*3.2. Three-Dimensional Model*

In addition, we calculated a three-dimensional model with a chargeable anomaly and compared the result with Reference [30]. The dimensions of the cell mesh were 70 × 70 × 70 , and the minimum grid size was 25 m. The modeling volume was 3500 <sup>×</sup> <sup>3500</sup> <sup>×</sup> 3500 m3. The size of the chargeable anomaly was 100 <sup>×</sup> <sup>100</sup> <sup>×</sup> 80 m 3, while the distance from the top to the bottom of the chargeable anomaly was 40 m. The parameters of the Cole–Cole model were σ∞= 0.1 S/m, τ= 0.1 s, η= 0.3, and c = 0.5. The background conductivity was σ∞= 0.001 S/m. A vertical point dipole emitter, which was located 30 m above the surface, was used, and the receiver and transmitter were at the same location. The calculation results are shown in Figure 7, from which it can been seen that the two IP effect curves were consistent. The relative error was less than 10%, which further verifies the correctness of the method.

In terms of computation load, the iterations in the fictitious wave field are as follows:

$$N\_l = \frac{\sqrt{3}R\_{\text{max}}}{\Delta \mathbf{x}} \times \sqrt{\frac{\sigma\_{\text{max}}}{\sigma\_{\text{min}}}},\tag{37}$$

where *Nt* represents the number of iteration steps, *R*max is the maximum transceiver distance, σmax and σmin are the maximum and minimum conductivity, respectively, and Δ*x* is the minimum grid size. Using Equation (37), the number of iteration steps was 76,681. It should be noted that only one transmitter rather than an array was selected in this work. Compared with Reference [30], the calculation efficiency was improved by about five-fold.

**Figure 7.** Comparison of this study with that of Reference [29].
