# Uncertainty of the 2D Resistivity Survey on the Subsurface Cavities
## 1 Introduction
The study in Reference [22] stressed on the measurement sensitivities of the arrays to compare the Wenner, dipole-dipole, pole-dipole, pole-pole, Wenner-Schlumberger, and gradient arrays. The dipole-dipole, pole-dipole, and pole-pole arrays were compared based on the depth of investigation [28]. Another study [25] performed numerical simulation for five synthetic models using different arrays: pole-pole, pole-dipole, half-Wenner, Wenner, Schlumberger, dipole-dipole, Wenner-\(\beta\), \(\gamma\)-array, moving gradient, and midpoint-potential-referred measurement arrays. They suggested the moving gradient array, pole-dipole, dipole-dipole, and Schlumberger arrays. However, the final choice of the arrays should be decided based on the type of expected geology as the subsurface geological distributions have a significant impact on the arrays' imaging ability. Various numerical simulations for different noise perturbations were conducted by emphasizing the data-acquiring ability of the arrays: Wenner, dipole-dipole, Wenner-Schlumberger, and linear grid [29]. Comparison of arrays (Wenner, Wenner-Schlumberger, dipole-dipole, pole-dipole, and pole-pole) for imaging buried tunnels showed better results using the Wenner-Schlumberger and dipole-dipole arrays [30]. The Wenner-Alph and Wenner-Schlumberger showed a better result than the dipole-dipole array for reconstructing the landslide model [31]. Among the Wenner, dipole-dipole, pole-dipole, and pole-pole arrays used for detecting the cleared-wall foundations, the Wenner and dipole-dipole arrays were selected as the best methods [32]. From the numerical model ing using the dipole-dipole, pole-dipole, dipole-pole, and pole-pole arrays, the pole-dipole array showed the best result for modeling sinkhole [33]. The dipole-dipole array imaged the sinkhole better than the Wenner and Schlumerger arrays [21]; in contrast, the Wenner array showed better model resolution than the dipole-dipole array for surveying the underground three-dimensional cavity [34]. Even though these studies have evaluated the effectiveness of resistivity imaging for different geological conditions, there are no studies that assess the constraints of resistivity imaging as well as the configuration best-suited for imaging subsurface cavities. In this study, we present the resistivity imaging uncertainties using synthetic and experimental cavity models. We simulated a cavity model with different depths, sizes, orientations, geometries, and filling materials, as these features substantially change the model result of the resistivity imaging [25]. Additionally, arrays' spatial resolution and sensitivity were examined. The modeling was performed for the DD, PD, WS, and PP arrays since the resolution of data inversion is also constrained by the type of arrays. A model with cells of a given resistivity value was constructed, and the apparent resistivity data were formulated using the finite-element method. Inversion of measured resistivity data was provided with the two-dimensional (2D) geoelectric models. We examined the constraints of the resistivity method on recovering cavity information for different cavity models. Moreover, the potential capability of arrays that can reveal the cavity structures was tested and identified.