## 3 Analysis of Spatial Transformation and Proposal of Critical Distance  
To detect the internal defects of the tunnel structure, the vehicle-mounted detection system runs at a specific speed in operational tunnels, that is, the position of the vehicle-mounted detection system dynamically changes, as shown in Figure 1. Taking the tunnel entrance as an example, the medium below the coil system and above the right does not change when the vehicle-mounted detection system enters the tunnel. In contrast, the medium above the left contains both air medium and uniform surrounding rock medium. The coil system can not only receive the electromagnetic induction signals generated by the surrounding rock below and above the right, but also receives the electromagnetic induction signals generated by the surrounding rock above the left. With the operation of the vehicle-mounted detection system, the electromagnetic induction signals generated by the surrounding rock above the left also increase. Therefore, the running state of the vehicle-mounted detection system in the tunnel entrance section is called transient electromagnetic spatial transformation, that is, from the 3/4 space state to the full space state. Similarly, when the vehicle-mounted detection system gradually approaches the exit of the tunnel, there is also a spatial transformation in the transient electromagnetic space, that is, from the full space state to the 3/4 space state. In summary, the running state of the vehicle-mounted detection system is running from the entrance or exit of the tunnel to the exit or entrance of the tunnel when the vehicle-mounted detection system is running in a limited length of the tunnel. From the perspective of transient electromagnetic spatial transformation, the vehicle-mounted detection system first converts from the 3/4 space state to the full space state, and then converts from the full space state to the 3/4 space state. Therefore, the electromagnetic induction signals at different positions need to be comprehensively analyzed to understand the spatial transformation law of the VMTEM. Based on the complexity and difficulty of the analytical derivation method, the finite element numerical simulation method was used to investigate the transient electromagnetic response law under different distances from the entrance and exit of the tunnel. Due to the investigation of spatial transformation law, the size of the finite element model neededto be set to be large enough to ensure that the transmitting coil was sufficiently far from the boundary, so that the transient electromagnetic field had sufficient space for diffusion. Considering the calculation ability of the computer, the size of the finite element model was set to 4000 m \(\times\) 4000 m \(\times\) 8000 m (length \(\times\) width \(\times\) height). In the numerical simulation, it was ensured that the electrical parameters of the transmitting coil and the receiving coil were constant, and only the position parameters changed. Other parameters, such as the size of the infinite element and the grid size, could be set according to the parameters in references [14,22]. The upper part of the medium on the left of the model was set as air medium, and the other positions were set as surrounding rock medium. Meanwhile, it was assumed that the influence of the landform characteristics of the tunnel mountain and the operational tunnel section were not considered. Taking the typical distance between the vehicle-mounted detection system and the entrance and exit of the tunnel as an analysis object, the analysis parameters were 0 m, 10 m, 25 m, 50 m, 100 m, 150 m, 200 m, 250 m, and 300 m, respectively. The transient electromagnetic response law under different offset distances was calculated, and the offset distance of 0 m corresponded to the 3/4 space state.