## 3 Accuracy and Efficiency Verification of the Calculation Method  
### Half Space Model with IP Effect  
In the field measurement with GREATEM, only the change of the underground secondary field is considered. In the process of numerical simulation, people usually divide the real space into two parts (air and ground), without considering the interface between the ground and air. Therefore, in the research process of this paper, the ground and the interface are not considered. In order to verify the effectiveness of this method, we design a half-space model incorporating the IP effect, as shown in Figure 2. Let the conductivity of the air layer \(\sigma_{\rm air}\)\(=10^{-6}\) S/m, conductivity at the infinite frequency of the half-space model \(\sigma_{\infty}=0.1\) S/m, chargeability \(\eta\)\(=0.6\), characteristic time constant \(\tau\)\(=1\) s, and frequency dependence \(c=0.5\). Tx represents the transmitter, Rx is the receiver, the horizontal distance between Tx and Rx (offset distance) is \(300\) m, and the flight altitude is \(\rm h=0\) m. In Figure 3, the calculation results are compared with Reference [29]. We can see that the solution of the fictitious domain finite difference method (FW-FDTD) is in good agreement with that of the transformed frequency domain method. The average relative error of both methods is less than \(10\%\).  
Figure 2: The half-space model with induced polarization (IP) effect.  
When the earth contains the IP effects, the polarization parameters have great influence on the induced-polarization (IP) effects. In order to analyze the influence of polarization parameters on IP effects, we take the uniform half space model (Figure 2) as an example. Set the air layer conductivity \(10^{-6}\) S/m, a 200-m-long wire source is selected as the transmitter, and the offset distance is r = 300 m. Furthermore, chargeability \(\eta\)= 0.6, conductivity at infinite frequency \(\sigma_{\infty}\)= 0.1 S/m, frequency dependence \(c\) = 0.5, and flight altitude h = 25 m. The characteristic time constant is selected as \(\tau\)= 1 s, \(\tau\)= 0.1 s, and \(\tau\)= 0.01 s. The IP response under different characteristic time constants is calculated as shown in Figure 4. Other parameters remain unchanged. The characteristic time constant is set to \(\tau\)= 0.01 s, and \(\eta\)= 0.5. The conductivity at infinite frequency is \(\sigma_{\infty}\)= 0.01 S/m, \(\sigma_{\infty}\)= 0.05 S/m, and \(\sigma_{\infty}\)= 0.1 S/m. The IP response under different conductivity is calculated as shown in Figure 5. Furthermore, \(\sigma_{\infty}\)= 0.01 S/m, \(\tau\)= 0.01 s, and the chargeability is \(\eta\)= 0.3, \(\eta\)= 0.5, and \(\eta\)= 0.7. The response curves under different chargeability are calculated as shown in Figure 6.  
From Figures 4-6, it can be seen that characteristic time constant, chargeability, and conductivity at infinite frequency affect the occurrence time of negative response, and all responses are monotonic. Compared with the conductivity at infinite frequency, the effect of characteristic time constant and chargeability on the IP response is lower, mainly in the late stage, and the change trend of the early induction field is basically the same. With the decrease in characteristic time constant, the time of minus response is gradually advanced. With the decrease in chargeability, the time of minus response is delayed. The conductivity at infinite frequency has a great influence on the IP effect. In addition to the minus response at the later stage, it also has a great influence on the early induction field. In the  
Figure 4: Influence of characteristic time constant on IP effect.  
Figure 3: The response curve of the half-space model.  
early stage, the response amplitude of the induction field increases gradually with the increase in conductivity at infinite frequency. In the later period, a smaller conductivity at infinite frequency results in the minus response appearing earlier.