## 1 Introduction  
In direct current electrical resistivity methods, an electric field is generated by applying an electromotive force to a pair of current electrodes planted on the ground and the intensity of the generated current is measured [1]. The difference in electric potential is measured between two other electrodes, thus obtaining a measure of apparent resistivity given by the ratio between the potential difference \(\Delta V\) and the current intensity \(I\) multiplied by a geometric factor \(G\), which depends on the electrode array. The solution to the direct problem is based on the equations governing the current flow associated with an electric field generated by point sources of electric current. The subsoil is discretized into cells and the solution to the problem is calculated based on the finite difference method [2] or the finite element method [3]. The inverse problem is nonlinear and ill-posed and is commonly solved with damped least squares methods [4]. Contrasts in electrical resistivity are often caused by lithological changes [5] and variations in porosity or water content [6], but they can also be caused by the presence of clayey sediments [7], metallic material, pollutants, and leachate. In these cases, the combined use of electrical resistivity tomography (ERT) and induced polarization tomography (IPT) is useful [8; 9]. IPT investigates the capacitive properties of the subsoil [10] which are strongly linked to the presence of clay, sulfides, and metal salts in water solution, or leachate [11; 12]. In the last two decades, the method of electrical resistivity tomography (ERT) has been developed rapidly and successfully [13] thanks to the emergence of automatic devices capable of simultaneously acquiring large quantities of potential measurements with the same current dipole [14]. At the same time, 2D and 3D inversion algorithms [15] have become increasingly efficient. Conventional 3D electrical tomography investigation techniques involve the acquisition of grid-shaped distributed ERT-2D profiles, using roll-along techniques to acquire data in 3D [16]. In these cases, however, there is the risk of performing many current inputs and, consequently, spending too much time on data acquisition. To overcome this problem, different arrays and combinations of measures have been designed to reduce the number of observations while maintaining adequate resolution and data quality for a 3D inversion [17]. [PERSON] and [PERSON] [15] proposed the \"cross diagonal survey\" technique, based on the pole-to-pole array, in which the potential measurements are acquired by considering electrodes along the orthogonal and diagonal directions of the grid passing through the current electrode. [PERSON] et al. [18] proposed the \"Maximum Yield Grid\" array, based on potential dipoles aligned in correspondence with the direction of the maximum gradient of the electric field, to minimize the number of measurements, considering few current dipoles, and consequently the times of acquisition and the invasiveness. However, when planning a 3D survey, it is not always possible to use a regular grid in which the electrode distances are the same in the two orthogonal directions. In these cases, if the difference is too large, the resolution decreases drastically. [PERSON] and [PERSON] [19] demonstrated that to obtain a sufficient resolution of the inverse model, the maximum separation between the electrode arrays should not exceed twice the in-line distance between the electrodes. Although many authors have obtained appreciable results by inverting together apparent resistivity data obtained by acquiring separate 2D ERTs [20] or by interpolating models obtained from 2D inversions [21], nevertheless these models suffer from a significant reduction in resolution compared to the corresponding 3D models. Furthermore, in urban or particularly rough areas, the spaces in which it is possible to carry out parallel electrode laying are drastically reduced.