## 1 Introduction
The SBTEM method has early applications in geophysics, where the source consists of grounded wires or large loops deployed on the surface, with receivers positioned along boreholes to detect nearby electrical conductors [22; 23]. This method is widely utilized not only for detecting oil and gas reservoirs [24; 25] but also for various engineering applications, such as monitoring coal seam roof grouting [26], CO\({}_{2}\) injection [27], etc. Over time, the SBTEM method has evolved from theoretical development to practical implementation. Key issues, such as casing effects, anisotropic media, and zero-band distribution, have been addressed through forward modeling [28; 29]. In terms of inversion, the focus has shifted from one-dimensional (1D) to three-dimensional (3D) models, with advancements moving from single SBTEM inversions to joint inversions that combine STEM and SBTEM data [30; 31]. The SBTEM method allows for the deployment of large loops or long wires at the surface, thus providing a stronger source signal. However, considering the cost implications associated with much deeper boreholes in underground engineering, the SBTEM method is more suitable for exploring shallow geological targets [32]. The RBTEM and BTEM methods are widely used in coal mines and underground engineering. In the RBTEMmethod, transmitters are placed within roadways, while the BTEM method positions transmitters inside boreholes; both methods deploy receivers exclusively in boreholes [33; 34]. They operate under a full-space framework, which is a key distinction from surface-based methods. These techniques leverage underground conditions to enhance proximity to target structures and bypass complex surface topography, thereby improving detection accuracy and simplifying deployment [35; 36; 37]. However, technical limitations persist; both methods employ small coils that generate weak induced signals. Increasing coil turns amplifies self- and mutual-inductance effects, further degrading signal quality [38]. Additionally, grounded-wire sources which offer stronger signals are incompatible with roadway environments due to explosion risks from gas leakage. Consequently, resolving this source constraint remains a critical unsolved challenge in underground exploration [39]. This paper proposes a cross-hole grounded-wire-source TEM exploration technique for the purpose of isolating it from the roadway space. The method involves placing a grounded-wire source in existing boreholes along the direction of the roadway, with data acquisition conducted in other boreholes. This method enhances electromagnetic detection resolution while mitigating interference in the roadway, thereby optimizing the signal-to-noise ratio. It also provides a practical solution for pinpointing water inrush hazards. To investigate the feasibility of this new TEM detection technique, numerical forward modeling is employed, utilizing the vector finite-element (FE) method [32] to construct 3D models and calculate the electromagnetic field. After validating the accuracy and efficiency of the algorithm, we analyze the response characteristics of the three components of the electric field, summarizing the diffusion behavior in full space. Subsequently, the response patterns and detection capabilities for anomalous bodies with different properties and locations are explored. The paper adopts first-order finite-difference calculations to process multi-channel data, thereby enhancing the ability to identify anomaly boundaries. Finally, the effectiveness of the proposed method is further validated by integrating a complex trap column model with a multi-borehole receiver configuration, demonstrating its potential for the reliable detection of subsurface anomalies. Together, the numerical examples demonstrate that the cross-hole grounded-wire TEM method proposed in this paper is more effective for detecting targets far away from the surface. This approach not only yields a stronger response signal but also effectively mitigates various types of metal interference within the roadway.