## 3 Results: Discussion and Comparison
As the distance between the resistive block and the survey line increased, the resistivity contrast decreased, while the extent of the anomaly initially increased and then decreased as well. Figure 4: Inverse models obtained starting from the 3D model of cube-shaped resistive block. (**a**) Central section of the 3D ERT and (**b-j**) 2D ERT when varying the orthogonal distance \(d\) between the electrode line and the projection in the surface of the center of the cube. The solid black line indicates the boundaries of the cube when the section intersects it. The dashed black line indicates the projection of the boundaries of the cube when it is not intersected by the section. Figure 6 summarizes the 2D inverse models obtained starting from the 3D prism-shaped models (see Figure 2). For these simulations, it was considered that the electrode lines always passed above the center of the prism perpendicular to its axis. Therefore, the orthogonal distance \(d\) between the electrode line and the projection on the surface of the center of the cube was always equal to zero, instead varying the orthogonal width \(s\) of the prism. The number of iterations needed to stop the inversion was comparable to the previous case (\(N_{it}\) ranged from 6 to 10), while the data misfit was slightly higher (0.16% \(\leq L_{1N}\leq\) 0.26%). Additionally, for these inversions, there was no correlation between the low misfit values and the likelihood of the inverse models. The shape and value of the anomaly were close to those of the corresponding 2D model (Figure 6a) when the ratio \(s/l>4\) (Figure 6b-d). For prisms with \(s/l<3\), the prism was still identifiable, but its size and resistivity were progressively underestimated as \(s\) decreased. For the same prism-shaped models, the central sections extracted from the 3D ERT inverse models are reported in Figure 7. In all these sections, \(d=0\) while the orthogonal length \(s\) of the prism varied from 0 to 5 times the side \(l\) of the square vertical section. In the 3D inversions, the number of iterations \(N_{it}\) ranged from 5 to 9, while the \(L_{1}\)-norm data misfit ranged from 0.07% to 0.20% and was generally less than that in the respective 2D inversions. For all models of prisms in which \(s>l\) (Figure 7b-i), the central sections of the inverse 3D models showed the shape of the anomaly that closely approximated the square section of the prism. The resistivity values of the anomalies, while continuing to be significantly lower than those of the model, were only slightly lower than those shown by the 2D ERT (Figure 7a). When \(s\ \to l\), the anomaly was flattened, and its resistivity was significantly lower (Figure 7)). Figure 5: Trend of the inversion effectiveness parameters \(\mathbf{P_{1}}\), \(\mathbf{P_{2}}\) and \(\mathbf{P_{3}}\), referring to the cube-shaped model shown in Figure 1, as the ratio \(d/l\) between the orthogonal distance \(d\) and the side of the cube \(l\) increases. Figure 8 summarizes the trends of parameters \(\mathbf{P}_{1}\) and \(\mathbf{P}_{3}\), calculated for the results obtained from the models shown in Figures 2 and 3. Considering the 2D ERT of Figure 6 centered over the prism, \(\mathbf{P}_{1}\) (white circles) increased as \(s/l\) increased, approaching 1 when \(s/l\geq 5\). It follows that, considering the returned resistivity value, a prismatic structure could be considered comparable to a two-dimensional structure when the ratio between the length of the prism and the side of its section was at least equal to five. Parameter \(\mathbf{P}_{3}\) (white squares) followed the same trend as \(\mathbf{P}_{1}\), albeit while showing higher values, and in any case greater than one, except when the prism approached the dimensionality of a cube. For all other values, the anomalous area was always overestimated, and this overestimation increased with the perpendicular length \(s\).