A MATHEMATICAL SOLUTION TO CONSISTENT INTERPRETATIONS OF COAL GEOCHEMICAL DATA REGARDLESS OF THE REPORTING BASIS

Due to interferences caused by organic constituents, coal samples are commonly ashed prior to geochemical analysis; this practice results in concentrations of trace metals and major oxides being reported on an ash basis. Often, however, researchers are interested in the concentration of these elements not in the ash but in the parent coal sample. By using the known ash-content of this starting coal sample, concentrations reported on the ash basis are easily back-calculated to their equivalent concentrations on a whole-coal basis. Problematically, relationships between and among constituent elements can vary widely depending on which reporting basis the researcher uses (e.g., ash vs. whole-coal). These differences are not real, however, but the result of a mathematical phenomenon known as subcompositional incoherence. Since most geochemical data are compositional in nature (in that they are reported relative to the whole, as in %, ppm, etc.), they contain unique curvilinear features which make statistical tests dependent on Euclidean geometry inappropriate, including calculating means or correlations. Applying a log-ratio transformation to compositional data “opens” them and solves two problems in coal geochemistry: (a) it eliminates erroneous basic univariate and bivariate statistics within the data set; and (b) it produces results which allow consistent interpretations of the data regardless of which reporting basis is used. We present a case study of the usefulness of isometric log ratio transformations on coal geochemical data using trace metal and major oxide concentrations in the Pond Creek coal of eastern Kentucky.