# GA-PSO Algorithm for Microseismic Source Location
## 1 Introduction  
Mine rockbursts, air-mining zones, and mine gas leaks can cause serious disasters. To prevent these accidents, microseismic monitoring technology has been integrated into the mineral extraction process, enabling the prediction of small earthquake locations and magnitudes, thus mitigating serious injuries and fatalities. Accurate microseismic source location is crucial for microseismic monitoring, and many classic and widely used algorithms exist for locating microseismic events. Unlike traditional classification methods, source location algorithms are categorized into heuristic and non-heuristic algorithms. Non-heuristic algorithms include the classical location method proposed by [PERSON] and the simplex location algorithms introduced by [PERSON] et al. [1, 2]. To reduce [PERSON]'s dependence on velocity models, [PERSON] et al. [3] integrated a linear positioning approach with the Geiger method. This hybrid strategy addresses non-convergence issues caused by large initial value errors in time residual functions through iterative coordinate solving. [PERSON] et al. [4] proposed a parameter-free, population-based simplex method (APS). This approach performs a local search by constructing a hypersphere around the best individual, where each population member selects a simplex and adjusts the diversification probability threshold according to the simplex's volume. [PERSON] et al. [5] applied the Gravitational Search Algorithm (GSA) to source localization. In addition to these non-heuristic methods, several other innovations in seismic source localization have emerged. For instance, [PERSON] et al. proposed a novel data compression framework for seismic sensor networks using Distributed Principal Component Analysis, significantly improving the overall performance of seismic monitoring systems and the accuracy of seismic positioning [6]. [PERSON] et al. introduced an interferometric travel time positioning method that iteratively solves the minimum residual function, eliminating certain errors and achieving accurate positioning [7]. [PERSON] et al. [8] proposed a combination of PA-PDEI and phase-amplitude-based full waveform inversion methods, enhancing low-frequency and phase information to reliably reconstruct velocity models and improve deeper region resolution. [PERSON] et al. [9] developed an intelligent microseismic localization model using Fully Convolutional Neural Networks (FCNNs). Although non-heuristic algorithms exhibit theoretical simplicity, their strong dependence on initial values, computational complexity of derivatives, and reliance on objective function differentiability have driven researchers toward heuristic algorithms. The latter demonstrate enhanced search robustness by simulating natural phenomena. Heuristic algorithms mainly include population intelligence optimization methods such as the GA, PSO algorithm, and the simulated annealing (SA) algorithm. [PERSON] et al. improved the accuracy of microseismic location by optimizing the \(\Omega\) penalty function using ant colony optimization [10]. [PERSON], [PERSON] et al. proposed a nonlinear modification to the PSO algorithm to prevent it from becoming trapped in local optima [11]. [PERSON] et al. [12] integrated multiple strategies with the PSO algorithm to enhance PSO optimization performance. [PERSON] and [PERSON] introduced the Cuckoo Search Algorithm, optimizing the search by simulating the breeding behavior of cuckoos [13]. [PERSON] and [PERSON] developed the Seagull Optimization Algorithm, which performs global searches during migration and local searches during attacks [14]. [PERSON] et al. [15] employed the GA for seismic data inversion of the Okada model in their experiments, optimizing convergence through an elitism strategy and an adaptive mutation rate. This method demonstrated reasonable accuracy in estimating earthquake magnitude and azimuthal direction.