## 4 Laboratory Experiment Verification of space state Transformation  
### Theory and Design of the Indoor Model Experiment  
According to the similarity criterion of the transient electromagnetic method [12; 14], the basic similarity criterion is obtained as shown in Formula (17), and the additional similarity criterion is expressed as shown in Formula (18):  
\[\sigma_{m}=\frac{L^{2}}{T}\sigma_{p} \tag{17}\]  
where \(p\) and \(m\) indicate the prototype and model, respectively, \(\sigma_{p}\) and \(\sigma_{m}\) are the conductivity of the prototype and model, respectively, \(L\) represents the geometric similarity ratio between the prototype and the model, and \(T\) denotes the time similarity ratio between the prototype and the model. \[\frac{V_{m}(t)/I_{m}}{V_{p}(t)/I_{p}}=\frac{N_{Tm}N_{Rm}}{N_{Tp}N_{Rp}}\frac{ l_{Tm}{}^{2}I_{Rm}{}^{2}}{}_{2}\frac{T^{2}a}{b} \tag{18}\]  
where \(V(t)\) and \(I\) are the induced voltage and emission current in different models, respectively. \(N_{T}\) and \(N_{R}\) represent the turn of the transmitting coil and receiving coil, respectively, \(l_{T}\) and \(l_{R}\) denote the length of the transmitting coil and receiving coil, respectively, and \(a\) and \(b\) are the ratio factor of electric field and magnetic field between the prototype and the model, respectively. The PROTEM47 transient electromagnetic instrument is a time-domain transient electromagnetic instrument produced by Geonics in Canada, which is suitable for various occasions [12]. The PROTEM47 transient electromagnetic instrument was adopted in the laboratory experiment, so the time of the two models was consistent. The time similarity ratio was equal to 1, and Formula (17) could be simplified as \(\sigma_{m}=L^{2}\sigma_{p}\), which indicated that the geometric similarity was the main control condition of the basic similarity criterion. Formula (18) described the proportional relationship between the observed data of the prototype and the model. Since the two proportional factors of the electromagnetic field between the prototype and the model were assumed to be a fixed constant, the proportionality coefficient depended on the specific size of the transmitting coil and receiving coil. Therefore, the coil system could not be designed according to the geometric similarity, which brought significant convenience to the design of two coils in the laboratory experiment. The PROTEM47 transient electromagnetic instrument could convert the induced voltage of the receiving coil into the rate of change of magnetic induction intensity \(d_{B}/d_{t}\) according to the corresponding input parameters. If the electromagnetic field proportional factor b = 1 was selected, the transformation result \(d_{B}/d_{t}\) obtained by field detection equaled \(d_{B}^{\prime}/d_{t}^{\prime}\) in the physical experiment [15]. Using the interface menu of the PROTEM47 transient electromagnetic instrument and inputting the parameters of each device in the experiment according to Formula (18), the experiment data consistent with that in the field could be obtained. The experiment mainly verified the response difference of transient electromagnetic effect in the full space state, the 3/4 space state, and the half space state. During the operational process of the vehicle-mounted detection system of the high-speed railway tunnel, the space size involved in the spatial transformation of the VMTEM could reach several hundred meters or even several kilometers. In contrast, the size that could be simulated in the laboratory experiment could only reach several meters, which was relatively small. Therefore, a similar model experiment was used to verify the spatial transformation of the VMTEM.