Mapping of coal quality using stochastic simulation and isometric logratio transformation with an application to a Texas lignite

Coal is a chemically complex commodity that often contains most of the natural elements in the periodic table. Coal constituents are conventionally grouped into four components (proximate analysis): fixed carbon, ash, inherent moisture, and volatile matter. These four parts, customarily measured as weight losses and expressed as percentages, share all properties and statistical challenges of compositional data. Consequently, adequate modeling should be done in terms of a logratio transformation, a requirement that is commonly overlooked by modelers. The transformation of choice is the isometric logratio transformation because of its geometrical and statistical advantages. The modeling is done through a series of realizations prepared by applying sequential simulation for the purpose of displaying the parts in maps incorporating uncertainty. The approach makes realistic assumptions and the results honor the data and basic considerations, such as percentages between 0 and 100, all four parts adding to 100% at any location in the study area, and a style of spatial fluctuation in the realizations equal to that of the data. The realizations are used to prepare different results, including probability distributions across a deposit, E-type maps displaying average properties, and probability maps summarizing joint fluctuations of several parts. Application of these maps to a lignite bed clearly delineates the deposit boundary, reveals a channel cutting across, and shows that the most favorable coal quality is to the north and deteriorates toward the southeast.