The complex scattering behaviour of minerals within a soil sample may be addressed by model approaches that assume either linear or non-linear reflectance of the constituents.
Imaging spectrometry, simultaneous measurement of spectra and images in up to hundreds of spectral channels or bands, is a proven technology for identifying and mapping minerals based on their reflectance or emissivity signatures. Also known as hyperspectral imaging or “HSI”, extraction of key spectral signatures from these data allows direct identification of iron minerals such as hematite, goethite, and jarosite in the visible/near infrared (VNIR); clays, carbonates, micas, sulfates, and other minerals in the short wave infrared (SWIR); and silicates and carbonates in the long wave infrared (LWIR). The unique capability of imaging spectrometry to produce detailed maps of the spatial distribution of specific minerals, mineral assemblages, and mineral variability on the surface of Earth makes it an ideal tool for enhanced geomorphic mapping. Case histories illustrate the use of HSI for characterizing and mapping active and relict geothermal/hydrothermal systems and determining relations between mineralogy and derived landforms. Imaging spectrometry, used in conjunction with complimentary datasets such as InSAR (Interferometric Synthetic Aperture Radar), Light Detection and Ranging (LiDAR), or stereo (photogrammetric-derived) digital elevation models (DEMs), provides a unique means of visualizing the spatial distribution and association of mineralogy with topography, thus contributing to the understanding of the relations between geology and landscape and to improved interpretation of surface geologic processes.
Basically, you can also use approaches that use diagnostic absorptions features more directly like the Tetracorder approach from USGS:
http://speclab.cr.usgs.gov/software.html
Using this software you will get a list of 'fitting' minerals for each spectrum you analyse. Especially for soils any kind of mineral unmixing is quite complex and requires more sample information. Tetracorder results often correlate with those from geochemical analyses (XRD).