## 4 Results
### The Fusion of the Selected Sentinel-2 MSI and Landsat-8 Components
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c c} \hline \hline  & & & & \multicolumn{4}{c}{**Field Points**} & \multicolumn{4}{c}{**Mining Leases**} & \multicolumn{4}{c}{**Accuracy**} \\ \cline{3-14}
**S. No** & **Techniques** & & & & **(Ground Truth)** & & & & & **(Ground Truth)** & & & & \\ \cline{3-14}  & **P1** & **P2** & **P3** & **P4** & **P5** & **P6** & **P7** & **ML1** & **ML2** & **ML3** & **ML4** & **MML** & \\  & **(G)** & **(G)** & **(G)** & **(G)** & **(G)** & **(M)** & **(G)** & **(G)** & **(G)** & **(G)** & **(G)** & **(M)** & & \\ \hline \multirow{3}{*}{1} & Proposed weighted linear & & & & & & & & & & & & & & \\  & combination of FPCS & G & G & G & G & G & M & M & G & G & G & G & M & 100\% \\  & components & & & & & & & & & & & & & & \\ \hline \multirow{3}{*}{2} & FCC of PCs obtained after & & & & & & & & & & & & & & & \\  & PCA applied to 17 raw & V\({}_{\rm L}\) & V\({}_{\rm L}\) & S & G & G & G & G & G & G & G & V\({}_{\rm L}\) & G & 44\% \\  & bands from 3 data sources & & & & & & & & & & & & & & \\ \hline \multirow{3}{*}{3} & FCC of PCs obtained after & & & & & & & & & & & & & & & \\  & PCA applied to 17 & & V\({}_{\rm L}\) & G & G & G & M & M & G & G & G & M & 82\% \\ \cline{3-14}  & stretched bands from & & & & & & & & & & & & & & \\  & 3 data sources & & & & & & & & & & & & & & \\ \hline \multicolumn{14}{c}{G, granite; M, marble; V\({}_{\rm L}\), light vegetation; V\({}_{\rm D}\), dense vegetation.} \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Validation of results after they were compared with known locations of granite Leases (locations ML-1–ML-4, MMLs, and field survey points P1–P7 in Figure 2 of Shewa Shahbazghari and Ambela complexes. The petrographic study in Shewa Shahbazgarhi also highlighted the presence of potassium feldspar and silica-rich granite rock bodies and calcite-rich marble rock bodies in the Shewa Shahbazgarhi region. It indicated that the stacked FPCS could highlight small differences for geological mapping in the study area. The application of the methodology in Malakand and Karoonjhar Mountains showed the effectiveness of this technique to provide economic geological maps of an area. The results from the proposed methodology were compared with the PCA of stacked bands from all three datasets. PC2, PC3, PC4, and PC9 of the raw stacked data had significant information from the SWIR and TIR spectral ranges to discriminate granite and marble. Likewise, PC1-PC9 of the stretched stacked data provided useful information about the targeted rock bodies. However, each PC being a mixture of 17 bands made it difficult to select a specific PC retaining distinctive spectral response of granite and marble. Therefore, the FPCS application on bands from the same data sources separately is preferred due to a 100% accuracy based on the field survey and the known mining leases of granite and marble. On the other hand, stacking all the bands from all three datasets resulted in 50% and 75% accuracies in raw and stretched bands because of spectral mixing. Tables 6 and 7 present the eigen loadings of the selected FPCS components for mapping granite outcrops of the Malakand and Nagarparkar in Thar region. PC2 of ASTER raw data reported granite in bright due to positive loadings of 0.4825 and 0.2368 in the TIR1 and TIR2 bands, respectively, as given in Table 6, showing the low emissivity of granite against opposite (negative) loadings on B1, B2, and B3N. PC5 of the stretched Landsat-8 data showed the maximum positive loadings of 0.515 and 0.534 in B10 (TIR1) and B11 (TIR2) bands, respectively, corresponding to the significantly low emissivity (shown in bright which can be seen in dark after the negation of the component) due to granite rock in the thermal wavelengths. On the other hand, this component had opposite-sign (negative) loadings for the SWIR1 band (\(-\)0.44) corresponding to the reflection of granite-associated quartz in the SWIR1 band and no information about the SWIR2 band.