PhysLoc‐DeepONet: Physics‐Constrained DeepONet for Passive Seismic Source Localization With Limited Differential Travel‐Time Data

Abstract Passive source localization plays a critical role in understanding subsurface stress dynamics during hydraulic fracturing, assessing seismic risks, and exploring mineral resources. However, existing passive source localization methods often face challenges such as high computational costs, reliance on high‐quality data, and the need for large‐scale training data sets, which limits their practical application. To overcome these limitations, we propose a physics‐constrained deep operator network model (PhysLoc‐DeepONet) designed to address performance degradation in scenarios with sparse or low‐quality data. The model integrates physical constraints with deep learning techniques to achieve efficient and accurate source localization using limited seismic data. Compared with existing methods, PhysLoc‐DeepONet accounts for data sparsity in its network architecture and introduces innovations in training data set construction and loss function optimization, thereby maintaining high localization accuracy even under limited data conditions. Multiple numerical simulations and field tests are conducted based on microseismic monitoring scenarios to validate the effectiveness of the proposed method. Experimental results demonstrate that the model not only achieves fast ( s), high‐precision source localization in complex geological environments but also exhibits strong adaptability to various monitoring conditions and data quality levels. Further analysis indicates that incorporating additional physical information and data constraints can further enhance localization accuracy, yielding satisfactory results even under resource‐limited conditions. With its solid theoretical foundation and broad applicability, PhysLoc‐DeepONet enables efficient, accurate, and cost‐effective real‐time source localization, showing strong promise for practical implementation.