## 2 Theoretical Notes  
Geophysical techniques have become of crucial importance in the preliminary phase of archaeological site detection and mapping; indeed, they are able to provide quick and inexpensive high-quality information on the presence and distribution of remains in many different archaeological scenarios. The probability of a successful application rapidly increases if multi-methodological approaches are adopted, according to a logic of objective complementarity of information and global convergence toward a high quality multi-parametric imaging of the buried structures [41]. In detail, GPR represents an excellent tool to support the archaeologists to identify and reconstruct the real geometry of the objects located in the soil. The GPR lies in electromagnetic (em) theory where the full electromagnetic field is mathematically described by Maxwell's equations. GPR allows for the study of the scattering phenomena of em waves caused by variations of some physical properties of the investigated medium as dielectric permittivity (\(\varepsilon\), F/m), electrical conductivity (\(\sigma\), S/m), and magnetic permeability (\(\mu\), H/m). These physical variations generate reflections related to contrasts in the em impedance; further, the em properties of the soil barely influence the velocity of propagation of em waves and the attenuation of the energy introduced in the subsoil. In low-loss conditions, velocity and the attenuation of em waves can be approximated as follows [42]:  
\[v\approx\frac{c}{\sqrt{k}} \tag{1}\]  
\[\alpha\approx\frac{1}{2}\frac{\sigma}{\sqrt{k}}\sqrt{\frac{\mu_{0}}{\varepsilon _{0}}} \tag{2}\]  
where \(c=\frac{1}{\mu_{0}\varepsilon_{0}}\) is the velocity of light in a vacuum (m/s), \(\mu_{0}\) and \(\varepsilon_{0}\) are the magnetic permeability (\(4\pi\times 10^{-7}\) H/m) and dielectric permittivity (\(8.854\times 10^{-12}\) F/m) in the free space and \(k\) the dielectric constant \(k=\frac{\varepsilon}{\varepsilon_{0}}\) (dimensionless) with magnetic permeability considered negligible and \(\varepsilon\) the dielectric permittivity of the medium (F/m). The above two expressions show that the dielectric permittivity (\(\varepsilon\)) controls em wave velocity, while the electrical conductivity (\(\sigma\)) has a large effect on attenuation. For this reason, GPR works well where the soil conductive is low [42; 43; 44; 45]. Nowadays, GPR is probably one of the most used non-invasive geophysical techniques in the archaeological field witnessed by an increasing amount of scientific research published in the last four decades [7; 46; 47; 48; 49; 50; 51; 52; 53; 54; 55; 56; 57; 58; 59; 60; 61; 62; 63]. Direct current (DC) electrical methods are among the oldest and most popular techniques for the non-invasive geophysical investigations. Among them, ERT allows to investigate the horizontal and vertical electrical resistivity variations of the subsurface materials potentially induced by the presence of anomalous bodies. DC method is based on the measurement of an electric field artificially created in the ground with suitable electronic devices; it normally consists of two pairs of electrodes fixed in the ground, of which: a pair constitutes the current injection circuit, the other the measuring circuit of the potential difference (\(dV\)) generated in the ground by the passage of the current itself. The fundament of this technique is Ohm's Law, which indicates that the potential difference \(dV\) (\(V\)) at the ends of a conductor, at a given temperature \(T\), is proportional to the electric current \(I\) (\(A\)) passing through it by means of a quantity constant and typical of the conductor, said resistance \(R\) (\(\Omega\)):  
\[I=-\frac{dV}{R} \tag{3}\]  
\[R=\frac{\rho L}{A} \tag{4}\]  
where \(\rho\) (\(\Omega\)m) is the electrical resistivity, \(L\) (m) is the conductor length, and \(A\) (m\({}^{2}\)) is the conductor area. Generally, a switched square wave is the current waveform used [64].