Compositions, Log Ratios and Bias - From Grade Control to Resource Definition

Document Type

Conference Proceeding


Australian Institute for Mining and Metallurgy


Faculty of Health, Engineering and Science


School of Engineering/Natural Resources Modelling and Simulation Research Group




This article was originally published as: Ward, C., & Mueller, U. A. (2013). Compositions, log ratios and bias - from grade contol to resource definition. In Iron Ore 2013 : 12-14 August 2013, Perth, Western Australia. (pp. 313-319). Carlton, Australia: Australasian Institute of Mining and Metallurgy. Original article available here


Compositional geostatistics is an approach developed to ensure that the constant sum constraint induced by geochemical iron ore analysis is respected in estimation and simulation. Jack-knifing and cross-validation were used within this framework to compare the results from ordinary cokriging of the additive log ratio (alr) variables with those from conventional ordinary cokriging. Two methods were used to back-transform the alr estimates: the crude additive generalised logistic back transformation and numerical integration via Gauss-Hermite quadrature. Previous work on a blasthole data set from a Yilgarn iron ore mine showed promising results, with the Gauss-Hermite quadrature method returning results comparable to ordinary cokriging from the point of view of bias, but superior in that the constant sum constraint imposed by geochemistry of the data was honoured. Other practitioners have noted that the linear interpolation of non-linear log ratio transformations will result in biased results, and that this bias can be masked in a (grade control) setting where the spatial density is high. To test this assertion, the methodology has been extended to successively lower spatial density data sets. The results and applicability to routine iron estimation are discussed