The Discovery of Buried Archaeological Structures at Saepinum and the Villa of Neratii (Valley of Tammaro River, Italy) Through Data-Adaptive Probability-Based Electrical Resistivity Tomography Using the Tensorial Acquisition Mode

Abstract

The Valley of Tammaro River lies between the regions of Molise and Campania in central southern Italy. The area has been inhabited since ancient times due to its fertile soil and plentiful water resources. The interest in this region is enhanced by the many urban centers and the isolated and rural building complexes that date back to the Samnite era and are connected by a road system that is still in use today. Saepinum, regarded as the symbol of Roman civilization in the Molise area (Italy), is one of these. Before becoming a Roman municipium and then a medieval and contemporary rural community, it was a Samnite trade forum and service center. A suburban villa belonging to the Gens Neratia, a family originally from the Roman municipality of Saepinum, is connected to it approximately 2 km northeast. Both sites were partially excavated, and much more can be learned from the material still available. To this end, geoelectrical studies using the tensor acquisition mode were used to conduct geophysical surveys in certain sectors. The data were processed using Data-Adaptive Probability-Based Electrical Resistivity Tomography, here adapted for the first time to Apparent Resistivity Tensor Analysis. The trace of the apparent resistivity tensor provides distortion-free maps and demonstrates that the anomalies are closely constrained on the source bodies.

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).

2. Materials and Methods

The general principles of apparent resistivity tensor analysis are here described, following [14], explaining the concept of apparent resistivity tensor and the tensor invariant departure concept in detail. The resistivity anomaly occurrence probability (RAOP) function [12] and mathematical steps of the probability-based ERT inversion (PERTI) [10] are instead deferred to Appendix A for in-depth theoretical analysis.

2.1. Apparent Resistivity Tensor Analysis

2.1.1. The Concept of Apparent Resistivity Tensor

Following [14], a generic 3D resistivity structure buried beneath a plane-free surface is examined. Different bipole current sources are assumed to be used to conduct a resistivity study inside area S. Following [20], using the notion of apparent resistivity tensor ${\mathit{\rho }}^{\left(a\right)}$, the law relating the measured electrical field vector ${\mathit{E}}_i$ to the current density vector ${\mathit{J}}_i$ for a uniform half-space is introduced for the generic i-th bipole source:

$${\mathit{E}}_i={\mathit{\rho }}^{\left(a\right)}{\mathit{J}}_i$$

(1)

vector ${\mathit{J}}_i$ for a uniform half-space, using the concept of apparent resistivity tensor ${\mathit{\rho }}^{\left(a\right)}$. ${\mathit{\rho }}^{\left(a\right)}$, is obtained using two bipoles (i = 1, 2) as in [4]:

$${\mathit{\rho }}^{\left(a\right)}=\left(\begin{array}{cc}{\rho }_{11}^a& {\rho }_{12}^a\\ {\rho }_{21}^a& {\rho }_{22}^a\end{array}\right)={\displaystyle \frac{\left(\begin{array}{cc}{E}_{1x}{J}_{2y}-E_{2x}{J}_{1y}& E_{2x}{J}_{1x}-E_{1x}{J}_{2x}\\ E_{1x}{J}_{2y}-E_{2y}{J}_{1y}& E_{2y}{J}_{1x}-E_{1y}{J}_{2x}\end{array}\right)}{J_{1x}{J}_{2y}-J_{2x}{J}_{1y}}}$$

(2)

This form can be used to define rotational invariants, which are independent of both the individual current source bipoles and the direction of the electrical field. The invariant P associated with the trace of ${\mathit{\rho }}^{\left(a\right)}$ [4] is taken into account, which has the crucial characteristic of offering anomalies that are closely contained to the sources. P is provided as

$$P={\displaystyle \frac{1}{2}}\left[{\rho }_{11}^a+{\rho }_{22}^a\right]={\displaystyle \frac{1}{2}}{\displaystyle \frac{E_{1x}{J}_{2y}-E_{2x}{J}_{1y}+E_{2x}{J}_{1x}-E_{1x}{J}_{2x}}{J_{1x}{J}_{2y}-J_{2x}{J}_{1y}}}$$

(3)

A reference coordinate system (x, y, z) where the z-axis is positive downward and S is on the xy-plane is considered. The coordinates of two fixed current electrode pairs, $A_i$ (positive) and $B_i$ (negative) (i = 1, 2), are put with ${\mathit{r}}_{A_i}\equiv \left(x_{A_i}, y_{A_i},0\right)$ and ${\mathit{r}}_{B_i}\equiv \left(x_{B_i}, y_{B_i},0\right)$. The intensity of the energizing current through the i-th current bipole ${A_{i}B}_i$, the $J_{ix}$ and $J_{iy}$ (i = 1, 2) terms in Equation (3), is expressed with $I_i$ (i = 1, 2) at the generic variable point $\mathit{r}\equiv \left(x, y,0\right)$, where the electrical field components are measured. These are given as

$$J_{ix}={\displaystyle \frac{I_i}{2\pi }}\left({\displaystyle \frac{\mathit{r}-{\mathit{r}}_{A_i}}{{\left|\mathit{r}-{\mathit{r}}_{A_i}\right|}^3}}-{\displaystyle \frac{\mathit{r}-{\mathit{r}}_{B_i}}{{\left|\mathit{r}-{\mathit{r}}_{B_i}\right|}^3}}\right)·\mathit{i},$$

(4a)

$$J_{iy}={\displaystyle \frac{I_i}{2\pi }}\left({\displaystyle \frac{\mathit{r}-{\mathit{r}}_{A_i}}{{\left|\mathit{r}-{\mathit{r}}_{A_i}\right|}^3}}-{\displaystyle \frac{\mathit{r}-{\mathit{r}}_{B_i}}{{\left|\mathit{r}-{\mathit{r}}_{B_i}\right|}^3}}\right)·\mathit{j},$$

(4b)

in which i and j are the unit vectors describing the x-axis and y-axis, respectively.

2.1.2. The Tensor Invariant Departure Concept

The subsoil is supposed to be composed of Q elementary cells with constant resistivities ${\rho }_q$ (q = 1, …, Q) and volume ΔV in accordance with [14]. When ${\mathit{\rho }}^{\left(a\right)}$ is expanded in a Taylor series, the following expression is obtained:

$${∆\mathit{\rho }}^{\left(a\right)}={\mathit{\rho }}^{\left(a\right)}-{\mathit{\rho }}_0^{\left(a\right)}={\sum }_{q=1}^Q{\displaystyle \frac{\partial {\mathit{\rho }}_0^{\left(a\right)}}{\partial {\mathit{\rho }}_{0,q}}}{∆\rho }_q+\sum (higher-order derivatives),$$

(5)

where ${∆\mathit{\rho }}^{\left(a\right)}$ is the deviation of ${\mathit{\rho }}^{\left(a\right)}$ from the apparent resistivity tensor ${\mathit{\rho }}_0^{\left(a\right)}$ of a reference resistivity model, ${mod}_0$. Thus, ${∆\rho }_q$ is the difference between the actual resistivity ${\rho }_q$ and the resistivity ${\rho }_q$q in ${mod}_0$ in the q-th cell.

Using Equation (3), the tensor invariant departure ∆P of the real tensor invariant P from the tensor invariant $P_0$ associated with ${mod}_0$ is easily derived, since the trace of a sum of matrices is equal to the total of the traces of the single matrices:

$$∆P=P-P_0={\sum }_{q=1}^Q{\displaystyle \frac{\partial P_0}{\partial P_{0,q}}}{∆\rho }_q+\sum (higher-order derivatives)$$

(6)

Using Equation (3), the term ${\displaystyle \frac{\partial P_0}{\partial P_{0,q}}}$ is calculated as follows:

$$∆{\displaystyle \frac{\partial P_0}{\partial P_{0,q}}}={\displaystyle \frac{\left(\frac{\partial E_{0, 1x}}{\partial {\rho }_{0,q}}\right)J_{2y}-\left(\frac{\partial E_{0, 2x}}{\partial {\rho }_{0,q}}\right)J_{1y}+\left(\frac{\partial E_{0, 2y}}{\partial {\rho }_{0,q}}\right)J_{1x}-\left(\frac{\partial E_{0, 1y}}{\partial {\rho }_{0,q}}\right)J_{2x}}{2\left(J_{1x}{J}_{2y}-J_{2x}{J}_{1y}\right)}}.$$

(7)

The Frechet derivative of the electric potential for the uniform half-space can be used to analytically compute ${\displaystyle \frac{\partial P_0}{\partial P_{0,q}}}$, for simplification and without compromising generality, making the assumption that ${mod}_0$ is a uniform and isotropic half-space [21,22]. At a point $\mathit{r}\equiv \left(x,y,0\right)$ on the ground’s surface, the electrical potential ${\varphi }_i$ varies because of a slight change in the resistivity in a volume ΔV submerged in a uniform half-space around the point ${\mathit{r}}_q\equiv \left(x_q, y_q,z_q\right)$, and it is expressed as

$$∆{\displaystyle \frac{\partial {\varphi }_i}{\partial {\rho }_{0,q}}}={\displaystyle \frac{\partial {\varphi }_{A_i}}{\partial {\rho }_{0,q}}}+{\displaystyle \frac{\partial {\varphi }_{{AB}_i}}{\partial {\rho }_{0,q}}},$$

(8)

in which

$$∆{\displaystyle \frac{\partial {\varphi }_{A_i}}{\partial {\rho }_{0,q}}}={\displaystyle \frac{I_i}{4{\pi }^2}}{\displaystyle \frac{{\mathit{r}}_{A_i}-{\mathit{r}}_q}{{\left|{\mathit{r}}_{A_i}-{\mathit{r}}_q\right|}^3}}-{\displaystyle \frac{\mathit{r}-{\mathit{r}}_q}{{\left|\mathit{r}-{\mathit{r}}_q\right|}^3}},$$

(9a)

$${\displaystyle \frac{\partial {\varphi }_{B_i}}{\partial {\rho }_{0,q}}}={\displaystyle \frac{I_i}{4{\pi }^2}}{\displaystyle \frac{{\mathit{r}}_{B_i}-{\mathit{r}}_q}{{\left|{\mathit{r}}_{B_i}-{\mathit{r}}_q\right|}^3}}-{\displaystyle \frac{\mathit{r}-{\mathit{r}}_q}{{\left|\mathit{r}-{\mathit{r}}_q\right|}^3}}.$$

(9b)

Finally, the formulas are used to calculate the Frechet derivatives of the electrical field components from Equations (9a) and (9b), omitting the straightforward but laborious mathematical stages:

$${\displaystyle \frac{\partial E_{0,ix}}{\partial {\rho }_{0,q}}}={\displaystyle \frac{\partial }{{\partial }_x}}\left({\displaystyle \frac{\partial {\varphi }_{A_i}}{\partial {\rho }_{0,q}}}+{\displaystyle \frac{\partial {\varphi }_{B_i}}{\partial {\rho }_{0,q}}}\right),$$

(10a)

$${\displaystyle \frac{\partial E_{0,iy}}{\partial {\rho }_{0,q}}}={\displaystyle \frac{\partial }{{\partial }_y}}\left({\displaystyle \frac{\partial {\varphi }_{A_i}}{\partial {\rho }_{0,q}}}+{\displaystyle \frac{\partial {\varphi }_{B_i}}{\partial {\rho }_{0,q}}}\right).$$

(10b)

3. Case Studies

The sites studied are located in central southern Italy between the Molise and Campania Regions. The area, previously within the dominion of the Samnites Pentri, was to be incorporated, during the Augustan era, into Regio IV—Sabina et Samnium, a territory of central Apennine and Adriatic Italy.

Between them, at an altitude of 953 m a.s.l., was Terravecchia di Sepino, a Samnite walled settlement from the fourth century B.C. located at the base of the mountains that faces the valley of Tammaro River (Figure 1). The site and the first settlement, located downstream, of which some traces remain under the Augustan city, are the precursor of the Roman city of Saepinum. The Villa of Neratii is an example of a private building from the Roman period [23]. It is located in Località Crocella in the Municipality of San Giuliano del Sannio (Figure 1). The complex falls within the territory of the Roman municipality of Saepinum between the upper Tammaro and the Tappino River Valley [24]. Like many other Roman municipalities, it was divided into centuratio, an organization of the agricultural system according to a regular pattern in which roads, canals, and agricultural land were arranged following an orthogonal grid plan. Remains of these land divisions were identified north of Saepinum (Figure 1, red dotted lines) such as to suggest a cadastral subdivision of 15 × 15 actus with an inclined module in a northerly direction 18° east [25,26].

3.1. Saepinum

The Samnite settlement of Saepinum was conquered in 293 B.C. [27] during the third Samnite war [28,29]. The population then relocated downstream at the junction of two road axes, one at the valley bottom (now the Pescasseroli-Candela “tratturo”, a transhumance route), and the other, perpendicular to the latter, descending from the Matese Mountain and continuing towards the Tammaro valley’s hills [30]. The center was abandoned, as were numerous fortified centers of the Samnites, at the beginning of the first century B.C., after the bloody social bellum (91–88 B.C.).

Approximately 12 hectares in size, the Roman city is bounded by walls that were built between the second century B.C. and the fourth century A.D. [31]. The circuit, which is over 1270 m long, was coated using the opus quasi reticolatum technique, which uses stones placed in almost 45-degree oblique layers. The circuit was composed of four triumphal arch-style access gates and 19 round towers, which are now visible and which were spaced at regular intervals of approximately 25–30 m. The doors today are called the Terravecchia Gate (SSW side, towards the Matese Mountain), Beneventum Gate (SSW side, towards the city of Benevento), Bovianum Gate (NW side, towards the city of Bojano, Figure 2e), and Tammaro Gate (NNE side, in front of the Tammaro river’s plain) [24] (Figure 2a).

Only a minor portion of the Roman city was revealed by archaeological excavations that started in the 1950s. Saepinum was at its most magnificent period during the Augustan era, when the city experienced a major urban expansion as a result of the construction of its most prominent structures [32]. The specific monuments that were discovered are as follows (Figure 2a):

• The theater (1 in Figure 2a,b) and the porticus complex (2 in Figure 2a) in the city’s northern section, which were built in the first half of the first century A.D.;
• The basilica, which was constructed in the first century B.C. in the vicinity of the forum area. It possesses a rectangular plan with dimensions of 31.60 × 20.40 m and is internally divided by a peristyle comprising twenty smooth-shafted columns, four on the shorter sides and eight on the longer sides. These are surmounted by ionic-style capitals (7 in Figure 2a,c);
• The macellum [33,34,35], situated along the decumanus, which represents the market building of the first century A.D. The central room, which has a hexagonal plan, contains a circular basin with a diameter of 2 m. The sides of this room lead into small rooms (shops) with a trapezoidal and rectangular plan (6 in Figure 2a);
• The first century A.D. cult buildings on the decumanus, adjacent to the macellum (5 in Figure 2a);
• The Augustan-era forum, which is situated at the intersection of the cardo and the decumanus and has a trapezoidal plan (1412 m²) and paved flooring (8 in Figure 2a);
• The second-century A.D. thermal complex that is affixed to the walls close to Bovianum Gate (3 in Figure 2a,f);
• The housing district and production buildings along the decumanus in the area between the forum and Beneventum Gate, which was in use from the Augustan era until the fifth century A.D. (4 in Figure 2a,d).

Another temple that is now being studied was discovered in 2017 and is most likely from the first century B.C. Two necropolises can be found outside the wall circuit. One is near Bovianum Gate and dates back to the first century A.D., as indicated by an inscription to Publius Numisius Ligus. The other is of the Augustan period and is situated outside the Beneventum Gate, where C. Ennius Marsus’s funeral monument is located [36] (9 in Figure 2a). Archaeological excavations near the latter necropolis revealed the remnants of a fourteenth-century medieval town.

The city served as the diocesan office in the fifth and sixth centuries A.D. [37], but in the nineteenth century, its significance was quickly overshadowed by the increasing development of the nearby city of Bojano. The majority of Saepinum’s population relocated to Castellum Sepini [38], a hill that would eventually become known as Sepino. Documents dating back to the twelfth century mention Sepino, but at that time the city’s prominence diminished and it was relegated to the status of a minor village.

As was the case throughout the Molise region, curiosity about Saepinum’s archaeological past started to grow in the middle of the nineteenth century. Numerous investigations have been conducted up to this point [24,39,40,41,42,43,44,45,46,47,48,49]. However, only about 10% of the walled area was subject to archaeological excavations. In order to address the unexplored regions in the eastern portion of the northern thermae, between the theater and the decumanus, non-invasive geophysical prospections were recently conducted (shown in a black and white map in Figure 2a) [50]. The results highlighted different anomalies interpreted as part of a thermal complex based on their articulation and geometric features enhanced by apsidal settings [50].

Figure 2. (a) Map of Saepinum showing walls, main buildings, gates, roads, and GPR results [50] and pictures of the Saepinum archaeological site: (b) the theater, (c) the basilica, (d) the decumanus flanked by private houses close to (e) the Bovianum Gate, and (f) the northeastern thermae. Modified from [50], copyright to the authors.

Figure 2. (a) Map of Saepinum showing walls, main buildings, gates, roads, and GPR results [50] and pictures of the Saepinum archaeological site: (b) the theater, (c) the basilica, (d) the decumanus flanked by private houses close to (e) the Bovianum Gate, and (f) the northeastern thermae. Modified from [50], copyright to the authors.

3.2. Villa of Neratii

The Villa of Neratii, considering the visible and best-preserved structures (Figure 3, A and B walls indicated in a light blue color), is oriented according to the centurial axes, and recent archaeological data proposals hypothesize a connecting road to Saepinum that may be found in the eastern sector [23]. Over the years, ten inscriptions referable to the gens Neratia, native of Saepinum, were found around the villa, emphasizing the importance of the site for agricultural activities between the third and fourth centuries A.D.

The complex has been under research since 2004 [23]. The excavations were carried out until 2010 and resumed in 2018. From the first moments, the monumentality of the site emerged considering the long wall in opus reticulatum (Wall A), which supports the road (walls Aa–Ae in Figure 3 and Figure 4a–c,e).

Two sections of the wall are well preserved inside the two still-existing nineteenth-century houses (walls Ac and Ad in Figure 3 and Figure 4b). The technique, generally used for luxury private construction and public buildings, involves the use of 5.5 cm × 5.5 cm quadrangular stones arranged in rows inclined at 45 degrees. A second wall (wall B, Ba, and Bb in Figure 3 and Figure 4d) is placed parallel to and south of the first wall (wall A) at a distance of 3.8 m.

The articulation of the two walls suggests the presence of a cryptoporticus, used as a cool place for walking but also with a structural function. In fact, it served to regularize the natural difference in height of the terrain [23]. Excavations in the eastern sector exposed a wall (wall Ra in Figure 3 and Figure 4e) in opus reticulatum but different in orientation and construction technique connected to wall A. It is inclined 20 degrees to the south and appears to have the function of an access ramp [23].

4. Survey Plan

The instrument used to collect the data was an ADD-01 (see Acknowledgments) which is composed of two lightweight, portable boxes connected by a wireless radio frequency device. The boxes include a current generator and a measurement and control unit, respectively. It is distinguished by a 50 W low-power generator and was designed mainly for archaeological research down to a few tens of meters of depth at most. The frequency at which a current sine wave is generated can be chosen from 8 to 33 Hz. On the control unit, the exciting current intensity can be adjusted between 1 and 400 mA. The acquisition board has a bandpass filter to remove unwanted noise.

The yellow polygon in Figure 2a and the green polygon in Figure 3 outline the investigated area at Saepinum (2014–2016 field campaigns) and the Villa of Neratii (2008–2011 field campaigns).

Figure 5 shows the electrode array used for the tensorial resistivity measurements. The current electrode distance was fixed to 10 m and two perpendicular directions were used (A1-B1 and A2-B2). Potential electrodes M1-N1 and M2-N2 (with an equidistant space of Δ_x = Δ_y = 50 cm) were placed in the central rectangular area between the current electrodes. Once a grid was completed, the pattern was moved into the investigation area without overlapping with the previous one. In total, 258 tensors were obtained for each grid. The white polygon in Figure 3 indicates the sample grid moved in the investigation area in order to cover the surface bordered by the green polygon at the Villa of Neratii.

5. Results and Discussion

Figure 6a shows the three-dimensional volume rendering obtained for the site of Saepinum. By blanking low resistivity values, a complex and well-defined structure emerges (Figure 6b). This feature defines an internal space with an oval shape that has a major axis of about 31 m and a minor axis of about 20 m. In Figure 7, the georeferenced horizontal slices relating to 1 m, 1.5 m, 2 m, and 2.5 m were overlaid on a Google satellite image.

The major axis is perpendicular to the decumanus and the theater scene with which it has similar dimensions. The structure is located to the northeast of the theater and the porticus following the same orientation. The resistive anomaly is characterized by two interruptions along the external perimeter and a highly conductive internal area. The interruptions visible in Figure 7b–d are located both on the long side (northwest) and on the short side (southeast), suggesting the presence of two distinct accesses. Internally (about 394 m²) the area does not appear to show a paved floor but a homogeneous ground, a possible beaten surface.

Considering the size of the structure, its location, and its orientation, two hypotheses are proposed on the possible function of the structure:

• It could indicate the presence of a theatre/odeion, oriented northeast/southwest, preceding the one currently visible oriented northwest/southeast (Figure 8a). This supposition could be justified by the need to create a new structure, which could contain the increase in the number of users following a demographic increase in Saepinum that the previous theatre could no longer accommodate.
• It could represent a single monumental complex belonging to the same phase as the theater and the porticus. In this regard, it is appropriate to analyze the result taking into consideration an inscription reused as a paving stone or as an entrance threshold of the proscenium of the theater which contains the following text: [.H]erennius M(arci) f(ilius) Obellianus/[ca]mpum piscinam porticum s(ua) p(ecunia) f(ecit) [51]. The information reports the existence in Saepinum of a large complex including a campus, a swimming pool, and a porticus, presumably located behind the theater building [47]. The campus–swimming pool–porticus complex therefore appears to have been designed at the same time as the theater and includes a space where gymnastic exercises and gladiatorial games took place; a U-shaped portico that hosted theater spectators during intervals and in the case of bad weather; and a garden in which a fountain made with recycled materials was placed in the late imperial era. By analyzing the shape of the geophysical anomaly according to the historical-archaeological sources, it is possible to associate the result with the presence of the campus of Saepinum, a large space dedicated to physical activity surrounded by structures (Figure 8b).

Figure 9, Figure 10 and Figure 11 show, respectively, the three-dimensional volume rendering, the georeferenced horizontal slice relating to 0.75 m in depth overlaid on a Google satellite image, and the interpretation of the results obtained at the Villa of Neratii. The images evidence numerous regular geometries drawn by high-resistivity anomalies of almost certainly anthropic nature.

The most interesting features are concentrated in the central part of the map, near the archaeological tests carried out over the years. In detail, two rectangular rooms can be recognized (1 and 2 in Figure 11) in the northern sector in continuity with wall Bc (excavated after the geophysical surveys). A square room is connected and aligned to it (3 in Figure 11). Further south there are open areas (4 and 5 in Figure 11) separated by a segment in extension of the partition of rooms 1 and 2. Below them, in continuity, there are four square cells connected to each other and of equal shape (6–9 in Figure 11). Rooms 1–3 are perfectly aligned with rooms 6–9. If the articulation of walls A and B suggests the presence of a cryptoporticus [23], it is possible to hypothesize that rooms 6–9 could belong to a second lower cryptoporticus with a sequence of steps to normalize the natural topography.

Other areas with high resistivity (indicated in magenta) are also worthy of note. These, although with a different alignment compared to those just described, are distributed in a regular manner. In detail, to the south of the cryptoporticus, the reported band has the same width as bands 6–9 and could indicate the presence of similar poorly preserved structures. To the east, however, they seem to enclose a large room whose function is difficult to establish.

6. Conclusions

The 2D tensor apparent resistivity acquisition mode was added to the Data-Adaptive Probability-Based Electrical Resistivity Tomography Inversion Method (PERTI), which was first created for the scalar resistivity method. The position and orientation of the current source with respect to the body being studied determine the apparent resistivity measurements obtained with traditional resistivity arrays. A more thorough understanding of the subsurface structure and its anisotropy can be obtained by examining the resistivity components in various directions. For archaeological research where buried constructions may have intricate geometries, the potential to more precisely detect lateral resistivity fluctuations is a significant opportunity. One benefit of the probability tomography approach is that, in theory, the imaging procedure can be started without rigorous adherence to the geometry of the anomaly sources as an a priori constraint. It simply has to do with the electrical stimulation of the buried structures’ purely physical components. It is believed that a probability parameter must be used in order to recognize resistivity patterns beneath. In fact, the quest for a deterministic solution of the true shape and size of target bodies has essentially much less common sense than is thought due to intrinsic equivalency and sources of natural and/or cultural noise contamination. It was shown that the anomalies are tightly restricted to the boundaries of source bodies and that the trace of the apparent resistivity tensor produces distortion-free maps. The high-resolution, target-oriented probability tomography results in this study are significantly improved by such a feature.

The accuracy of the method for analyzing near-surface archaeological buildings was tested in the two case studies that were presented. As a result, the supposition of buried built areas and void anomalies is obtained by providing a hypothesis of their spatial distribution and, by analyzing the shape, of their function. The absence of other surface evidence or artifact scatters, given that the environment was unaltered for years, and of further archaeological and epigraphical data, in addition to those already considered in the discussion, cannot strengthen the assumptions formulated. Furthermore, the type of results, although to be confirmed with direct archaeological verifications, has allowed us to increase the knowledge of the investigated sites by hypothesizing the discovery of important complex structures such as a theater/odeion/campus in Saepinum and structures connected to the Villa of Neratii.