# Applications of Microseismic Monitoring Technique in Coal Mines: A State-of-the-Art Review
## 3 Interpretation of Mining-Induced Microseismicity
### Microsesismic Focal Mechanism
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Description** \\ \hline Seismic energy \(E\) & The energy of the microseismic event reflects the intensity of rock fracturing. Seismic energy of the P-wave or S-wave can be calculated as \(E_{P,S}=\frac{\beta}{8}\pi\rho v_{P,S}\,R^{2}\int_{0}^{t_{*}}\,i_{\text{corr}}( t)dt\), where, \(\rho\) denotes rock density [61]. \\ Seismic moment \(M_{0}\) & A parameter measures the inelastic deformation at the microseismic source, and can be calculated as \(M_{0}=\mu P\), where, \(\mu\) denotes rock shear modulus. \\ Apparent stress \(\sigma_{A}\) & Apparent stress is the ratio of the seismic energy \(E\) to the seismic potency \(P\)[61]. \\ Apparent volume \(V_{A}\) & Apparent volume, often used together with the energy index, scales the rock volume with the inelastic change, and is written as \(V_{A}=M_{0}{}^{2}/(2\mu E)\)[62]. \\ Energy index \(EI\) & Energy index is the ratio of seismic energy \(E\) of a microseismic event to the average energy \(\overline{E}(P)\) of microseismicities with potency \(P\), and can be calculated as \(EI=E/\overline{E}(P)\)[63]. \\  & A parameter measures the spatio-temporal complexity of seismic flow and reflects the potential instability, and can be calculated as \(Sc=\frac{4\mu^{2}\Delta V\Delta t(\overline{t})\sum_{i=1}^{2}E_{s}}{\mu( \overline{X})\sum_{i=1}^{2}M_{0}}\), where, \(\Delta V\) denotes the volume of interest, \(\Delta t\) is the time step, \(\overline{t}\) is the mean time of microseismicities, \(t_{1}\) is the start time of a time period, \(t_{2}\) is the end time of a time period,\(\overline{X}\) denotes the mean distance between interacting microseismicities, \(M_{\overline{t}}\) is the seismic moment [64]. \\ Fault total area \(A(t)\) & Fault total area is defined as \(A(t)=\sum\limits_{k=t_{0}}^{k-1}N(k)L^{k=k_{0}}(L=4.5)\), where, \(k_{0}\) and \(k\) are the lower limit energy level and energy level of the microseismicity, respectively, \(N(k)\) denotes the event count of a given energy level \(k\)[58]. \\ \multirow{2}{*}{\(b\) value} & The slope of the Gutenberg and Richter relation written as \(\log N=a\)-\(bM\), where \(M\) is the magnitude, \(N\) is the number of seismicities with magnitude larger than \(M\), \(a\) is a constant reflecting the level of seismicities [65]. \\ Lack of shock \(b_{L}\) & A statistical parameter defined as \(b_{L}=\frac{0.43\Delta t_{0}}{M-M_{0}}\), where, \(\overline{M}\) is the average energy level, and \(M_{0}\) is the initial energy level [66]. \\  & Z value is a parameter to describe the rockburst risk defined as \(Z=\frac{\overline{M}-\overline{m}}{\sqrt{\sigma_{M}^{2}/N-\sigma_{m}^{2}/n}}\), where, \\ \multirow{2}{*}{\(Z\) value} & \(\overline{M}\) and \(\overline{m}\) are the arithmetic mean of average magnitude samples in the statistical period and the observation period, respectively, \(N\) and \(n\) are the numbers of \(\overline{M}\) and \(\overline{n}\) samples, \(\sigma_{M}\) and \(\sigma_{m}\) are their standard deviations, respectively [58]. \\ \hline \hline \end{tabular}
\end{table} 
Table 2: _Cont._[PERSON] et al. [76] revealed the focal mechanisms of microseismic events of irregular coal pillars in the Dongtan coal mine through a moment tensor, and the result suggested that the tensile failures were dominant at the coal pillar edge with the focal mechanism solution of reverse fault sliding, while the coal pillar core area experienced compression failures with the focal mechanism solution of normal fault sliding (Figure 5). [PERSON] et al. [77] inverted the focal mechanisms of microseismic events in the floor of a panel of the Dongjahe coal mine by moment tensor analysis and found that the hidden reverse fault has a dip angle and a rupture length of approximately 70\({}^{\circ}\) and 21 m, respectively. [PERSON] et al.