Date of Award

2010

Degree Type

Thesis

Degree Name

Bachelor of Science Honours

Faculty

Faculty of Computing, Health and Science

First Advisor

Ute Mueller

Second Advisor

Dr Steven Richardson

Abstract

Geostatistics is a branch of applied mathematics that deals with spatially correlated data. Analysing and modelling spatially correlated data can be difficult and time consuming, especially for a multivariate data set. One of the techniques used to make analysis and modelling easier involves decorrelation, whereby a linear transformation on the sample variables is used to associate the spatially correlated variables with a set of decorrelated factors which are statistically and spatially independent. PCA was one of the first multivariate techniques and is mostly used as a data reduction technique. A popular alternative decorrelation technique often used in the mining industry is MAF. A study conducted by Bandarian (2008) found a relatively new decorrelation technique known as ACDC to be the method which produced the best spatial decorrelation for a multivariate moderately correlated data set consisting of four variables. In this thesis the PCA, MAF and ACDC methods are described and then applied to a multivariate data set supplied by Rio Tinto's Iron Ore Operations. Secondly, we explore whether it is preferable for the data set to be standardised or transformed via Gaussian anamorphosis to normal scores before being decorrelated. The data set consists of ten variables; however the three decorrelation methods were only applied to a subset of five variables (Fe, Ah03, Si02, LOI and Ti02) which have the greatest similarity from a statistical and spatial point of view. The three methods were applied to both standardised and normalised data. For ACDC, additional inputs such as weights, number of iterations, tolerance and an initial guess for the diagonalising matrix were explored and investigated in order to get the best spatial decorrelation results possible. The overall best spatial decorrelation was achieved by performing ACDC on the standardised variables, using the matrix of eigenvectors of the correlation matrix as the initial guess for the diagonalising matrix as well as the first four experimental semivariogram matrices in the decorrelation. Transforming the variables to normal scores before decorrelation was found to be of no benefit, as the factors that were derived from the normalised variables with the exception of one, were not normally distributed following the decorrelation.

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