Non-linear Spectral Un-mixing Using Hapke Modeling: Application to Remotely Acquired M3 Spectra of Spinel Bearing Lithologies on the Moon

Introduction: Rocks and soils are mostly an intimate mixture of component minerals. Photons of light falling onto such a target are multiply scattered and in the process interact with more than one type of mineral. The reflected photons received at the detector therefore carry information from multiple components present in the mixture, with individual components contributing to the reflected photons, in proportion of the number of times a photon interacted with a component and not necessarily in proportion to their abundance. The non-linear nature of photon interaction with the intimate mixtures makes it difficult to quantify the proportions of endmembers present in remotely sensed VNIR spectra of natural surfaces using linear combination of contributions from individual components. Non-linear mixing models [e.g. 1,2] provide physically reasonable solutions to such problems and aid in computing proportions of component minerals in a mixture which are more realistic. Non-linear un-mixing is an especially important tool in maximizing the interpretation of planetary remote sensing datasets where the availability of ground truth is always a problem. Objectives: The present study aims at carrying out non-linear un-mixing analysis on a suite of remotely acquired spectra from a Mg-spinel bearing lithology identified recently on the surface of the Moon [3, 4] by Moon Mineralogy Mapper instrument (M3) on-board Chandrayaan-1, India's first mission to the Moon [5,6]. M3 is an imaging spectrometer operating in the wavelength range of ~400-3000 nm with spectral resolution of 10-20 nm & spatial resolution of 140 m in the global mode (coarse resolution). The occurrence of Mg-spinel bearing lithology on the Moon in the form of relatively large exposures was not known until very recently [3,4]. In view of the discovery of the spinel lithology occurring on a scale of hundreds of meters to kilometers, it is important to understand the geological setting of the region in terms of associated mineralogy, structural setting, presence of any anomalies etc. The present study is focused towards identifying the mineral assemblage occurring with spinel and quantifying the proportions of each endmember to the first order. The results of this study are expected to have important implications for understanding the character and origin of this spinel-bearing lithology & accordingly on the development of suitable models for explaining its formation.