## 3 Results and Discussion
### Waveform Analysis
#### 3.3.2 Peak Decay Amplitude Analysis  
The next step is to solve and fit the nine sets of mine seismic waveforms within the effective range, obtaining the upper envelope and fitting curves as shown in Figure 10. Among them, Figure 10a-c represents the pillar-type strong mine seismic events, Figure 10d-f represents the fault-type strong mine seismic events, and Figure 10g-i represents the roof-type strong mine seismic events. The corresponding fitting coefficients m and attenuation coefficients \(n\) are shown in Table 6. It is obvious from Figure 10 that the fitting curves of events M2, B2, and D2 deviate significantly from the envelope, with low fitting accuracy (<0.90), indicating large errors. The fitting accuracy of the other six events is relatively high, all exceeding 0.90, with M3, D3, and B1 events reaching 0.95 or above, indicating very small fitting errors. The envelope decay trends of M2 and M3 are similar, and the average of their decay coefficients can be used as the decay coefficient of the pillar-type strong mine seismic  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Event**} & **First Main** & **Second Main** & **Third Main** & **Frequency** \\  & **Frequency/Hz** & **Frequency/Hz** & **Frequency** & **Range/Hz** \\ \hline D1 & 60.8 & 50.8 & 33.1 & \\ D2 & 45.3 & 57.6 & 35.2 & [30; 60] \\ D3 & 69.1 & 38.7 & 8.7 & \\ \hline \hline \end{tabular}
\end{table}
Table 4: Main frequency characteristics of roof-type dynamic load waves.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Event**} & **First Main** & **Second Main** & **Frequency Range/Hz** \\  & **Frequency/Hz** & **Frequency/Hz** & **Frequency** & **Range/Hz** \\ \hline M1 & 13.1 & 30.7 & \\ M2 & 15.6 & 27.6 & [10; 40] \\ M3 & 12.7 & 49.1 & \\ \hline \hline \end{tabular}
\end{table}
Table 3: Main frequency characteristics of fault-type dynamic load waves.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Event**} & **First Main** & **Second Main** & **Third Main** & **Fourth Main** & **Frequency** \\  & **Frequency/Hz** & **Frequency/Hz** & **Frequency** & **Frequency** & **Range/Hz** \\ \hline B1 & 61.8 & 39.8 & 12.1 & 23.4 & \\ B2 & 45.7 & 49.4 & 22.9 & 11.1 & [40; 80] \\ B3 & 83.4 & 77.2 & 68.4 & 49.6 & \\ \hline \hline \end{tabular}
\end{table}
Table 5: Main frequency characteristics of coal pillar-type dynamic load waves.  
events. Similarly, the envelope decay trends of D1 and D2 are similar, so their average decay coefficients can be used as the decay coefficient of fault-type strong dynamic load. Likewise, the average of B1 and B2 decay coefficients can be used as the decay coefficient of roof-type strong dynamic load. The average decay coefficient of pillar-type strong mine seismic events is 1.57, the fault-type is 1.41, and the roof-type is 4.53. Overall, roof-type strong mine seismic waves decay the fastest, while fault-type strong mine seismic waves decay the slowest, as they are generated by distant fault movement, and their propagation paths generally do not pass through fractured roof strata, resulting in less energy dissipation.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Event** & **Fitting Coefficient \(m\)** & **Decay Coefficient \(n\)** & **R\({}^{2}\)** \\ \hline M1 & \(1.75\times 10^{-7}\) & 3.71 & 0.94896 \\ M2 & \(2.22\times 10^{-6}\) & 1.09 & 0.84846 \\ M3 & \(1.95\times 10^{-6}\) & 1.24 & 0.95688 \\ D1 & \(4.63\times 10^{-7}\) & 1.73 & 0.93215 \\ D2 & \(2.41\times 10^{-6}\) & 1.09 & 0.77968 \\ D3 & \(8.19\times 10^{-8}\) & 5.21 & 0.96950 \\ B1 & \(2.32\times 10^{-7}\) & 4.91 & 0.96279 \\ B2 & \(7.73\times 10^{-8}\) & 4.14 & 0.81614 \\ B3 & \(6.92\times 10^{-6}\) & 2.18 & 0.94912 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Fitting parameters of decay curve of peak amplitude after strong dynamic load wave.  
Figure 10: Decay curve of peak amplitude after strong dynamic load wave. (**a**) M1. (**b**) M2. (**c**) M3. (**d**) D1. (**e**) D2. (**f**) D3. (**g**) B1. (**h**) B2. (**i**) B3.