Date of Award
Master of Science (Mathematics and Planning)
School of Engineering
Health, Engineering and Science
Associate Professor Ute Mueller
Dr Johnny Lo
Common implementations of geostatistical methods, kriging and simulation, ignore the fact that geochemical data are usually reported in weight percent, sum to a constant, and are thus compositional in nature. The constant sum implies that rescaling has occurred and this can be shown to produce spurious correlations. Compositional geostatistics is an approach developed to ensure that the constant sum constraint is respected in estimation while removing dependencies on the spurious correlations. This study tests the applicability of this method against the commonly implemented ordinary cokriging method. The sample data are production blast cuttings analyses drawn from a producing iron ore mine in Western Australia. Previous studies using the high spatial density blast hole data and compositional geostatistical approach returned encouraging results, results other practitioners suggested were due to the high spatial density. This assertion is tested through sub-sampling of the initial data to create four subsets of successively lower spatial densities representing densities, spacings, and orientations typical of the different stages of mine development. The same compositional geostatistical approach was then applied to the subsets using jack-knifing to produce estimates at the removed data locations. Although other compositional geostatistical solutions are available, the additive logratio (alr) approach used in this study is the simplest to implement using commercially available software. The advantages of the logratio methodology are the removal of the constant sum constraint, allowing the resulting quantities to range freely within the real space and, importantly, the use of many proven statistical and geostatistical methods. The back transformation of linear combinations of these quantities and associated estimation variances to the constrained sample space is known to be biased; this study used numerical integration by Gauss-Hermite quadrature to overcome this drawback. The Aitchison and Euclidean distances were used to quantify both the univariate and compositional errors between the estimates and original sample values from each estimation method. The errors of each method are analysed using common descriptive and graphical criteria including the standardised residual sum of squares and an assessment of the accuracy and precision. The highest spatial density dataset is equally well reproduced by either method. The compositional method is generally more accurate and precise than the conventional method. In general the compositional error analyses favour the compositional techniques, producing more geologically plausible results, and which sum to the required value. The results support the application of the logratio compositional methodology to low spatial density data over the commonly implemented ordinary cokriging.
Ward, C. (2015). Compositions, logratios and geostatistics: An application to iron ore. https://ro.ecu.edu.au/theses/1581