Quantify the Abundance of Granite Composit Minerals Using the Hapke
Model from Bidirectional Reflectance
Abstract
Quantitatively assessing the abundance of the composite minerals of
terrestrial granite is crucial for understanding the evolutionary
history of the Earth’s crust and for mineral exploration. Prevalent
methods based on the Hapke model to estimate mineral abundance by
setting the optical constants of endmembers ahead are no longer
applicable to terrestrial granite because of the complexity of natural
granite, which will lead to remarkable uncertainties in estimations. In
this study, we retrieved such specific photometric parameters from the
bidirectional reflectance spectra measured at a range of incidence,
emergence, and phase angles before they were inputted to the Hapke model
to estimate mineral abundance. Four different kinds of granite samples
of main rock-forming minerals (quartz, alkali feldspar, and plagioclase)
comprising the bulk of granite were used to test the effectiveness of
our proposed method. The effects of 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 for the Hapke model accurately estimated the abundances of
quartz, alkali feldspar, and plagioclase for both natural and synthetic
granite samples. Furthermore, the results also prove that the retrieved
particle sizes of particulate samples are all within their measured
ranges. These results indicate that the proposed approach provides a
more accurate and efficient estimation of the compositions of
terrestrial granite and is feasible for quickly assessing the abundance
of minerals contained in granite.