Inversion model combination for microseismic source positioning with Multi-Objective Grasshopper Optimization Algorithm

Abstract

The precise determination of microseismic source locations is one of the core components of theoretical research in microseismic monitoring technology. Multi-objective intelligent optimization is an effective approach for microseismic source positioning, but it faces challenges such as unclear rationality of model combinations, susceptibility to local optima, and significant variability in positioning results. To address these issues, four distinct mathematical models for microseismic source positioning were designed based on the arrival time difference model and the arrival time difference quotient model. These models were then combined in pairs to form six different microseismic source positioning model combinations, which were used as the optimization objective functions for the multi-objective computational algorithm. A set of microseismic source forward modeling experiments based on three-dimensional polyhedral array shapes, two sets of engineering microseismic data validation experiments, and one set of multi-objective computational method comparison experiments were designed. the multi-objective grasshopper optimization algorithm (MOGOA) was introduced to solve the six model combinations and employed in four sets of microseismic source positioning experiments. Multiple statistical metrics were applied to evaluate the performance of each model combination. The experimental results indicate that the microseismic inversion mathematical model combination (TDA, TDA-P1), combined with the MOGOA algorithm’s multi-objective optimization positioning strategy, can achieve high microseismic source positioning accuracy under relatively reliable microseismic event data, and the model calculations are relatively robust. Under microseismic blasting data, the average positioning error over 100 rounds reached 27.6035 m, with standard deviation and interquartile range averages of only 3.2114 m and 5.5896 m, respectively, outperforming other inversion model combinations and similar multi-objective positioning methods. For microseismic event data with significant systematic errors, the microseismic inversion mathematical model combination (TDA-P1, TDQA-P1) demonstrates superior positioning performance, with an average positioning error of 151.1915 m over 100 iterations, significantly outperforming other model combinations. These model combination positioning performance studies hold practical application value in the field of microseismic monitoring.

Keywords

Microseismic source positioning / Multi-objective optimization / Combination of inversion mathematical models / Time difference quotient of arrival / Time difference of arrival / Multi-Objective Grasshopper Optimization Algorithm

Acknowledgments

None.

Funding

This research was financially supported by Mahasarakham University; the Scientific Research Fund from Institute of Seismology, CEA and National Institute of Natural Hazards, Ministry of Emergency Management of China (Grant No. IS202226322 and IS202436357); the Open Fund of Wuhan Gravitation and Solid Earth Tides, National Observation and Research Station (Grant No. WHYWZ202406); the Spark Program of Earthquake Science and Technology, China Earthquake Administration (Grant No. XH25019C and XH24025YC); the 2025 Hubei Provincial Key Laboratory Targeted Commissioned Project (Grant No. 2025CSA083); the Green Data Integration Intelligence Research and Innovation Project of Chengdu Jincheng College (Grant No. 2025–2027); and the Mathematics and Finance Research Center Project of Dazhou Social Science Federation Key Research Base (Grant No. SCMF202505).

Conflict of interest

The authors declare they have no competing interests.

Author contributions

Conceptualization: Cong Pang, Tianwen Zhao, Sirui Liu, Xingxing Li, Ya Xiang

Formal analysis: Cong Pang, Guoqing Chen, Tianwen Zhao, Ya Xiang

Investigation: Tianwen Zhao, Sirui Liu, Xingxing Li, Piyapatr Busababodhin

Methodology: Cong Pang, Tianwen Zhao, Guoqing Chen, Piyapatr Busababodhin

Validation: Cong Pang, Shirui Liu, Tianwen Zhao, Guoqing Chen

Writing-original draft: Cong Pang, Tianwen Zhao, Guoqing Chen, Piyapatr Busababodhin

Writing-review & editing: Cong Pang, Tianwen Zhao, Guoqing Chen, Piyapatr Busababodhin

Availability of data

Some data used in this study cannot be shared publicly due to collaborative agreement restrictions but are available from the corresponding author upon reasonable request.

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