## 5 Numerical Examples
### Complex Geological Model  
Figure 15 shows the complex geological model. The resistivity of the air layer is set to \(10^{6}\)\(\Omega\)-m, and the resistivity of the homogeneous half-space is 500 \(\Omega\)-m. The surface  
Figure 14: Migration imaging for differential pulses with different pulse widths: (**a**) pulse width of 0.4 ms; (**b**) pulse width of 2 ms; (**c**) pulse width of 5 ms; (**d**) stacked imaging. Figure 13: Migration imaging for square waves with different pulse widths: (**a**) pulse width of 0.4 ms; (**b**) pulse width of 2 ms; (**c**) pulse width of 5 ms; (**d**) stacked imaging. consists of Quaternary sediments with a resistivity of 300 \(\Omega\cdot\)m; the shallow geothermal reservoir has a resistivity of 100 \(\Omega\cdot\)m, while the deep geothermal reservoir has resistivities of 50 \(\Omega\cdot\)m and 10 \(\Omega\cdot\)m, and the resistivity of the geothermal fluid is 8 \(\Omega\cdot\)m. The length of these geological anomalies in the y-direction is 1 km. The grounded wire source used in this study is 6 km in length, with endpoints at coordinates (\(-\)3 km, \(-\)100 m, 0 m) and (3 km, \(-\)100 m, 0 m). The receiver line is parallel to the transmitter, with an offset of 200 m and a point spacing of 20 m. The endpoints of the receiver line are located at (\(-\)2.5 km, 100 m, 0 m) and (2.5 km, 100 m, 0 m). Based on the qualitative relationship between differential pulse width and detection depth, and through extensive experiments, differential pulses with pulse widths of 1 ms, 4 ms, and 12 ms were selected as the transmitted waveforms. Figure 16 presents the computational results for differential pulses with pulse widths of 1 ms, 2 ms, 4 ms, 8 ms, and 12 ms. Figure 16a,d,g,j,m show \(\mathbf{b}_{\mathrm{z}}\) with low-resistivity anomalies for differential pulses of varying widths, while Figure 16b,e,h,k,n show \(\mathbf{b}_{\mathrm{z}}\) without anomalies for the same pulses. Since the electromagnetic response characteristics of differential pulses with different pulse widths cannot be directly reflected in \(\mathbf{b}_{\mathrm{z}}\), relative anomalies are used for characterization. As seen in Figure 16c, when the 1 ms differential pulse is used to excite the electromagnetic field, only the shallow geothermal reservoir shows prominent anomalous features. As the pulse width increases to 4 ms, the electromagnetic anomaly of the shallow geothermal reservoir weakens, while the anomalous features of the deeper geothermal reservoir with a resistivity of 50 \(\Omega\cdot\)m and the shallow geothermal fluid become more pronounced. When the pulse width increases to 12 ms, the deeper geothermal reservoir with a resistivity of 10 \(\Omega\cdot\)m and the deeper geothermal fluid show distinct anomalous features, while other low-resistivity anomalies are less prominent. Figure 17 shows the virtual wavefields for differential pulses with different pulse widths. It can be observed that differential pulses with smaller pulse widths provide higher resolution for the electrical interfaces of shallow strata. As the pulse width increases, the  
Figure 15: Complex geological model. resolution of the shallow strata gradually decreases, while the resolution of the electrical interfaces of deeper strata improves. Figure 18 presents the migration imaging results for differential pulses with different pulse widths. Figure 18a-e correspond to differential pulses with pulse widths of 1 ms, 2 ms, 4 ms, 8 ms, and 12 ms, respectively, Figure 18f shows the stacked imaging profile. The figures demonstrate that using differential pulses with varying pulse widths to excite the electromagnetic field allows for high-resolution imaging of electrical interfaces at different depths. The stacked migration imaging clearly delineates the electrical interface features from shallow to deep strata. However, due to volume effects, discrepancies exist between the migration imaging of the deep geothermal reservoir with a resistivity of 10 \(\Omega\cdot\)m and the geothermal fluid, and the theoretical model.