## 6 Conclusions  
1. A time-efficient methodology for fusing selective FPCS components from stretched and raw Landsat-8 OLI + Landsat-8 TIRS, ASTER, and Sentinel-2 MSI is presented to map granite and marble of Shewa Shahbazghari area. The process took 147.14 s on the GEE Cloud computing platform to carry out PCA in three multispectral data sources' raw and stretched forms.
2. A weighted linear combination of PCs was carried out based on each component's granite and marble indicating features to enhance granitic spectral features while suppressing others. The results were validated by matching all the exposed granite and marble quarries successfully.
3. The TIR bands of the ASTER had a 90 m resolution that did not perform well in densely vegetated areas; therefore, a combination of Landsat-8 and Sentinel-2 components discriminated the granite/marble rock types better in Shewa Shahbazgarhi due to much better resolutions. Furthermore, the non-availability of granite absorption features from the TIR bands in Sentinel-2 MSI datasets was overcome by Landsat-8 TIR bands. As a result, the high-resolution SWIR bands from Sentinel-2 and the medium-to-low-resolution TIR bands from Landsat-8 TIRS helped obtain the final FCC map for discriminating granite from marble.
4. The weighted PCs extrapolation to other granite outcrops across Pakistan showed the technique's usefulness to obtain results with ease and accuracy. In less vegetated regions, i.e., the Kotah Dome, Malakand, and non-vegetated Karoonjhar Nagarparkar, the ASTER component was helpful due to the granite-specific TIR2 band. The advantage of Sentinel-2 components was highlighted in all case studies, which shows that high-spatial-resolution SWIR bands support TIR bands from the ASTER and/or Landsat in mapping granite and accessory minerals. The information about accessory granite minerals due to their spectral absorption in the SWIR2 band is incorporated in granite through the high-spatial-resolution Sentinel-2 components bearing high-resolution SWIR2 bands.
5. Based on the analysis of eigenvector loadings, the low emissivity in Landsat-8 TIR1 and the reflection of the SWIR1 (1570 nm-1660 nm) and SWIR2 (2110 nm-2290 nm) bands were observed due to orthoclase and quartz in granite. The SWIR2 components from Landsat-8 and Sentinel-2 indicated absorption characteristics of granite accessory minerals, i.e., muscovite, epidote, and amphibole. Similarly, marble showed absorption features in the SWIR2 (2110-2290 nm) band of Landsat-8 OLI and Sentinel-2.
6. The methodology can be further used for high-end RS applications: 1. Predicting geotechnical properties through mineralogy using freely available multispectral or commercial high-resolution datasets (Worldview3, Quick bird, Spot Eye, etc.). 2. Unsupervised classification for better data annotation before using machine learning/deep learning algorithms.  
Conceptualisation, K.M., S.U.D. and M.F.A.K.; methodology, S.U.D., M.F.A.K., K.M. and M.S.; software, M.F.A.K. and S.U.D.; validation, M.S., K.M., S.U.D. and M.F.A.K., formal analysis, K.M., S.U.D., M.F.A.K., M.S., S.B. and A.K.; investigation, K.M. and S.U.D., M.F.A.K., M.S., S.B. and A.K.; resources, K.M., S.B. and A.K.; data curation, M.F.A.K. and S.U.D.; writing--original draft preparation, S.U.D., M.F.A.K. and K.M.; writing--review and editing, K.M., S.U.D., M.F.A.K., M.S., S.B. and A.K.; supervision, K.M., S.B. and A.K. All authors have read and agreed to the published version of the manuscript.  
The Higher Education Commission funded this research under the grant for: National Center of AI, and The APC was funded by Authors.  
Not applicable.  
**Acknowledgments:** The authors of the manuscript acknowledge the funds and support provided by the Higher Education Commission (HEC) of Pakistan under the grant for: National Centre of Artificial Intelligence.  
**Conflicts of Interest:** The authors declare no conflict of interest.