## 3 Overview and Mechanism of Mining-Induced Earthquake Events at the 3308 Working Face
### Analysis of Microseismic Activity Patterns Before and After High-Energy Mining-Induced Earthquakes
#### 3.3.2 Calculation of Mining-Induced Earthquake Source Mechanism  
This study conducted microseismic localization and source mechanism analysis for the two high-energy mining-induced earthquake events on 10 September and 20 December. The waveform diagrams for these events are shown in Figures 12 and 13. Eight sensors with clearer waveforms (highlighted in red), selected from sensors 1, 4, 5, 6, 7, 9, 11, 14, 15, and 16, were used for picking arrival times and performing localization calculations. Assuming the source coordinates are \((x_{s},y_{s},z_{s})\), the coordinates of the _i-th_ sensor are \((x_{i},y_{i},z_{i})\), the propagation velocity of seismic waves is \(v\), the occurrence time of the source event is \(t_{0}\), and the arrival time recorded by the _i-th_ sensor is \(t_{i}\). The distance between the source and the sensor can then be expressed as [31]:  
\[d_{i}=\sqrt{\left(x_{s}-x_{i}\right)^{2}+\left(y_{s}-y_{i}\right)^{2}+\left(z_ {s}-z_{i}\right)^{2}}=v\cdot\left(t_{i}-t_{0}\right) \tag{2}\]  
Figure 11: Distribution map of microseismic event locations: (**a**) microseismic event location base map (3–12 September); (**b**) microseismic event location base map (13–22 December). For multiple sensors, a set of nonlinear equations can be established to determine the source coordinates and the event occurrence time. In this study, eight sensors were selected, allowing for the formation of eight equations:  
\[ \begin{array}{l}\sqrt{\left(x_{s}-x_{1}\right)^{2}+\left(y_{s}-y_{1}\right)^{2 }+\left(z_{s}-z_{1}\right)^{2}}=v\cdot\left(t_{i}-t_{1}\right)\\ \sqrt{\left(x_{s}-x_{2}\right)^{2}+\left(y_{s}-y_{2}\right)^{2}+\left(z_{s}-z _{2}\right)^{2}}=v\cdot\left(t_{i}-t_{2}\right)\\ \bullet\\ \bullet\\ \bullet\\ \bullet\\ \sqrt{\left(x_{s}-x_{8}\right)^{2}+\left(y_{s}-y_{8}\right)^{2}+\left(z_{s}- z_{8}\right)^{2}}=v\cdot\left(t_{i}-t_{8}\right)\end{array}  \tag{3}\]  
By using the least squares method or nonlinear optimization techniques to solve these nonlinear equations [32], the three-dimensional location of the seismic source and the occurrence time \(t_{0}\) can be obtained. The moment tensor \(M_{ij}\) is a second-order tensor used to describe the seismic source, with the physical significance of characterizing the mechanical features of fault slip during source rupture. The calculation formula for the moment tensor is as follows [33]:  
\[M_{ij}=\mu\cdot A\cdot\mu_{i}\cdot\mu_{j} \tag{4}\]  
In this formula, \(\mu\) represents the shear modulus, reflecting the stiffness of the medium; \(A\) is the area of the rupture surface; and \(\mu_{i}\) and \(\mu_{j}\) are the components of the normal vector and the slip direction vector on the rupture surface, respectively. The seismic moment \(M_{ij}\) is the modulus of the moment tensor and can quantify the scale of the rupture event. Its calculation formula is as follows:  
\[\mathrm{M}_{0}=\sqrt{\sum_{i=1}^{3}\sum_{j=1}^{3}M_{ij}^{2}} \tag{5}\]  
For a microseismic event, the volume \(V\) of the rupture body is related to the seismic moment \(M_{0}\) and the average slip \(D\). The calculation formula is as follows:  
\[V=\frac{M_{0}}{\mu\cdot D} \tag{6}\]  
In this formula, \(M_{0}\) is the seismic moment, \(\mu\) is the shear modulus, and \(D\) is the average slip on the rupture surface. In more precise source analysis, the released energy can be represented comprehensively through the seismic moment and slip amount [34]:  
\[E=\frac{M_{0}\cdot D}{2\cdot\mu\cdot V} \tag{7}\]  
Moment magnitude is a measure of earthquake size in seismology, based on the seismic moment and directly related to the energy released by the source. The calculation formula for moment magnitude is as follows [35]:  
\[M_{w}=\frac{2}{3}\log_{10}(M_{0})-6.0 \tag{8}\]  
In this formula, \(M_{w}\) represents the moment magnitude, and \(M_{0}\) is the seismic moment, measured in Newton-meters (\(N\cdot m\)). The seismic moment is typically obtained through seismic wave inversion or estimated based on source parameters.