Spectral Analysis of Multiple Mineral Groups Maike Buddensiek Travis Crosby ObjectiveObjective To identify unknown rock mineral groups by comparing their spectral signature with those of know minerals. Both characteristic absorption troughs and larger-scale curve trends are analyzed. Spectral Analysis of Multiple Mineral Groups Data Sets Preprocessing steps Original spectrum 1st order fin. Diff. Filtered Median filtered (21x1) Correlation of all minerals Global correlation of all minerals with each other Mean value of the correlation values within a group Correlation of the unknowns Standard deviation of the means to estimate probabilities of ambiguous correlation values Mean correlation value of M1 to M7 with group A to E - some ambiguities Analysis of General Large-Scale Trends Problem Curves from different minerals produce troughs at the same position. Solution Make point by point curve comparisons using statistical tools. Analysis of General Large-Scale Trends Sum of the point by point difference between the best fitting curve in each group and each unknown (smaller number = greater correlation). GR AGR BGR CGR DGR E PREDICTED MINERAL Is it right? M SulfateNO ? M MicaYes M Sulfate No M Oxide Yes M Oxide No ? M Mica No M Carb Yes Analysis of General Large-Scale Trends Standard Deviation of the point by point difference between the best fitting curve in each group and each unknown (smaller number = greater correlation). GR AGR BGR CGR DGR E PREDICTED MINERAL Is it right? M SulfateNO ? M Mica Yes M Oxide Yes M Oxide Yes M Oxide No ? M Clay No M Carb Yes Analysis of General Large-Scale Trends Variance between the best fitting curve in each group and each unknown (smaller number = greater correlation). GR AGR BGR CGR DGR E PREDICTED MINERAL Is it right? M SulfateNO ? M Mica Yes M Oxide Yes M Oxide Yes M Oxide No ? M Clay No M Carb Yes Analysis of General Large-Scale Trends Correlation Coefficient (absolute value) between the best fitting curve in each group and each unknown (smaller number = greater correlation). GR AGR BGR CGR DGR E PREDICTED MINERAL Is it right? M CarbYes ? M Mica Yes M Oxide Yes M Oxide Yes M Clay No ? M Clay No M Carb Yes Final Results Convolution Correlation SumStandard Dev VarianceCorrelation Coefficient True Mineral M1 Carb (or Sulfate) Sulfate CarbCarb ? M2 Mica Mica or Clay M3 OxideSulfateOxide M4 Oxide M5 CarbOxide ClayCarb ? M6 Carb (or Clay or Sulfate) MicaClay Sufate M7 Carb Various Methods Unknown Minerals