# GA-PSO Algorithm for Microseismic Source Location
## 3 Experiments and Results
### Simulation Validation of Microseismic Location Algorithms
#### 3.1.3 Comprehensive Comparative Experiments of Microseismic Location Algorithms  
To verify the stability of the algorithm's location accuracy, this manuscript re-evaluated detector arrivals under wave speed fluctuations of \(\pm\)1%, \(\pm\)3%, and \(\pm\)5%. The P-wave velocity fluctuation is typically simulated by perturbing the wave velocity within a range of \(\pm\)1% to \(\pm\)5%, to reflect the natural variability commonly observed in geological environments [38]. Specifically, \(\pm\)1% simulates minor environmental disturbances, \(\pm\)3% simulates disturbances caused by moderate changes in the rock layer structure, and \(\pm\)5% simulates disturbances under extreme conditions. In the experiment, the base P-wave velocity is set to 2570 m/s, with fluctuations introduced within the \(\pm\)1%, \(\pm\)3%, and \(\pm\)5% ranges of this velocity through random sampling. The fluctuated P-wave velocity is calculated using the formula below:  
\[V_{pi}=V_{b}\times(1+\delta_{i}) \tag{15}\]  
where \(V_{pi}\) represents the P-wave velocity at the \(i\)-th detector after incorporating the velocity fluctuation; \(V_{b}\) is the base P-wave velocity; \(V_{ci}\) is a random variable; and \(\delta_{i}\) represents the uniformly distributed perturbation coefficient, where \(\delta_{i}\sim U(-r,r)\), with \(r\in\{0.01,\ 0.03,\ 0.05\}\). The geo-regime-specific bounds satisfy \(\left\|\delta\right\|_{\infty}\leq 5\%\), preserving physical realizability in accordance with poroelasticity constraints. Table 6 presents the sensor arrival times under varying wave speed fluctuations. As observed in Figure 4a, when the wave speed fluctuates by \(\pm\)1%, the positioning error of both the PSO algorithm and the GA is minimal, with the GA-PSO algorithm demonstrating slightly better convergence results and maintaining a certain degree of accuracy. The NM-PSO algorithm performs slightly worse than the GA-PSO algorithm, demonstrating a certain level of robustness. The PSO-ACO algorithm also demonstrates good accuracy; however, its overall performance, particularly when compared to GA-PSO and NM-PSO, is slightly inferior. When the wave speed error is \(\pm\)3% (Figure 4b), the impact on the GA-PSO algorithm remains minimal. It is evident that both the GA and the PSO algorithm display varying degrees of fluctuation in source location accuracy under different wave speed variations. Although GA has a strong global search capability to avoid falling into local optimal solutions, its search process is more random and prone to larger error fluctuations, and PSO's updating mechanism makes its error fluctuations relatively small; the hybrid mechanism of GA-PSO algorithm is able to balance the advantages of both and thus maintains a small error fluctuation rate in most of the search process, which suggests that the GA-PSO algorithm achieves more accurate localization despite fluctuations in wave speed. Among the three hybrid algorithms, the PSO-ACO algorithm is more significantly affected by velocity fluctuations, mainly because its pheromone update mechanism does not quickly adapt to changes in velocity, resulting in inaccuracies during the search process. Meanwhile, the error rate of the NM-PSO algorithm increases more rapidly than that of the GA-PSO when subjected to velocity fluctuations. Figure 4c clearly demonstrates that in the NM-PSO algorithm, the limited adaptability of the Nelder-Mead method to global fluctuations results in error accumulation, which gradually increases due to velocity fluctuations. As each local solution may no longer represent the global optimum, the error eventually converges to a value similar to that of the PSO-ACO algorithm. In contrast, the localization effect of the GA-PSO algorithm is more pronounced. As can be seen in Figure 5a, in the early stages of iteration, the GA-PSO algorithm leverages the crossover and mutation operations of GA to explore a larger search space.