## 6 Numerical Simulation Analysis of the Dual-Electrode Excitation Method
### Calculation of the Aggregate Current Distribution of the Target Well  
To analyze the electric field formed by the current source in the form of an electric dipole in the homogeneous formation, the triaxial orthogonal intensity distribution of the current density at the interface (10,\(Y\),\(Z\)) in the formation with distance \(d\) = 10 m is calculated according to Equation (4). According to Equation (8), the current amplitude gathered on the target casing is calculated in the coordinate system (\(X\),\(Y\),\(Z\)) when the distance \(d\) = 10 m and the axis angle \(\theta\) = 0\({}^{\circ}\). Figure 2 results indicate that when the two well axes are placed parallel to each other, a symmetrical distribution of the casing current amplitude is observed. On the metal casing 10 m away from the drilling well, the maximum value of the casing current amplitude is reached at point M, with an amplitude close to 0.95 A. With the increase in the distance from the ranging point M, the current amplitude roughly decreases with the rate of the cosine characteristics. Calculation of the Magnetic Induction Intensity Distribution in the Formation Around the Target Well  
Since the two wells are parallel and on the interface (\(X\),\(0\),\(Z\)), the direction of the induced magnetic field vector generated by the casing current is perpendicular to this interface, and the induced magnetic field intensity distribution of the interface (\(X\),\(0\),\(Z\)) can be obtained according to Equation (14). According to Equation (14), the calculation results are extracted along the axis coordinate \(Z^{\prime}\) of the drilling well. The induced magnetic field intensity curve on the axis of the drilling well is depicted in Figure 3. The result from Figure 3 indicates that the attenuation characteristics of the induced magnetic field intensity \(B_{c}\) are approximately consistent with the concentrated current flow in the casing of the target well and exhibit a symmetrical distribution trend with the metal casing ranging point M as its center. The maximum value for the induced magnetic field intensity at the Q point along the drilling well axis reaches an amplitude of 7.64 nT. At the installation positions for the upper/lower low-frequency magnetic measurement subs (z\({}^{\prime}\) = \(\pm\)2.5 m), the induced magnetic field intensity reaches 7.2 nT, meeting the requirements for the amplitude range necessary for low-frequency magnetic measurements. Figure 2: The amplitude distribution of the casing current in the target well. Calculation of the Corresponding Curve of Magnetic Induction Intensity and the Distance Measurement at the Magnetic Field Measuring Point of the Drilling Well  
According to Equation (15), \(\theta\) = 0\({}^{\circ}\) is set, and the corresponding curve between the magnetic induction intensity \(B_{u}\) and ranging \(d\) of the magnetic field measurement point \(H_{u}\) on the drilling well axis under different upper/lower electrode distances is drawn, as shown in Figure 4.  
The calculated results show that the induced magnetic field intensity \(B_{u}\) at the magnetic field measuring point \(H_{u}\) decreases exponentially with the increase in distance \(d\). When \(L\) = 10 m and \(d\) increases from 1 m to 50 m, the amplitude of \(B_{u}\) decreases from 3391.45 nT to 0.121 nT. Meanwhile, the decrease in the electrode distance \(L\) will also increase the attenuation rate of the \(B_{u}\) amplitude. When \(L\) = 2 m and \(d\) = 50 m, the theoretical value of the \(B_{u}\) amplitude is only 0.024 nT. It should be noted that in the calculation process, the Z coordinate values of the magnetic field measuring points \(H_{u}\) and \(H_{d}\) on the drilling well axis are set to \(L\)/4 and \(-L\)/4, respectively, and the Z coordinate values of \(H_{u}\) and \(H_{d}\) should be adjusted according to different values of \(L\). In practical engineering applications, the installation positions of \(H_{u}\) and \(H_{d}\) can be flexibly adjusted according to different electrode distances to facilitate the downhole ranging operations.