# Uncertainty of the 2D Resistivity Survey on the Subsurface Cavities
## 1 Introduction  
Resistivity imaging is a geophysical method, which has become a powerful tool to investigate shallow subsurface features. The technique has been widely used in several fields of geosciences, such as structural geological [1, 2, 3, 4, 5], hydrogeological [6, 7], geohazard [8, 9], and environmental [10, 11, 12, 13] studies. Subsurface cavity structures most commonly occur in carbonate terrain through the dissolution of carbonate rocks. Isostatic subsidence of the developed cavity can impose substantial damage on structural, environmental, and human values. Engineering structures require subsurface investigation to map and assess the presence of cavities, which reduces construction risks. Several geophysical methods are applied in order to determine the size, position, and depth of the subsurface cavities. Among the geophysical methods, resistivity imaging is a commonly used technique to identify cavity structures [14, 12, 15, 16]. Despite the applicability success, resistivity imaging often leads to non-unique models of the subsurface. It is well-known that the resistivity method produces uncertainties in final model interpretation because of the inherited ambiguity in data inversion. This is because the inversion of electrical resistivity data is a non-linear problem, while the solutions are obtained using a linearized forward model [17; 18; 19]. The resistivity survey measures a limited number of data points at a discrete electrode spacing, which also constrained to obtain a unique resistivity response of the subsurface structures [20]. Thus, the delineation and mapping of subsurface cavities remain challenging in environmental studies using resistivity imaging [11; 21]. Different factors can be considered in cavity studies, such as target size, depth, orientation, geometry, filling materials, and resistivity contrast with the host medium. The measured apparent resistivity data gives an average value representing a volume of geological material. The volume-averaging property of the resistivity method may obscure the small-scale cavity. The sparse sampling and less sensitivity characteristics of the resistivity method with increased survey depth may also obscure cavity information [15; 22]. These factors may delimit the technique and the type of array to be used in resistivity imaging [23; 24]. Even though the cavity depth is small and situated at a relatively deeper depth, substantial resistivity contrast between the cavity and the host medium can reveal suitable imaging results [12; 21; 25]. Moreover, selecting the best electrode configuration to recover the material variations over a cavity zone is the main problem in resistivity study. Among the commonly used electrode configurations, the dipole-dipole (DD) array is widely used to detect subsurface lateral changes, yet it is more vulnerable to measurement noises and often produces a low signal-to-noise ratio. The pole-dipole (PD) configuration has relatively higher signal strength compared to the DD array. However, the PD array provides asymmetrical resistivity data that adds bias to the inverted models [21; 25], whereas the Wenner-Schlumberger (WS) configuration is moderately sensitive to both lateral and vertical variations. The WS array also has a higher signal-to-noise ratio, yet it recovers a relatively lower resistivity contrast compared to the DD arrays [26; 27]. On the other hand, the pole-pole (PP) array can produce comprehensive horizontal data coverage and survey greater depths as compared to other types of arrays. However, its remote electrode is highly sensitive to ambient (telluric) noises [21; 25]. Therefore, each array has its advantages and limits in relation to cavity imaging, and a comprehensive study is needed to ascertain which configuration is the most suitable one. Many studies have been carried out to compare the pros and cons of the most commonly used resistivity imaging arrays.