## 5 Conclusions and Discussion  
This paper mainly investigated the diffusion characteristics and proportional coefficients of three ideal space states, analyzed the spatial transformation process of operational tunnels, and put forward the critical distance. A laboratory experiment was also carried out. The main conclusions are as follows:  
1. The induced current in half space gradually spreads to both ends, and the induced current in full space diffuses to both ends of the horizontal symmetric center. However, the induced current in 3/4 space is not symmetric, and the angle between the induced current in 3/4 space and the horizontal plane is approximately 15\({}^{\circ}\). 2. Taking the amplitude of induced voltage in the vertical direction of the transmitting coil as the research object, the space correction method and correction coefficient of the VMTEM are proposed. As for the condition of the uniform medium, the response signal of three space states all exhibit a linear decrease under the double logarithmic  
Figure 16: Response curve of the saline model under different coil offset distances. coordinate system. The correction coefficient of full space to half space is 2.50, and the correction coefficient of 3/4 space to half space is 1.42. 3. The correction of different space states can be realized by substituting the proportional coefficient of the corresponding space at different stages. Aiming at the spatial transformation problem of vehicle-mounted detection systems, the space correction coefficient formula is proposed. Combined with the proposed time window of the vehicle-mounted detection system, the critical distance is determined to be 300 m.
4. By analyzing the response values under different space conditions and coil offset conditions, the indoor saline model experiment verified the phenomenon of spatial transformation in transient electromagnetic space. The critical distance, without considering the influence of transient electromagnetic spatial transformation, was also verified. In the present study, the inhomogeneity of surrounding rock distribution and the presence of low-resistivity water body were not considered for the transient electromagnetic diffusion law of different space states. Meanwhile, the shape of the tunnel surrounding rock was not fully considered in the analysis of the spatial transformation process. Therefore, the proportional coefficients of different spaces were based on ideal conditions, and there was a certain inconsistency with the actual surrounding rock environment. In future study, the surrounding rock environment of this complex condition will be further considered and modified proportional coefficients of different spaces obtained. As for the indoor saline model experiment, the experiment size was only 1.0 m and still quite small, which could not realistically illustrate the actual situation. Besides, the amount of experimental data were not enough, and there may have been some response curve characteristics that were not found. These two aspects of the model experiment need to be improved in further research. Conceptualization, J.X. and W.Q. ; methodology, J.X., Y.X. and B.W. ; validation, H.Z. and Y.X. ; formal analysis, S.L., H.Z. and R.Z. ; investigation, S.L. ; resources, J.X., H.Z., B.W. and W.Q. ; data curation, J.X., H.Z., Y.X. and W.Q. ; writing--original draft preparation, J.X. ; writing--review and editing, W.Q. ; visualization, H.Z. ; supervision, B.W. and W.Q. ; funding acquisition, B.W. and W.Q. All authors have read and agreed to the published version of the manuscript. This work was supported by the National Natural Science Foundation of China (Grant No. 52208395), Science and Technology Plan Project of Department of Communications of Zhejiang Province (Grant No. 2021051), and Nantong Science and Technology Plan Project (Grant Nos. JC2021169 and JC2020142). The authors appreciatively acknowledge the financial support of the abovementioned agencies. Not applicable.