## 2 Diffusion Characteristics and Proportional Coefficients of Space States
### Diffusion Analysis of Transient Electromagnetic Field in Three Space States  
Based on the transient electromagnetic method, numerical simulation calculation of half space electromagnetic response under the condition of the three-dimensional uniform medium was carried out. The transient electromagnetic response curves of the numerical models were calculated by the COMSOL Multiphysics (Version 5.4, AC/DC module), the size of the finite element model was set to 400 m \(\times\) 400 m \(\times\) 800 m (length \(\times\) width \(\times\) height), and the thickness of the infinite element was 50 m. The resistivity of surrounding rock medium was assumed to be 1000 \(\Omega\cdot\)m, the transmitting and receiving coils were laid out in the center of the model, the shape of the coil was simplified to a circle, and the main calculation parameters of coils referred to a previous reference in [14]. The magnetic field and induced current density with a turn-off delay of 1 \(\upmu\)s in a half space state could be obtained, as shown in Figure 2. Based on the half space model, the parameters of the air medium above the model were set as those of the surrounding rock medium, and the same model size and mesh division was maintained. The numerical simulation calculation of the electromagnetic response in the full space under the condition of the three-dimensional uniform medium was carried out. The magnetic field and induced current density in the full space state are shown in Figure 3. Based on the full space model, the parameters of the upper-left surrounding rock medium were set as those of air medium, and the same model size and mesh division were maintained. The numerical simulation calculation of the electromagnetic response in the 3/4 space under the condition of the three-dimensional uniform medium was carried out. The magnetic field and induced current density in the 3/4 space state are shown in Figure 4.  
Figure 1: Schematic diagram of the vehicle-mounted transient electromagnetic detection system. Figure 4: Schematic diagram of transient electromagnetic response in the 3/4 space state under the three-dimensional uniform medium. (**a**) Magnetic field distribution (A/m); (**b**) Current induction density (A/m\({}^{2}\)). Figure 3: Schematic diagram of transient electromagnetic response in the full space state under the three-dimensional uniform medium. (**a**) Magnetic field distribution (A/m); (**b**) Current induction density (A/m\({}^{2}\)). Figure 2: Schematic diagram of transient electromagnetic response in the half space state under the three-dimensional uniform medium. (**a**) Magnetic field distribution (A/m); (**b**) Current induction density (A/m\({}^{2}\)). As shown in Figure 2, the magnetic field presented a symmetrical distribution in the half space, and the magnetic field propagated outward in the radial direction. The magnetic field was mainly distributed near the transmitting coil, and the maximum value of the magnetic field was distributed in the center of the model. In addition, the induced current was symmetrically distributed in the longitudinal direction of the half space. There was no induced current in the air medium with high resistivity above, and the induced current was only produced in the surrounding rock with low resistivity below. The induced current gradually spread below the syncline. The maximum value of the induced current was distributed at both ends of the diffusion cone, and the amplitude of the induced current in the middle part was the smallest. It can be seen from the results in Figure 3 that the magnetic field presented a symmetrical distribution in the full space state, and the magnetic field propagated outward in the radial direction. The magnetic field was mainly distributed near the transmitting coil, and the maximum value of the magnetic field was distributed in the center. In addition, the induced current was symmetrically distributed in the transverse and longitudinal directions of the full space.