# Uncertainty of the 2D Resistivity Survey on the Subsurface Cavities
## 2 Methodology
### Forward-Inverse Modeling  
We developed resistivity conceptual models to represent karstic subsurface structures in limestone terrain. In nature, cavities have different depth of burial, size, geometry, and orientation that can be air-filled, water-filled, or sediment-filled [37; 38]. To study the effect of these cavity properties on the recovering ability of the 2D resistivity methods (DD, PD, WS, and PP arrays), we generate different synthetic models. The cavity depths, sizes, orientations, and geometries were considered in our numerical modeling. Since the survey depth has a significant effect on the resistivity model resolution, we focused on the arrays' performance with cavity depths. We set an air-filled cavity model at six different depths, naming cavity targets as T\({}_{1}\), T\({}_{2}\), T\({}_{3}\), T\({}_{4}\), T\({}_{5}\), and T\({}_{6}\), with the depths of 2.2, 4.2, 6.2, 8.2, 10.2, and 12.2 m, respectively (as shown in Figure 1). The target cavity T\({}_{2}\) was used for further analysis as its depth is more common in cavernous limestone terrain. We numerically modelled the conductive cavities by using a filling of dry and saturated clay; however, the resistivity of the cavity filling material is a function of the particle size, saturation, and resistivity of the pore fluid [39]. As this study specifically examines the case of cavities in karstic terrain, the conceptual models' host medium was considered as uniform dry limestone rock with a resistivity value of 1000 \(\Omega\cdot\)m. Only in the case of conductive cavity modeling, when the water table is above the cavity, did we use a resistivity value of 450 \(\Omega\cdot\)m for the host limestone [38; 40]. We used the resistivity value of 10,000 \(\Omega\cdot\)m for the air-filled cavity [11], 90 \(\Omega\cdot\)m for the cavity filled with dry clay [41], and 50 \(\Omega\cdot\)m for the cavity filled with saturated clay [33]. The arrays such as DD, PD, WS, and PP were used for surface probing, which apply 89 electrodes with 1 m spacing. Furthermore, the synthetic reconstruction test, known as the checkerboard resolution test, was implemented in this study. The checkerboard test is often applied in seismic studies to examine the lateral resolution of the tomographic image. The alternating pattern of positive and negative anomalies along a spatial dimension is used to develop the checkerboard model. Inversion was performed for synthetically measured data to evaluate the recovered model resolution [42; 43; 44]. We applied the checkerboard resolution test to assess the resolution of resistivity tomogram in-depth cross-section along the survey profiles. Three different size scenarios of checkerboard cells were used to examine the anomaly size effect on the spatial resolution of the recovered models. We used a checkerboard cell size with 1 (vertical) \(\times\) 2 m (horizontal) dimensions in scenario 1. In scenario 2, the size increased by the factor of two, i.e., 2 \(\times\) 4 m cell size, while the factor of four was used in scenario 3, i.e., 4 \(\times\) 8 m cell size. The background resistivity (1000 \(\Omega\cdot\)m) was perturbed by \(\pm\)20% resistivity anomaly; thus, the checkerboard cells were assigned by alternating resistivity values of 800 and 1200 \(\Omega\cdot\)m.  
Sensitivity in resistivity study can be used in different ways [22; 45; 46; 47; 48]. In this study, sensitivity was used to assess how the arrays are sensitive to different resistivity perturbations (contrasts). In addition to evaluating the spatial resolution of the inverted tomogram, we applied the checkerboard test to examine the sensitivities of the array (DD, PD, WS, and PP).