## 1 Introduction  
Today, electrical resistivity tomography (ERT) is a widely used method in many geological and environmental applications [1]. It is often preferred to opt for 2D arrays because they are easier and quicker to carry on compared with 3D arrays, especially in urban environments. The latter requires not only the dense data coverage to be significant, therefore having a higher acquisition cost, but also a consequent use of more memory and powerful computers. This problem, however, is less important today than in the past, thanks to the development of multi-channel data acquisition systems. In fact, for the optimal exploitation of these characteristics, new and different arrays and acquisition methods have been proposed for surveys that involve thousands of electrode positions [2; 3; 4; 5; 6; 7; 8], as well as the use of more powerful computers and better-performing software [6; 9].  
When heterogeneity is present, three-dimensional imaging of 2D electrical resistivity data sets should provide a more accurate and reliable picture of the subsurface than single analyzed 2D ERTs [10] and generally increases the resolution of the resistivity survey [11].  
Another effective data acquisition strategy for 3D sensing is to combine perpendicular 2D slices and interpret them together [11; 12; 13; 14].  
Unfortunately, 2D electrical resistivity tomographies are sufficient to derive realistic subsurface models only when the subsoil is geologically quite simple [15]. Conversely, when in the presence of structures that cannot be simplified as 2D with respect to the survey line, such as complex geological structures or anthropogenic structures such as building foundations or underground cavities, 2D surveys can produce misleading models due to the three-dimensional nature of these structures [16; 17]. Indeed, the 2D ERT inversion algorithms assume that the electrical resistivity does not change in the direction perpendicular to the ERT profile. When the subsoil does not respect this assumption, they generate 3D effects [18; 19] which should be quantified or at least recognized in 2D inversions.  
While the effects of 2D structures on 1D resistivity modeling have been studied [20], the effects of three-dimensional structures on 2D ERT are less understood [21; 22].  
Recently, some studies have been conducted on the topographical effects of embankment structures located next to 2D apparent resistivity pseudosections [23; 24; 25; 26]. However, little information is available on the deformations of the 2D ERTs caused by underground three-dimensional structures crossing the tomographic section or coming close to it [27; 28]. In this regard, [PERSON] et al. [29] investigated the boundary effects on 2D ERT by varying some potential factors, such as the resistivity contrast, depth and size of buried objects and electrode spacing.  
This work aims to study the effects on the 2D ERT inversion of three-dimensional structures present below or near the survey line using data derived from synthetic models and field measurements. For this purpose, several numerical simulations have been performed on resistivity models with resistive blocks of a regular shape, and some parameters have been calculated to quantify the 3D effects on the inversion reliability. Furthermore, based on a detailed speleological study carried out on a quarry, a complex three-dimensional model of the quarry was simulated. The results were considered and compared with the field results for the same quarry.