## Appendix A  
### Resistivity Anomaly Probability Tomography  
Appendix A.1.1. The Resistivity Anomaly Occurrence Probability (RAOP)  
The idea of \(\Delta P\)-signal energy \(\Lambda\) throughout the entire survey surface S in order to enhance the resistivity anomaly probability tomography approach is presented as  
\[\Lambda=\sum_{n=1}^{N}(\Delta P_{n})^{2} \tag{1}\]  
The main contribution \(\Lambda_{1}\) associated with the first-order derivatives is extracted using the expansion on the right side of Equation (6) as follows. \[\Lambda_{1}=\sum_{q=1}^{Q}\Delta\rho_{q}\sum_{n=1}^{N}\Delta P_{n}\bigg{[} \frac{\partial P_{0}}{\partial P_{0_{d}}}\bigg{]}. \tag{2}\]  
Using Schwarz inequality and the single \(q\)-th term from Equation (2), the following expression is obtained:  
\[\left[\sum_{n=1}^{N}\Delta P_{n}\left[\frac{\partial P_{0}}{\partial P_{0_{d}} }\right]\right]^{2}\ \leq\ \sum_{n=1}^{N}\Delta P_{n}^{2}\sum_{n=1}^{N}\left[\frac{\partial P_{0}}{ \partial P_{0_{d}}}\right]^{2} \tag{3}\]  
Finally, a resistivity anomaly occurrence probability (RAOP) function \(\eta_{q}\) is introduced by dividing the square root of the left-hand term of inequality (3) by the square root of the right-hand term as follows:  
\[\eta_{q}=C_{q}\sum_{n=1}^{N}\Delta P_{n}\bigg{[}\frac{\partial P_{0}}{\partial P _{0_{d}}}\bigg{]}, \tag{4}\]  
where \(C_{q}\) is  
\[C_{q}=\left[\sum_{n=1}^{N}(\Delta P_{n})^{2}\sum_{n=1}^{N}\bigg{[}\frac{ \partial P_{0}}{\partial P_{0_{d}}}\bigg{]}^{2}\right]^{-\frac{1}{2}}. \tag{5}\]  
The RAOP function satisfies the criterion  
\[-1\leq\eta_{q}\leq+1. \tag{6}\]  
The shape pattern of the \(\Delta P\)-function over \(S\) is caused by the likelihood that a resistivity anomaly will occur in the \(q\)-th cell, which is represented by each value of \(\eta_{q}\). Resistivity increases with regard to \(mod_{0}\) are correlated with positive \(\eta_{q}\) values, whereas resistivity decreases are correlated with negative values. The following justifies the role of probability assigned to \(\eta_{q}\). It is commonly known that a probability measure P is a function that assigns a real number P(\(\gamma\)) to each subset \(\gamma\) of a space of states \(\Gamma\) in such a way that [21]  
\[P(\gamma)\geq 0,\text{ for every }\gamma \tag{7a}\] \[P(\Gamma)=1,\] (7b) \[\text{if }\gamma=\alpha\cup\beta,\text{ with }\alpha\cap\beta\equiv 0,\] (7c) \[P(\gamma)=P(\alpha\cup\beta)=P(\alpha)+P(\beta). \tag{7d}\]Assuming that the presence of a resistivity departure at \(r_{q}\) does not depend on the presence of a resistivity departure at another point, the function  
\[\Lambda_{1}=\sum_{q=1}^{Q}\Delta\rho_{q}\sum_{n=1}^{N}\Delta P_{n}\bigg{[} \frac{\partial P_{0}}{\partial P_{0_{d}}}\bigg{]}. \tag{2}\]0  
where \(V\) is a generic volume including all non-vanishing values of \(\big{|}\eta\big{(}r_{q}\big{)}\big{|}\), can be defined as a probability density, allowing a measure of the probability of obtaining a resistivity departure at \(r_{q}\) to be obtained in agreement with axioms (11,12,13). Actually, the definition given in Equation (10) differs from that in Equation (10) for an unknown constant factor appearing at the denominator of Equation (10) and has the advantage of giving information on the sign of the sources. Therefore, \(\eta\big{(}r_{q}\big{)}\) can conventionally be assumed as a measure of the resistivity anomaly occurrence probability. The Probability-Based ERT Inversion (PERTI)  
Following [18], the starting assumption for the PERTI method is that the reference uniform resistivity is no longer pre-assigned but assumed to be the unknown value \(\rho_{q}\) that corresponds to a generic \(q\)th cell centered at \((x_{q},\,y_{q}\,,z_{q})\).