## 3 Synthetic Test
### Synthetic Results
Figure 3: Synthetic models for (**a**) resistivity (dyke anomaly) model, (**b**) resistivity (positive anomaly) model, (**c**) resistivity (positive and negative anomalies) model, (**d**) velocity (dyke anomaly) model, (**e**) velocity (positive anomaly) model, and (**f**) velocity (positive and negative anomalies) model. The dark red and green lines are used to mark the anomaly boundaries. The single objective genetic algorithm runs between 1000 and 1500 generations with an average population size of 250 individuals in both DC-resistivity and SR methods. The SR genetic algorithm runs were completed in about 748, 876, and 1194 min for the dyke, positive, and combined positive-negative anomalies synthetic models, respectively, while the processing times were measured as 176, 181, and 150 min for DC data. After applying the single objective (SOO) genetic algorithm in both geophysical methods (DCR and SR) separately, we performed the joint parameter estimation using the multi-objective (MOO) genetic algorithm. The non-dominated sorting genetic algorithm (NSGA II) used in the multi-objective global optimization showed that there were feasible solutions depicted by their Pareto optimal fronts (Figure 4). The compromised solution (the green star in Figure 4) was chosen and presented as the output of the MOO method. The NSGA II (for both geophysical methods) ran for about 3136, 2953, and 2891 min for the dyke, positive, and the combined positive and negative anomalies synthetic models, respectively. Figures 5-10 show the results of the local and combined optimization methods for the dyke anomaly model (Figures 5 and 6), positive anomaly (Figures 7 and 8), and the positive and negative anomaly models (Figures 9 and 10). The first column of each of the figures contains the inverted resistivity models, while the second column is the inverted velocity models. In addition, the first row in each figure contains the synthetic models, the second row is the individual (IIM)/single objective (SOO) inverted models, and the third row is the joint (JIM)/multi-objective (MOO) inverted models. Figure 4: Plots of the Pareto fronts showing the compromise solution (green star shape) for (**a**) a dyke anomaly model, (**b**) a positive anomaly model, and (**c**) positive and negative anomalies model. Figure 5: Dyke anomaly model inversion using local optimization method; (**a**) synthetic dc-resistivity model, (**b**) individual inverted resistivity model, (**c**) joint inverted resistivity model, (**d**) synthetic velocity model and its ray path coverage, (**e**) individual inverted velocity model, (**f**) joint inverted velocity model. The dark red line is used to mark the anomaly boundary. Figure 6: Dyke anomaly model inversion using combined optimization method; (**a**) synthetic dc-resistivity model, (**b**) single objective inverted resistivity model, (**c**) multi-objective inverted resistivity model, (**d**) synthetic velocity model and its ray path coverage, (**e**) single objective inverted velocity model, and (**f**) multi-objective inverted velocity model. The dark red line is used to mark the anomaly boundary. Figure 8: Positive anomaly model inversion using combined optimization method; (**a**) synthetic dc-resistivity model, (**b**) single objective inverted resistivity model, (**c**) multi-objective inverted resistivity model, (**d**) synthetic velocity model and its ray path coverage, (**e**) single objective inverted velocity model, and (**f**) multi-objective inverted velocity model. The dark red line is used to mark the anomaly boundary. Figure 7: Positive anomaly model inversion using local optimization method; (**a**) synthetic dc-resistivity model, (**b**) individual inverted resistivity model, (**c**) joint inverted resistivity model, (**d**) synthetic velocity model and its ray path coverage, (**e**) individual inverted velocity model, and (**f**) joint inverted velocity model. The dark red line is used to mark the anomaly boundary.