# Uncertainty of the 2D Resistivity Survey on the Subsurface Cavities
## 3 Results and Discussion
### Model Accuracy, Resolution, and Sensitivity  
#### 3.3.1 Model Accuracy  
Depth of Cavity  
We evaluated the model accuracy of arrays numerically using the image correlation between the actual and inverted resistivity models, as shown in Figure 6. The DD model correlation values were highest, varying from 0.29 (T\({}_{6}\)) to 0.82 (T\({}_{1}\)). On the other hand, the PD and WS models depicted moderate image correlation, ranging from 0.28 (T\({}_{6}\)) to 0.75 (T\({}_{1}\)) for the PD models and 0.24 (T\({}_{6}\)) to 0.81 (T\({}_{1}\)) for the WS models. The lowest correlation values were exhibited by the PP array, varying from 0.19 (T\({}_{6}\)) to 0.71 (T\({}_{1}\)). The correlation coefficients were directly associated with the accuracy of the obtained models. Figure 5: Arrays’ inversion error for varying air-filled cavity depths. Figure 6: The statistical correlation between the inverted resistivity models and actual air-filled cavity models. Moreover, the cavity region showed significant changes in model accuracy and resolution based on cavity depth. For the convenience of description, we categorized the air-filled cavity targets as shallower (T\({}_{1}\) and T\({}_{2}\)), intermediate (T\({}_{3}\) and T\({}_{4}\)), and deeper (T\({}_{5}\) and T\({}_{6}\)) based on the cavity situated depths. The shallower cavity models situated at 2.2 m (T\({}_{1}\)) and 4.2 m (T\({}_{2}\)) depths were accurately reconstructed by the DD, PD, and WS arrays, as depicted in Figures 7, 8 and 9a,b. The obtained images have also shown a strong statistical correlation with actual models (Figure 6). The PP array yielded a relatively lower resolution than the tested arrays (Figure 10a,b). The resistivity imaging displayed relatively wider anomaly sizes regarding the actual cavity models (Figures 7, 8, 9 and 10a,b). The obtained geometry accuracy was considerably varied for the upper and lower anomaly boundaries. For instance, the upper boundary of the T\({}_{1}\) anomaly coincided with an actual cavity model, while the bottom boundary extended beyond that of the actual models (Figure 7a). Generally, inversion artefact increases with the survey depth; however, the inversion for high resistivity contrast may also provide a noticeable artefact, especially nearby the anomalous body [62]. Even though we applied the robust inversion algorithm, inversion for the shallow depth cavities has generated considerable artefacts, as depicted in Figures 7, 8, 9 and 10a,b. The significant artefacts in inversions performed in all the air-filled cavity modeling had the resistivity value below 950 \(\Omega\cdot\)m, that is often misinterpreted as subsurface physical features. Figure 7: The inverted resistivity model using dipole-dipole (DD) array for the cavity targets: (**a**) T\({}_{1}\), (**b**) T\({}_{2}\), (**c**) T\({}_{3}\), (**d**) T\({}_{4}\), (**e**) T\({}_{5}\), (**f**) T\({}_{6}\). The rectangular boxes indicate the actual air-filled cavities. The broken lines represent the depth of investigation (DOI) threshold depths. For better anomaly illustration, we presented only a 40 m lateral model section. Figure 8: The inverted resistivity model using pole-dipole (PD) array for the cavity targets: (**a**) T\({}_{1}\), (**b**) T\({}_{2}\), (**c**) T\({}_{3}\), (**d**) T\({}_{4}\), (**e**) T\({}_{5}\), (**f**) T\({}_{6}\). The rectangular boxes indicate the actual air-filled cavities. The broken lines represent the DOI threshold depths. Figure 9: Inverted resistivity model using Wenner–Schlumberger (WS) array for the cavity targets: (**a**) T\({}_{1}\), (**b**) T\({}_{2}\), (**c**) T\({}_{3}\), (**d**) T\({}_{4}\), (**e**) T\({}_{5}\), (**f**) T\({}_{6}\). The rectangular boxes indicate the actual air-filled cavities. The broken lines represent the DOI threshold depths. Modeling for the intermediate cavities located at 6.2 m (T\({}_{3}\)) and 8.2 m (T\({}_{4}\)) depths showed reasonable model resolution in the tested arrays (Figures 7, 8, 9 and 10c,d). The DD array displayed slightly better resolution than the other arrays.