## 6 Discussion  
To enhance the coherence of inversion outcomes, weighted lateral and vertical constraints are employed to bolster the connectivity between neighboring stations. An adaptive regularization inversion approach is implemented, drawing on OCCAM inversion theory and a dynamic adjustment strategy for adaptive regularization factors. Leveraging the geological context of the Xiaolong Coal Mine in Xinjiang, a fault valley model depicting lateral resistivity variations is formulated. The optimal blend of lateral and vertical weighting factors is fine-tuned through the utilization of a control variable method, facilitating the analysis and interpretation of the collected data. The validation of the algorithm's feasibility and efficacy is conducted through a borehole data assessment. The following insights are gained:  
1. Lateral constraint inversion integrates multiple measurement points for inversion by incorporating weighted lateral roughness and vertical roughness constraints. These constraints enhance the coherence between the measurement points, ensuring smooth continuity in resistivity and layer thickness between adjacent points. This approach mitigates abrupt changes in individual point inversions and guarantees the consistency of inversion outcomes both laterally and vertically. 2. Weighting factors significantly impact inversion outcomes. Insufficient weighting factors result in weak lateral constraints, leading to a lack of smoothness. Conversely, excessive weighting factors yield overly smoothed model parameters, potentially averaging and smoothing geological features to the point of causing an inversion failure. In practical scenarios, selecting appropriate weighting factors based on geological conditions, constructing a 3D model grounded in the study area's geological context, and refining optimal weighting factors through numerical simulations are recommended approaches. 3. The numerical simulations of a fault valley model at the Xiaolong Coal Mine, utilizing the geological context, demonstrate that the lateral constraint inversion algorithm employed in this study effectively distinguishes between water-bearing and non-water-bearing goals. The pseudo-two-dimensional weighted lateral constraint inversion proves to be a valuable technique for analyzing the transient electromagnetic data of goals. However, the algorithm exhibits superior identification capabilities for low-resistivity interfaces compared to high-resistivity interfaces, particularly for deep and inclined interfaces. 4. The geological setting of the Xiaolong Coal Mine is characterized by stability and limited structural complexity. Consequently, the fault valley model established using the data from this mine is relatively straightforward. However, it is essential to acknowledge the potential impact of subsurface electrical disruptions resulting from structural shifts when determining inversion sections in regions with more pronounced structural features. Moreover, the weighting factors employed in this study are derived from a three-dimensional model, indicating a level of precision that may be insufficient. Future investigations will incorporate adaptive weighting factor selection to enhance accuracy. Conceptualization, Y.Z. ; methodology, Y.Z. ; investigation, B.X. and X.W. ; writing--original draft preparation, Y.Z. ; writing--review and editing, Y.Z. ; funding acquisition, Y.Z. All authors have read and agreed to the published version of the manuscript. This paper is financially supported by the Key Research and Development Program Project of the Autonomous Region of China (2024B03005-3). **Informed Consent Statement:** Not applicable. **Data Availability Statement:** Data associated with this research are available and can be obtained by contacting the corresponding author. **Acknowledgments:** We sincerely thank MDPI, especially its editorial team and anonymous reviewers, for their valuable contributions to this manuscript's publication.