Abstract: |
Complex multivariate relationships in ore deposits can be difficult to model using available geostatistical techniques. Geochemical data are usually reported in weight percent and lend themselves to treatment as compositional data. As information represented by compositions is relative, proponents of the approach describe a theoretical framework for estimation using log ratios, specifically the additive log ratio (?alr?). The use of log ratios facilitates the use of standard geostatistical techniques because the transformation results in unconstrained values in real space. This framework was implemented to test its applicability to an iron ore mine in Western Australia. Cross-validation of a single bench of 6m long blast hole (?BH?) samples was used to compare the results from ordinary co-kriging of the alr variables with those from conventional ordinary co-kriging, Both the Aitchison distance and the Euclidean distance were used to quantify the error between the estimate and the BH sample data. As an initial method, the additive generalised logistic (?agl?) back transformation was applied to the alr cokriged estimates; the results follow the required constraints and produce better estimates when considering the Aitchison distance. When the Euclidean errors are considered the OCK estimates are less biased but the distribution of errors for the alr estimates appear to be superior to the OCK estimates. Due to limitations with the additive normal logistic distribution, the agl back transform as applied initially is not strictly applicable to expected values and variances. This is due to a lack of an explicit form of the integral required to obtain estimates of the expected value or variance in the original sample space. However, as it is possible to get a reasonable approximation using Gauss-Hermite Quadrature; this approach is also illustrated in the case study presented. |
