## 2 Materials and Methods
### Geological Formation
#### 2.2.4 Weighted Overlay Analysis (WO)  
AHP analysis was performed to derive priority scales for use in WO analysis. The latter is defined as the process of creating a map by overlaying multiple raster layers and assigning a weight to each raster layer (criterion and its values) based on its importance [51]. The method is used to combine standardised components, in which each cell value is multiplied by the percentage weight of the criterion, and the results are added together to succeed in the creation of an output raster according to the following equation [25]:  
\[\text{Suitability}=\sum\omega_{\text{i}}\times\text{x}_{\text{i}} \tag{7}\]  
where \(\omega_{\text{i}}\) is the weight assigned to each criterion and \(\text{x}_{\text{i}}\) is the standardized score of each criterion's evaluation scale (0 to 9). The selection of the input rasters that will be used in the analysis is the first step in the process. As a result, all reclassified rasters that were assessed with the AHP analysis were included in the WO. The next step involves the selection of an evaluation scale for the assignment of the values of each raster. The range of the scale in WO was chosen to be the same as the intensity scale in AHP, which is determined from 1 to 9. Since the evaluation scale has been selected, the cell values for each input raster in the analysis are assigned values according to their importance. All the unwanted values are excluded from the analysis by setting the scale value to Restricted [52]. In the final step, each input raster is assigned an influence percentage based on its importance. For instance, the sigma 0 raster layer is given a weight of 52% influence, and its reclassified output value 1 (input values \(-\)23.38 dB to \(-\)10 dB) is assigned a standardized scale value of 8. The Land Cover raster layer has a weight of 26% influence, and its reclassified \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Sigma 0** & **1** & **2** & **3** & **Weight** \\ \hline
1 & 1 & 5 & 9 & 0.75 \\
2 & 0.2 & 1 & 3 & 0.18 \\
3 & 0.11 & 0.33 & 1 & 0.07 \\ \hline \hline \end{tabular} \(\lambda_{\text{max}}=3.02\), \(\mu=0.01\), RI = 0.52, \(\text{C}_{\text{ratio}}=0.02\) (acceptable consistency).  
\end{table} 
Table 10: Weights of the reclassified values with respect to the Sigma 0 criterion. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Slope** & **1** & **2** & **3** & **Weight** \\ \hline
1 & 1 & 2 & 9 & 0.58 \\
2 & 0.5 & 1 & 9 & 0.37 \\
3 & 0.11 & 0.11 & 1 & 0.05 \\ \hline \hline \end{tabular} \(\lambda_{\text{max}}=3.05\), \(\mu=0.02\), RI = 0.52, \(\text{C}_{\text{ratio}}=0.05\) (acceptable consistency).  
\end{table} 
Table 7: Weights of the reclassified values with respect to the Slope criterion. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Land Cover** & **1** & **2** & **3** & **Weight** \\ \hline
1 & 1 & 0.125 & 0.11 & 0.05 \\
2 & 8 & 1 & 0.33 & 0.31 \\
3 & 9 & 3 & 1 & 0.64 \\ \hline \hline \end{tabular} \(\lambda_{\text{max}}=3.10\), \(\mu=0.05\), RI = 0.52, \(\text{C}_{\text{ratio}}=0.09\) (acceptable consistency).  
\end{table} 
Table 9: Weights of the reclassified values with respect to the Land Cover criterion. output value 3 (input value Soil) is assigned value 6. Consider the rasters overlayed, then the cell values for the inputs mentioned above are transformed into the following:  
\[(8\,\times\,0.52)+(6\,\times\,0.26)=4.16+1.56=5.72\]  
However, the output raster from the WO analysis is integer; thus, the final output value is rounded to 6 [53]. Table 11 describes the percentage influence and the standardized scale values for each raster layer participating in the suitability analysis. The output product of the WO is a weighted raster layer illustrating all the candidate and restricted locations throughout the broader area, determining suitable CR sites in the candidate area of interest. The candidate locations were classified from the most to the least favourable as presented from darker to lighter blue colours in Figure 12.