# GA-PSO Algorithm for Microseismic Source Location
## 3 Experiments and Results
### Simulation Validation of Microseismic Location Algorithms
#### 3.1.2 Analysis of the Simulation Results for Microseismic Source Location  
To analyze the performance of the location algorithms, the PSO, GA, NM-PSO, PSO-ACO, and GA-PSO algorithms were compared. To ensure accuracy, the error and optimal function value for each seismic event were calculated, with each of the five algorithms being run 10 times. The number of particle swarms and populations was set to 20, and the number of iterations to 100. The maximum and minimum values of the final seismic source location results were excluded, and the average of the remaining results was taken as the convergence value, representing the final location result. Consequently, Table 5 presents the location results obtained from five algorithms for events A and event B. The distance between the calculated and actual seismic source locations was considered as the absolute error. Figure 3a illustrates a comparison of the absolute errors in the localization results for six simulated microseismic source events across five algorithms. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Arithmetic**} & \multicolumn{5}{c}{**Event A**} \\ \cline{2-7}  & & **X/m** & **Y/m** & **Z/m** & \begin{tabular}{c} **Optimal** \\ **Function** \\ **Value** \\ \end{tabular} & \begin{tabular}{c} **Search** \\ **Time/s** \\ \end{tabular} \\ \hline \multirow{3}{*}{PSO} & Convergence value & 54.7102 & 192.0557 & \(-287.1071\) & \multirow{3}{*}{\(5.097\times 10^{-3}\)} & \multirow{3}{*}{0.33} \\  & Real value & 55 & 192 & \(-287\) & & \\  & Errors & \(-0.2898\) & \(0.0557\) & \(-0.1071\) & & \\ \hline \multirow{3}{*}{GA} & Convergence value & 55.4110 & 191.7454 & \(-286.8794\) & \multirow{3}{*}{\(0.1310\)} & \multirow{3}{*}{1.18} \\  & Real value & 55 & 192 & \(-287\) & & \\  & Errors & \(0.4110\) & \(-0.2546\) & \(0.1206\) & & \\ \hline \multirow{3}{*}{PSO-ACO} & Convergence value & 54.9964 & 192.0141 & \(-286.9920\) & \multirow{3}{*}{\(3.613\times 10^{-3}\)} & \multirow{3}{*}{0.74} \\  & Real value & 55 & 192 & \(-287\) & & \\  & Errors & \(-0.0036\) & \(0.0141\) & \(0.0080\) & & \\ \hline \multirow{3}{*}{NM-PSO} & Convergence value & 54.9923 & 191.9981 & \(-287\) & \multirow{3}{*}{\(1.445\times 10^{-3}\)} & \multirow{3}{*}{0.33} \\  & Real value & 55 & 192 & \(-287\) & & \\  & Errors & \(-0.0077\) & \(-0.0019\) & \(-0.0038\) & & \\ \hline \multirow{3}{*}{GA-PSO} & Convergence value & 54.9987 & 191.9995 & \(-286.9993\) & \multirow{3}{*}{\(3.387\times 10^{-4}\)} & \multirow{3}{*}{0.17} \\  & Real value & 55 & 192 & \(-287\) & & \\  & Errors & \(-0.0013\) & \(0.0005\) & \(0.0007\) & & \\ \hline \multicolumn{7}{c}{**EventB**} \\ \cline{2-7}  & & **X/m** & **Y/m** & **Z/m** & \
\begin{tabular}{c} **Optimal** \\ **Function** \\ **Value** \\ \end{tabular} &
\begin{tabular}{c} **Search** \\ **Time/s** \\ \end{tabular} \\ \hline \multirow{3}{*}{PSO} & Convergence value & 417.4418 & 251.1682 & \(-96.3564\) & \multirow{3}{*}{\(5.219\times 10^{-3}\)} & \multirow{3}{*}{0.43} \\  & Real value & 417 & 251 & \(-96\) & \\  & Errors & \(0.4418\) & \(0.1682\) & \(-0.3564\) & & \\ \hline \multirow{3}{*}{GA} & Convergence value & 417.5229 & 251.0520 & \(-95.6258\) & \multirow{3}{*}{0.1474} & \multirow{3}{*}{0.89} \\  & Real value & 417 & 251 & \(-96\) & & \\  & Errors & \(0.5229\) & \(0.0520\) & \(0.3742\) & & \\ \hline \multirow{3}{*}{PSO-ACO} & Convergence value & 416.9981 & 251.0134 & \(-95.9990\) & \multirow{3}{*}{\(3.553\times 10^{-3}\)} & \multirow{3}{*}{0.72} \\  & Real value & 417 & 251 & \(-96\) & & \\ \cline{1-1}  & Errors & \(-0.0019\) & \(0.0134\) & \(0.0010\) & & \\ \hline \multirow{3}{*}{NM-PSO} & Convergence value & 417.0008 & 250.9989 & \(-95.9981\) & \multirow{3}{*}{\(4.283\times 10^{-4}\)} & \multirow{3}{*}{0.33} \\  & Real value & 417 & 251 & \(-96\) & & \\ \cline{1-1}  & Real value & 417 & 251 & \(-96\) & & \\ \cline{1-1}  & Errors & \(0.0008\) & \(-0.0011\) & \(0.0019\) & & \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Comparison of location results of five algorithms.