# GA-PSO Algorithm for Microseismic Source Location
## 3 Experiments and Results  
### Simulation Validation of Microseismic Location Algorithms  
#### 3.1.1 Developing a Simulated Source Spatial Model  
To validate the accuracy of the localization algorithm presented in this paper, 10 geophones and 6 microseismic events were deployed in a three-dimensional space. The model was constructed within a 500 m \(\times\) 500 m \(\times\) 500 m domain, with the microseismic event initiating at 0 s and a wave speed of 2570 m/s. The spatial distribution of the sensors and microseismic events is illustrated in Figure 2, and the geophone spatial coordinate are shown in Table 2.  
Figure 2: Detectors and source modeling.  
The simulated microseismic event coordinates are shown in Table 3, the principle of the positioning simulation verification is based on calculating the actual distance between each geophone and the simulated seismic source according to their three-dimensional spatial positions. The P-wave velocity and the initial time of seismicity (\(t_{0}\)) are assumed to determine the P-wave's initial arrival time.  
In this study, the arrival time of the P-wave is calculated using a geometric model based on the assumption of a uniform wave velocity, with the results representing theoretical predictions based on uniform propagation speed. The specific method is as follows: assuming the P-wave velocity, \(V_{p}\), to be 2570 m/s and the origin time, \(t_{0}\), to be 0 s, the locations of the seismic source and detectors are first defined, and the P-wave arrival time is then obtained using Equation (1).  
Upon obtaining the P-wave arrival time, these values, along with the geophone locations, are input into the GA-PSO algorithm. The results generated by the algorithm are then compared with the actual microseismic source location, thus verifying the accuracy of the algorithm. The obtained P-wave first arrivals are shown in Table 4.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Sensor Number**} & \multicolumn{6}{c}{**P-Wave Initial Arrival time/ms**} \\ \cline{2-7}  & **A** & **B** & **C** & **D** & **E** & **F** \\ \hline
1 & 136.052 & 193.031 & 191.274 & 143.858 & 220.123 & 185.311 \\
2 & 219.166 & 109.439 & 176.880 & 190.895 & 270.151 & 119.179 \\
3 & 238.359 & 108.745 & 241.322 & 170.803 & 229.551 & 164.539 \\
4 & 165.202 & 192.639 & 252.062 & 115.878 & 167.828 & 217.277 \\
5 & 117.488 & 166.632 & 204.003 & 85.943 & 167.828 & 178.394 \\
6 & 113.615 & 246.124 & 121.588 & 184.030 & 157.593 & 193.309 \\
7 & 198.321 & 176.207 & 93.324 & 210.851 & 206.255 & 121.055 \\
8 & 226.303 & 187.461 & 190.878 & 205.781 & 170.513 & 173.496 \\
9 & 147.274 & 245.816 & 204.288 & 163.094 & 67.435 & 224.137 \\
10 & 132.927 & 72.496 & 76.024 & 117.049 & 162.407 & 10.677 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Detector and P-wave initial arrival.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Sensor Number** & **X/m** & **Y/m** & **Z/m** \\ \hline
1 & 0 & 0 & 0 \\
2 & 500 & 0 & 0 \\
3 & 500 & 500 & 0 \\
4 & 0 & 500 & 0 \\
5 & 0 & 268 & 0 \\
6 & 0 & 0 & \(-\)500 \\
7 & 500 & 64 & \(-\)500 \\
8 & 500 & 500 & \(-\)500 \\
9 & 0 & 500 & \(-\)500 \\
10 & 391 & 145 & \(-\)247 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Geophone spatial coordinate position.