Quantifying the Abundances of Minerals of Granitic Composition Using the Hapke Model of Bidirectional Reflectance

Quantitatively assessing the abundances of the composite minerals in terrestrial granite is crucial to understanding the evolutionary history of the earth's crust and to mineral exploration as well. Prevalent methods of estimating mineral abundances based on the Hapke model by setting the optical constants of the endmembers ahead of time are no longer applicable to terrestrial granite because of the complexity of natural granite, which leads to remarkable uncertainties in these estimations. In this study, we retrieved specific photometric parameters from the bidirectional reflectance spectra measured at a range of incidence, emergence, and phase angles before they were input into the Hapke model and used to estimate the mineral abundances. Four types of granite samples containing the main granitic minerals (quartz, alkali feldspar, and plagioclase) were used to test the effectiveness of our proposed method. The effects of the particle size and dark minerals on the inversion results using the visible near and shortwave infrared (VNIR-SWIR) wavelengths were also examined. The results show that using the photometric parameters retrieved from multiangle measurements as inputs to the Hapke model can produce accurate estimations of the abundances of quartz, alkali feldspar, and plagioclase in both natural and synthetic granite samples. Furthermore, the results demonstrate that the retrieved particle sizes of the particulate samples are close to the ground measurements. Thus, the proposed approach provides a more accurate and efficient estimation of the compositions of terrestrial granites, making it feasible to quickly assess the abundances of the minerals contained in granite.