## 1 Introduction  
Geoelectrical methods are widely used in environmental research, geology, hydrogeology, engineering, and archaeology. In order to choose the best configuration for a given problem and obtain better results, a range of arrays is known in the geophysical literature [1, 2, 3]. Three criteria are used in the most recent classification [3]: collinearity (the electrode alignment in the linear), focusing (more than one circuit is applied), and superposition (more than one potential difference measurement).  
The simplest arrays, such as the Wenner, the dipole-dipole, or the Schlumberger arrays, are now frequently utilized due to the introduction of multichannel resistivimeters since they provide indisputable practical benefits during the acquisition phase and compatibility with the inversion software. The resistance values in these arrays are characterized as scalar quantities, and they are non-superimposed, non-focused, and collinear.  
Less standardized arrays include greater depth, can better identify lateral and/or vertical resistivity variations at a site, and can offer vector and anisotropy information. Since they reveal the location and orientation of the discontinuities, non-collinear arrays that use several dipole current sources in the apparent resistivity measurement might be regarded as suggestive of lateral discontinuities [4]. There is a lot of promise for archaeological applications with the superimposed, non-focused, and non-collinear tensor electrical resistivity approach [5; 6; 7; 8; 9].  
In this paper, the results of tensorial resistivity measurements obtained through the application of the Probability-based ERT inversion (PERTI) [10] are presented.  
The probability tomography methodology was originally created for the self-potential method [11] and later adjusted for the resistivity approach using conventional measurements [12; 13] and tensorial resistivity measurements [14]. The basic technique [12] did not estimate the intrinsic resistivities of the source bodies, but it was able to distinguish between high and low resistivities in the field data sets by considering a reference background resistivity [15; 16]. Subsequently, the data-adaptive probability-based ERT inversion approach (PERTI) [10] was formulated to estimate the intrinsic resistivities. The method is a nonlinear approach that, from a probabilistic point of view, determines which of the set of possible solutions is most likely to be compatible with the data set gathering strategy. The literature has documented numerous uses of the PERTI technique for near-surface prospecting related to archaeological issues [17; 18]. Lastly, in comparison to the original PERTI, the Extension of the Data-Adaptive Probability-Based Electrical Resistivity Tomography Inversion Method (E-PERTI) [19] was developed to optimize resistivity estimations and enhance robustness to noise. Through consecutive vertical scanning and horizontal windowing inside the datum space, as well as random selection, the PERTI method recovers a large number of different subsets of data from the apparent resistivity dataset [19]. The best estimate of the most likely resistivity in the same point--a more or less dense cluster of resistivity values in each point of the surveyed region--is ultimately predicted using an intrinsic linear regression model that employs ordinary least squares techniques.  
Here, the PERTI method is used for the first time to process field data sets obtained with tensorial resistivity measurements during the last two decades at two important archaeological sites in the Valley of Tammaro River (Molise region, Italy): the Roman Villa of Neratii and the ancient city of Saepinum (Figure 1).  
Figure 1: Location of the Villa of Neratii in the Valley of Tammaro River including the territory of Saepinum, the road system (in green), and traces of the centuratio (in red).