## 2 Microseismic Monitoring Method under Tunnel Construction
### Microseismic Location Detection Technology  
The microseismic location is the core link of microseismic monitoring technology, and the result of source solution is obtained from the microseismic location, which is related to the accuracy of microseismic monitoring and analysis. Research on more accurately determining the microseismic location has been a hotspot in the field of microseismic monitoring. The typical methods used for locating microseismic events mainly use the arrival time of the P-wave to locate the source. However, in a tunnel construction environment, because sensors are placed in limited locations, it is often difficult to cover the entire area where microseisms occur. In this scenario, it is necessary to use the S-wave arrival time for auxiliary location. In other words, two problems should be solved in determining the location of microseisms under tunneling construction: one is the S-wave arrival picking and the other is the location detection method based on the arrival times of the P- and S-waves. Because the arrival time of an S-wave is not evident, it is difficult to pick. Because of the lack of a suitable algorithm, the S-wave arrival typically depends on manual picking. In recent years, with the development of deep learning methods, researchers have proposed a method for picking P- and S-waves based on the deep neural network (DNN). For example, [PERSON] et al. [25] proposed a microseismic or AE sample pickup algorithm based on the long-short term memory (LSTM) network. Their results showed a high picking accuracy and robustness under different signal-to-noise ratios. The arrival time selection method proposed by [PERSON] and [PERSON] [26] employs a three-component seismic waveform as input, uses a DNN based on U-net, and simultaneously predicts the probability distributions of P-arrival, S-arrival, and noise. [PERSON] et al. (2018) [27] trained a CNN to estimate P-wave arrival times and first-motion polarities. The performance of the trained network was found to be on par with those of expert seismologists. The research results show that because of the higher accuracy of the picking results, the picking methods based on deep learning will replace conventional algorithms and become the mainstream in research and application. Based on different design ideas, researchers have proposed various of positioning methods. One of the classical methods is to establish an optimization function based on the residual vector formed by the difference between the calculated and observed arrival times of microseismic waves, and to solve the test source to minimize the optimization function, that is, the result of microseismic location (shown in Figure 4). The \(i\)th calculated arrival time \(t_{c_{i}}\) is estimated by the wave velocity and hypothetical source coordinates, which is expressed as:  
\[t_{c_{i}}=\frac{L_{i}(x_{0},y_{0},z_{0})}{v}+t_{0} \tag{1}\]  
where \(L_{i}\) is the distance from the \(i\)th observation point to the source; \((x_{0},y_{0},z_{0},t_{0})\) is the coordinate of the test source; \(t_{0}\) is the occurrence time of the test source; \(v\) is the wave velocity. The optimization function constructed by the L2 norm of the residual vector is expressed as follows:  
\[Q(x_{0},y_{0},z_{0},t_{0})_{\text{min}}=\frac{1}{n}\sum_{i=1}^{n}{(t_{o_{i}}- \frac{L_{i}(x_{0},y_{0},z_{0})}{v}-t_{0})^{2}} \tag{2}\]  
where \(t_{o_{i}}\) is the \(i\)th observed arrival time; \(n\) is the total number of observed arrival times. For a tunnel environment, this includes not only the picked P-wave arrival time, but also the S-wave arrival time. This positioning method is simple and effective; the other positioning methods proposed can be considered as a derivative of this method. In recent years, the methods for locating the source under tunneling and other engineering conditions have been optimized and improved, and many new results have been obtained. For example, in the method proposed by [PERSON] et al.