## 1 Introduction
Additionally, high-current multi-turn small-loop devices have been used by [PERSON] et al. to assess water-rich rock mass, buried depth, and fracture zone spatial distribution in complex terrains [8]. [PERSON] et al. successfully identified grouting deficiency areas and water-bearing channels in the Suncun Coal Mine by integrating the small-loop transient electromagnetic and micro-motion methods, evaluating grouting effectiveness [12]. Furthermore, [PERSON] et al. combined transient electromagnetic single-point inversion results with GeoIPAS software in a coal mine in Tongliao City, Jilin Province, producing 2D and 3D interpretation maps that visually displayed the anomaly positions and distribution ranges [13]. In conclusion, the application of transient electromagnetic methods in coal mines has evolved significantly in recent years, expanding from goat exploration to more precise targets such as grouting and water channels. The exploration resolution has improved, leading to the joint application of multiple geophysical methods and multidimensional interpretation. The OCCAM inversion method, initially proposed by [PERSON] et al., is extensively utilized in various exploration techniques such as the magnetotelluric method, the controlled source audio magnetotelluric method, and the TEM due to its advantageous smooth model concept [14; 15; 16]. In the TEM, a single-point inversion based on the OCCAM theory may lead to resistivity discontinuities due to noise and inversion result uncertainties. The lateral constraint inversion technique, pioneered by [PERSON] et al. in DC data inversion, has been applied to 2D electromagnetic data inversion and subsequently to TEM data analysis and paleochannel exploration [17; 18; 19]. [PERSON] et al. employed weighted lateral constraints to invert airborne TEM data, addressing the lateral resistivity and layer thickness discrepancies in traditional single-point 1D inversions, effectively mitigating false anomalies [20]. [PERSON] et al. utilized subsection combination constraints to invert airborne TEM data, reducing the inversion computation time [21]. [PERSON] et al. applied lateral constraints to the pseudo-two-dimensional inversion of short-migration transient electromagnetic data, enhancing the profile lateral continuity and noise resistance [22]. The widespread application of lateral constraints in direct current and TEM inversions, particularly in the TEM, has extended from conventional ground loop source TEM to airborne and short-offset TEM data processing. Notably, the inversion outcomes of the TEM data between neighboring survey points should exhibit strong lateral continuity. Incorporating lateral constraints enhances the noise resistance of the inversion algorithm and ameliorates the lateral resistivity and layer thickness discrepancies in single-point one-dimensional OCCAM inversions. Following the OCCAM inversion theory, lateral weighting and vertical roughness constraints are implemented to enhance the correlation between the inversion outcomes of neighboring measurements. Additionally, an adaptive regularization factor is incorporated to enhance the reliance of the inversion results on the initial model. By utilizing the geological context of the Xiaolong Coal Mine, a fault valley model with varying resistivity levels is developed. Through the utilization of the control variable method, the optimal combination of lateral and vertical factors is determined. This optimized approach is then applied to invert the measured TEM data from the Xiaolong Coal Mine, validating the method's feasibility and efficacy. The proposed method holds promise for advancing the utilization of the small-loop TEM technique in the exploration of coal mine goats.