## 2 Diffusion Characteristics and Proportional Coefficients of Space States
### Proportional Coefficients of Different Space States
The proportional coefficients of full space to half space obtained by the two methods are consistent, so it is feasible to investigate the proportional coefficient of full space to half space by means of numerical simulation. The proportional coefficient of 3/4 space to half space is determined based on the normal direction of the transmitting coil, not the normal direction of the plane where the induced current diffuses. For the half space state, the plane of the induced current diffusion is parallel to the plane of the transmitting coil. For the 3/4 space state, due to the geometric asymmetry, that is, the lack of some space, the plane where the induced current diffusion is formed in the space is deflected. There is a certain angle between the plane where the induced current diffusion is located in the 3/4 space state and the plane where the transmitting coil is located, that is, the plane where the induced current diffusion is located in the 3/4 space state is not parallel to the plane where the transmitting coil is located. Since the vehicle-mounted detection system still measures the induced eddy current in the Z direction, the electromagnetic field component in the Z direction is still taken as the analysis object of different space coefficients. Therefore, the proportional coefficient of 3/4 space to half space is the vertical component in the normal direction of the transmitting coil. The 3/4 space state is an asymmetric structure, so it is impossible to derive the analytical formula of the secondary field component of the transient electromagnetic field in the 3/4 space state, and it is difficult to obtain the analytical formula of the proportional coefficient of the 3/4 space to half space in theory. Combined with the numerical simulation, the proportional coefficient of full space to half space is verified correctly. Under the same model size and meshing conditions, it is inferred that the numerical simulation results of the proportional coefficient of 3/4 space to half space under the same conditions can also correctly verify the results of the analytical solution. In the numerical simulation, the average value of the proportional coefficient of 3/4 space to half space was 1.42, and it could be ascertained that the electromagnetic field in the 3/4 space state included three parts. The first part was the electromagnetic field generated by the 1/2 space below. The second part was the electromagnetic field generated by the 1/4 space above (the deflection effect caused by space asymmetry). The third part was the additional electromagnetic field generated by the upper and lower two spaces (the space effect of 3/4 space to half space was significantly smaller than that of full space to half space). In summary, the proportional coefficient of full space and 3/4 space to half space is a constant value, that is, it shows a fixed multiple relationship. In addition, the numerical simulation results of proportional coefficients in different space states were consistent with the theoretical analysis results, which verified the feasibility of numerical simulation. It provided an essential theoretical basis for the subsequent analysis of the spatial transformation problem of VMTEM in operational tunnels.