## 1 Introduction  
The transient electromagnetic method is widely used because of the sensitivity property to the electromagnetic field signal of a low-resistivity body [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]. Meanwhile, the transient electromagnetic method in different engineering fields determines the space state of transient electromagnetism, and different space states have different electromagnetic field diffusion phenomena and data inversion. The space state of transient electromagnetism is a half space state in fields of Earth and aviation [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]. Correspondingly, the space state of transient electromagnetism is full space in the fields of mines and tunnels [7, 8, 9, 10, 11, 12, 13, 14, 15]. The data inversion can be divided into linear inversion, nonlinear inversion, and apparent resistivity inversion. The apparent resistivity inversion is the most intuitive and relatively fast. The half space transient electromagnetic inversion method has reached a mature and practical stage [4, 9, 12]. Since the half space transient electromagnetic field theory is relatively mature, most commercial software adopts the half space inversion to explore underground water and minerals with low resistivity, such as EMIT MAXWELL, Terra TEM and TEMINT [12, 13, 14]. However, the inversion results are quite different from the actual situation when the inversion method is directly applied to the inversion of full space transient electromagnetism [12]. Therefore, many relevant investigations on the full space effect of tunnel transient electromagnetism have been carried out in the full space inversion [7; 8; 9; 10; 11; 12; 13; 14; 15]. The proportional coefficient of full space transient electromagnetic inversion is proposed [13], so as to realize the correction of the half space inversion method. It is worth noting that the apparent resistivity result is larger without the proportional coefficient, and this leads to erroneous conclusions in the interpretation of field data. According to [PERSON] et al. [16], the induced voltage of the full space state is about 2.52 times that of the half space state, and the full space apparent resistivity value is about 1.842 times of the half space apparent resistivity value. As for the space state of the vehicle-mounted transient electromagnetic method (VMTEM), there are completely different space states at the entrance of the tunnel with the presence of surrounding rock conditions. Compared with the half space and full space states, this space state has similarities and differences. Therefore, the particular space states involved in vehicle-mounted transient electromagnetic detection also need to be further investigated. The space state of the VMTEM was assumed as the full space [14; 15]. However, the detection process of the VMTEM is a moving process from the entrance to the exit of operational tunnels, and the space state of tunnel surrounding rock changes dynamically with the position variation of the vehicle-mounted detection system. As for ideal conditions without the low-resistivity water body and uneven distribution, when the vehicle-mounted detection system is located at the entrance of the tunnel, the lower part of the coil system is the uniform surrounding rock medium, the upper-left is the air medium, and the upper-right is the uniform surrounding rock medium. The coil system can only receive electromagnetic induction signals generated by the lower and upper-right surrounding rock, that is, the three-quarters space (3/4 space) effect. When the vehicle-mounted detection system is located in the middle part of an infinite length tunnel, the above and below of the coil system are uniform surrounding rock medium. The coil system can receive electromagnetic induction signals generated by the above and below surrounding rock simultaneously, that is, the full space effect.