## 3 Experiment
### Field Data Application  
To demonstrate the efficacy and accuracy of the proposed approaches, we utilized field data from a railway tunnel construction site in Namyangju and Yangpyeong, Gyeonggi Province, South Korea. This area belongs to the central part of the Gyeonggi Massif, which is generally referred to as the basement rock of the Korean Peninsula, and the third-grade deep fault called the Gyeonggang Fault, which is known as a large-scale tectonic formation, passes through this area [36]. This area is mainly composed of Cambrian strata of the banded biotite gneiss, and small-scale rock bodies of mica schist and quartzite are isolated as structural enclaves [38]. The surveyed area has developed faults parallel to the foliation and is characterized by a fault zone with a width of approximately 10 m, identified through surface geological surveys. The geologic plan map of the surveyed area is shown in Figure 9. The electrical resistivity equipment used is the SuperSting R8/IP by AGI (Austin, TX, USA), with a maximum voltage of 800 Vp-p and a maximum current of 2.0 A. During field surveys, the contact resistance typically ranges from 1 to 2 k\(\Omega\), and the output current is around 200 to 300 mA. We conducted DC resistivity surveys using a dipole-dipole electrode configuration with a survey line length of 400 m, a dipole spacing of 20 m, and a maximum number of iterations per transmitter of 8. Unfortunately, borehole data were not available in the survey area, therefore, we performed DL-ERT inversion without incorporating borehole data. We compared the results of three methods, namely, DL-ERT inversion, deterministic inversion, and deterministic inversion with a DL-ERT initial model. Figure 15 presents the recovered models, the computed apparent resistivity data from the recovered models, and the differences between calculated and observed data for the three different approaches. All three models exhibited similar outcomes, with a conductive fault zone located at the center and resistive basement rock located on the sides of the survey area. However, the deterministic inversion approach displayed a steeper dip angle of the fault and less sharp boundaries of the fault and basement structures compared with the other methods. Because no ground truth or borehole data were available for validation, we computed the apparent resistivity data using electrical resistivity forward modeling and determined the RMSE (RMSE\({}_{\textbf{d}}\)) between the measured data from the recovered model and the observed data. The RMSE\({}_{\textbf{d}}\) value was obtained from the data misfit defined in Equation (9) as follows:  
\[\text{RMSE}_{\textbf{d}}=\sqrt{\Phi_{d}/N}\,, \tag{10}\]  
where \(N\) is the number of data points. Figure 15: Comparison of deterministic inversion and DL-ERT inversion: (**a**) ground truth, (**b**) deterministic inversion results, and (**c**) DL-ERT inversion results. The RMSE\({}_{\text{d}}\) of the DL-ERT inversion was calculated as 4.3832, while the deterministic inversion after 20 iterations was 3.3959, as shown in Figure 16. The deterministic inversion exhibits a better fit to the data in terms of data misfit, indicating a limitation in the applicability of deep-learning models when synthetic training data differ from the target field data. However, it is worth noting that the data misfit of the traditional deterministic inversion shown in Figure 17 does not decrease significantly beyond four iterations, indicating that it may become trapped in a local minimum. However, when the recovered model from the DL-ERT inversion was used as the initial model for the deterministic inversion, the RMSE\({}_{\text{d}}\) value decreased continuously and reached 1.6595 after 20 iterations. This significant improvement demonstrates the effectiveness of using the DL-ERT inversion as a starting point to enhance the accuracy and data fitting in the deterministic process.