Hron, KarelFilzmoser, Peterde Caritat, PatriceFiserova, EvaGardlo, Alzbeta2021-10-131874-8961http://hdl.handle.net/1885/250794The log ratio methodology converts compositional data, such as concentrations of chemical elements in a rock, from their original Aitchison geometry to interpretable real orthonormal coordinates, thereby allowing meaningful statistical processing and visualization. However, it must be taken into account that the original concentrations can be flawed by detection limit or imprecision problems that can severely affect the resulting coordinates. This paper aims to construct such orthonormal log ratio coordinates, called weighted pivot coordinates, that capture the relevant relative information about an original component and treat the redundant information in a controlled manner. Theoretical developments are supported by a thorough simulation study. Weighted pivot coordinates are then applied to the geochemical mapping of catchment outlet sediments from the National Geochemical Survey of Australia illustrating their advantage over possible alternatives.The paper was supported by the Grant COST Action CRoNoS IC1408 and the infrastructural part was supported from NPU I (LO1304).application/pdfen-AU© International Association for Mathematical Geosciences 2017Aitchison geometryOrthonormal coordinatesPivot coordinatesGeochemical mappingNational Geochemical Survey of Australia201710.1007/s11004-017-9684-z2020-11-23