\), then the judgment of factor \(j\) compared to \(i\,a_{ij}=1/a_{i}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Scale value meaning of analytic hierarchy process. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Ordinal Number (\(n\))** & **1** & **2** & **3** & **4** & **5** & **6** & **7** & **8** \\ \hline \(RI\) & 0 & 0 & 0.52 & 0.89 & 1.12 & 1.26 & 1.36 & 1.14 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Average random consistency indicator. The calculation process for the _CEI_ involves determining the correlation of the SSPs through analytical calculations of the fitting function and influence weight of SSP with seismic energy. Subsequently, the energy index corresponding to each SSP is derived from the correlation relationship between each SSP of the seismic source and the seismic energy, as delineated in Equation (11). \[W_{i}=\frac{\text{lg}m_{i}-b_{i}}{a_{i}} \tag{11}\]  
where \(a_{i}\) is the slope of the corresponding fit function and \(b_{i}\) is the intercept of the corresponding fit function. Upon establishing the fitted relationship between SSPs and seismic energy, the strength of the linear correlation between these two data sets can be measured further by the correlation coefficient \(R\), calculable through Equation (12). \[R=\frac{\text{Cov}(\text{X},\text{Y})}{\sqrt{\text{Var}[\text{X}]\times\text{ Var}[\text{Y}]}} \tag{12}\]  
where \(\text{Cov}(\text{X},\text{Y})\) is the covariance of the two sets of data and \(\text{Var}[\text{X}]\), \(\text{Var}[\text{Y}]\) are the variances of each of the two sets of data.