## 4 Calculation Results of the Three-Dimensional Chargeable Body Model
### Forward Modeling Results of 3D Chargeable Body  
In order to analyze the influence of system parameters on the IP effect, we build a three-dimensional model with the consideration of a chargeable body, as shown in Figure 8. The ground conductivity was \(\sigma_{\infty}\)\(=0.001\) S/m, the air layer conductivity was \(\sigma_{\rm air}\)\(=10^{-6}\) S/m, Tx was the long wire source, the length was L\({}_{\rm Tx}\)\(=400\) m, Rx represents the receiving point, the height from the ground was h \(=25\) m, and the offset distance was r \(=200\) m. The dimensions of the chargeable body were \(400\times 400\times 300\) m\({}^{3}\), which was 100 m below the surface. The model parameters of the chargeable body were selected as follows: chargeability \(\eta\)\(=0.5\), frequency dependence c \(=0.5\), and characteristic time constant \(\tau\)\(=0.01\) s. The conductivities at infinite frequency were \(\sigma_{\infty}\)\(=0.01\) S/m, \(\sigma_{\infty}\)\(=0.5\) S/m, and \(\sigma_{\infty}\)\(=0.1\) S/m. The calculation results are shown in Figure 9. The snapshots of the induced current system in the fictitious wave field are shown in Figure 10a,b.  
Figure 8: Three-dimensional (3D) model with IP effect.  
Figure 7: Comparison of this study with that of Reference [29].  
It can be seen from Figure 9 that, with the increase in conductivity at the infinite frequency, the attenuation of the early induction field gradually decreased, the attenuation of the late IP response gradually quickened, and the occurrence time of the inverse sign gradually delayed. This is because the influence of the induction field of the low-resistance body was greater than that of the high-resistance body. Therefore, the second field decayed slowly, and the negative response appeared later. Thus, the polarization phenomenon was more easily observed on the high-resistance body. The chargeable body position can be clearly observed from Figure 10, and the method of wave field transformation could effectively identify the polarizable body. Since we set the air layer as a finite high-resistance body, the conductivity was not zero, and the propagation of induced current in the air layer was not zero. In the fictitious wave field, due to the influence of the chargeable body, the propagation mode of the electromagnetic field changed, and it no longer propagated in the form of symmetry.  
After setting \(\sigma^{\infty}\)= 0.1 S/m, as well as the ground conductivity \(\sigma_{\mathrm{ground}}=0.001\) S/m, \(\sigma_{\mathrm{ground}}=0.01\) S/m, and \(\sigma_{\mathrm{ground}}=0.1\) S/m, which are associated with high-, medium-, and low-resistance areas, the IP effects were calculated as shown in Figure 11.  
With the increase in ground conductivity, the amplitude of the early induction field and the late polarization field increased. In the high- and middle-resistance regions, the negative responses occurred at 1.7 ms and 3.3 ms. On the other hand, in the low-resistance region, the negative response could not be observed. When the negative value reached the minimum, the curve decayed approximately exponentially. The GREATEM had better resolution in the low-resistance region, but it is more suitable for the high-resistance region when measuring the IP effect.  
Figure 10: The snapshots of the induced current system in the fictitious wave field (**a**) early time; (**b**) late time.  
Figure 9: Response curves under different conductivities.