## 5 Conclusions  
A series of simulations was performed on models characterized by rectangular section resistive blocks, using the inline dipole-dipole array with a wide range of electrode spacings and dipole-dipole distances and, consequently, a high amount of apparent resistivity data. This choice allowed a very high resolution, together with a short survey time. Consequently, it enabled the comparison between 2D and 3D inversion models with similar resolutions.  
The use of parameters defined in Equations (7)-(9) allowed a numerical estimation of the effects of the three-dimensionality, non-centrality of the resistive blocks and reliability of each inversion model.  
The results for the synthetic tests showed that the blocks with a limited extension orthogonal to the survey line were not detected correctly by the 2D ERT. The 2D inversion of a 3D resistive block underestimated the actual resistivity value much more than the inversion of the corresponding 2D model with an unlimited perpendicular extension. Furthermore, when the 2D ERT cut an anomalous structure perpendicular to its direction of elongation, the effects of three-dimensionality decreased as the structures stretched perpendicularly. The resistivity anomaly produced was comparable with that of the homologous two-dimensional block only when the ratio between the orthogonal length of the block and the side of its section was at least equal to five.  
On the other hand, when the 2D ERT was carried out near (but not above) a resistive block, this generally produced an artifact consisting of a low contrast resistivity anomaly in correspondence with the section, with an area less than that of the section.  
The effects of three-dimensionality can lead to interpretative errors, such as the detection of false cavities or resistive blocks along the vertical direction or a wrong estimate of the depth and dimensions of the structures, thus causing misleading statements. These errors can be gross, especially if in the presence of very complex structures.  
The results of the field test confirmed the considerations made for the simulations, showing how in the case of complex structures, the 2D inversion was even less realistic and more difficult to interpret than the 3D one. Ultimately, the simulations on the 3D model of the quarry seem to suggest that, if the data coverage is dense enough, then it might be advantageous to perform the 3D inversion rather than inverting each 2D profile individually.  
Conceptualization, R.M.; methodology, R.M.; software, R.M.; validation, R.M. and P.C.; formal analysis, R.M.; investigation, R.M. and P.C.; resources, R.M. and P.C.; data curation, R.M.; writing--original draft preparation, R.M.; writing--review and editing, R.M.; visualization, R.M.; supervision, R.M. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** Data can be obtained upon request from the corresponding author.  
**Acknowledgments:** The authors thank [PERSON] for carrying out the speleological surveys and making the results available.  
**Conflicts of Interest:** The authors declare no conflict of interest.