# Uncertainty of the 2D Resistivity Survey on the Subsurface Cavities
## 3 Results and Discussion
### Model Accuracy, Resolution, and Sensitivity
#### 3.3.2 Spatial Resolution  
The spatial resolution of resistivity imaging is a function of many factors, including subsurface material distribution, data accuracy, array sampling scheme, and the parameters used in the model (e.g., smoothing factors) [70, 71]. In this study, we used three different anomaly sizes as input models with the same inversion parameters to assess the spatial resolution of the arrays (DD, PD, WS, and PP). Figure 23 shows the resolution test for scenario 1 with a checkerboard cell size of \(1\times 2\) m. In this scenario, the DD array can resolve the anomalies in both rows; however, the resolution is significantly reduced for the second row. Other arrays can only resolve the top row of anomalies. The WS and PP arrays depicted smearing at selected locations, whereas the PD array showed vertical smearing across the profile. The anomaly geometries were not well resolved for the PD array. Figure 22: The inverted resistivity model of the experimental data for the: (**a**) DD array, (**b**) PD array, (**c**) WS array, (**d**) PP array. The rectangular box indicates the buried empty plastic box. The second scenario with a checkerboard cell size of 2 \(\times\) 4 m was better resolved in general compared to scenario 1, as shown in Figure 24. The DD array was able to recover the first and second rows, but the resolution was slightly reduced for the second row. The PD and WS arrays restored the entire checkerboard anomalies for the first row; however, the resolution of the second row was significantly reduced. The PP array recovered only the first row, and its anomaly was considerably smeared. The geometries of the checkerboard patterns were more accurately recovered by the DD, PD, and WS arrays, while the geometries could not be reproduced correctly for the PP array. The larger size of 4 \(\times\) 8 m was considered in the third scenario, as shown in Figure 25. The DD array resolved the first and the second rows; however, the resolution was slightly reduced for the second row. The PD, WS, and PP arrays consistently imaged the first row input checkerboard structures, but these were not resolved correctly in the second row. The second row checkerboards' geometry was not accurately recovered for all the arrays and displayed elongated checker anomalies instead of rectangular cells. Figure 23: Scenario 1 spatial resolution test for the 1 m (vertical) \(\times\) 2 m (horizontal) checkerboard cell sizes. (**a**) Checkerboard model, (**b**) DD array, (**c**) PD array, (**d**) WS array, (**e**) PP array. The checkerboard test results depicted that even though we used the same arrays, the resolution of the recovered anomalies can vary based on their sizes. In general, the checkerboard resolution test of the first scenario reproduced about 12.5% checkerboard patterns (Figure 23), while the second scenario (twice the size of scenario 1) restored about 25% of the checkerboard (Figure 24). The third scenario (twice the size of scenario 2) reproduced about 50% of the checkerboard patterns (Figure 25). Thus, the increase in target size can noticeably increase the obtained model resolution and recovery depth. If the uniform background resistivity anomaly has a low amplitude compared to the targeted anomaly, then the depth of recovery is higher (Figure 7). However, all the alternating anomalies have similar amplitudes in the checkerboard test (Figure 24), and the recovery depth is low. This is likely related to the concentration of current density at the first-row of the checkerboard, which significantly decreases with depth, as current density is concentrated at the top layer in stratified formation [72; 73]. As the resistivity data points are not uniformly distributed in the profile section, the inverted model resolution can considerably be biased. As shown in Figures 23 and 24, the center of the survey profiles is well recovered, but smearing is observed at the end of the profiles.