Mathematics – Logic
Scientific paper
Dec 2001
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2001agufm.p42a0558s&link_type=abstract
American Geophysical Union, Fall Meeting 2001, abstract #P42A-0558
Mathematics
Logic
5410 Composition, 5464 Remote Sensing, 5470 Surface Materials And Properties, 5494 Instruments And Techniques
Scientific paper
A simulated annealing algorithm capable of inverting thermal emission spectra and compositional data acquired from a common geologic target has been developed. The inversion allows for the identification and proportion estimation of low concentration mineral endmembers. This method will be especially applicable to the 2007 Mars Mobile Geobiology Explorer equipped with an emission spectrometer for mineralogical analyses and a Laser Induced Breakdown Spectrometer for the remote acquisition of elemental information. The coupled inversion is cast as a multidimensional minimization problem where the hyperspace volume to be investigated is defined by the library endmembers at the disposal of the algorithm. This is a vector space in which exists all possible combinations of the library endmembers, with the endmember suite serving as an orthogonal set of basis vectors that span the hyperspace. The goal of the minimization is to locate the hyperspace coordinate that has the lowest associated model error value. This will correspond to the best possible model composition and mineralogy that can be generated by linearly mixing members of the endmember mineral suite. As opposed to standard unmixing routines, the simulated annealing algorithm is flexible enough to minimize any type of model error function. This allows the algorithm to interpret elemental analyses at any level of rigor, including elemental presence, relative abundances, abundance ratios, or exact mole percent. A synthetic data set was developed and systematically degraded with noise of various form and magnitude prior to being inverted with the simulated annealing algorithm as well as two purely spectral unmixing procedures. The simulated annealing procedure outperformed both of the alternate algorithms with an overall factor of two improvement in the mean sum of squares of deviations in the solution parameters. The detailed results from synthetic data inversions as well as the analysis of laboratory data will be presented.
Arvidson Ray E.
Seelos Frank P.
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