## 3 Numerical Simulation and Verification for Hydraulic Fracturing
It can be seen from Figure 8 that the amplitude range of the differential anomaly field of the \(Ex\) component is \(1\times 10^{-6.75}\) V/m to \(1\times 10^{-6.25}\) V/m, which can be effectively detected on the surface. Figure 9 shows the comparison of \(Hx\) component responses received on the surface before and after simulated fracturing. Figure 9a is the real part of the \(Hx\) component of the background field before fracturing, Figure 9b is the real part of the \(Hx\) component after fracturing, and Figure 9c is the real part of the \(Hx\) component of the differential anomaly field. Figure 9d, Figure 9e, and Figure 9f are the imaginary parts of the \(Hx\) component in the three cases, respectively, and Figure 9g, Figure 9h, and Figure 9i are the total fields of the \(Hx\) component in the three cases, respectively. It can be seen from Figure 9 that the total field amplitude of the \(Hx\) component's electric field in the projection area is small. Although the differential anomaly field has an effective signal range in the X-axis direction, it is necessary to arrange the correct surface measuring point positions. Combined with the borehole-to-surface observation method, the background field is measured before fracturing, and the anomaly field is measured after fracturing. The two observations are subtracted to make the three components of the electromagnetic response observed on the surface more accurately reflect the information of subsurface anomalous bodies and improve the interpretation accuracy, and the \(Ex\) component more intuitively shows the low-resistance anomaly changes underground in the surface observation. Figure 8: Comparison of \(Ex\) component responses received on the surface before and after simulated fracturing with and without anomalous bodies: **(a,b)** the real part of \(Ex\) before and after the simulated fracturing; **(d,e)** the imaginary part of \(Ex\) before and after the simulated fracturing; **(g.h)** the total fields of \(Ex\) before and after the simulated fracturing; **(c,f,i)** are the real part, the imaginary part, and the total of the differential anomaly field, respectively. Based on the above model and observation mode (b), the longitudinal section response simulation calculations of surface \(Ex\) and \(Hx\) components were carried out. Figure 10 shows the comparison of electromagnetic \(Ex\) component responses in the longitudinal section before and after simulated fracturing. Figure 10a is the real part of the \(Ex\) component of the background field before fracturing, Figure 10b is the real part of the \(Ex\) component after fracturing, and Figure 10c is the real part of the \(Ex\) component of the differential anomaly field. Figure 10d, Figure 10e, and Figure 10f are the imaginary parts of the \(Ex\) component in the three cases, respectively, and Figure 10g, Figure 10h, and Figure 10i are the total fields of the \(Ex\) component in the three cases, respectively. It can be seen from Figure 10 that the differential anomaly field of the \(Ex\) component effectively propagates from the target body to the surface survey network. Figure 11 shows the comparison of electromagnetic \(Hx\) component responses in the longitudinal section before and after simulated fracturing. Figure 11a is the real part of the \(Hx\) component of the background field before fracturing, Figure 11b is the real part of the \(Hx\) component after fracturing, and Figure 11c is the real part of the \(Hx\) component of the differential anomaly field. Figure 11d, Figure 11e, and Figure 11f are the imaginary parts of the \(Hx\) component in the three cases, respectively, and Figure 11g, Figure 11h and Figure 11i are the total fields of the \(Hx\) component in the three cases, respectively. It can be seen from Figure 11 that the field of the \(Hx\) component does not propagate to the projection area of the anomalous body on the surface. If the \(Hx\) component is to be monitored, it is necessary to arrange measuring points over a larger range.