Author

Matthew Cobb

Date of Award

2016

Degree Type

Thesis

Degree Name

Master of Science (Mathematics and Planning)

School

School of Science

First Advisor

Associate Professor Ute Mueller

Second Advisor

Dr Johnny Lo

Abstract

The prediction of recoverable resources at an operating manganese mine is currently undertaken using univariate ordinary kriging of the target variable manganese, and 5 deleterious variables. Input data densities at the time of this calculation are considerably lower than at the time of final selection (grade control), and the potential for unnacceptable conditional bias to be introduced through the use of linear geostatistical methods when determining grade estimates over a small support has led to assessment of the potential benefit of employing the local change of support methods Localised Uniform Conditioning (LUC) and Conditional Simulation (CS). Allowances for the operating conditions, including time frames for estimation / simulation, and likely software limitations are accounted for by also requiring decorrelation to be used in instances where the data are considered in a multivariate sense. A novel method for decorrelation of geostatistical datasets, Independent Components Analysis (ICA), is compared against the more common method of Minimum-Maximum Autocorrelation Factorisation (MAF). ICA performs comparably against MAF in terms of its ability to diagonalise the variance-covariance matrix of the test dataset over multiple lags, for a variety of input data densities and treatments (log-ratio transformed and raw oxide data).

Based on these results, ICA decorrelated data were incorporated into a comparative study of LUC and CS against block ordinary kriging (BOK), using an input dataset of reduced density, treated variously as raw univariate oxide data, decorrelated oxide data, and log-ratio transformed decorrelated data. The use of the log-ratio transform, designed to account for the 100% sum constraint inherent to the input data, proved impractical for LUC due to difficulties associated with the discrete Gaussian model change of support method employed by this technique. Log-ratio data transformation was restricted to use with CS where back transformation to raw oxide space could take place on a pseudo-equivalent support to the input data, prior to change of support. While use of the log-ratio transformation for CS guaranteed adherence to the sum constraint for results (the only method to do so) it resulted in distortion to both the spatial and grade distribution of results.

Decorrelation by ICA also posed difficulties, with biases introduced to final back transformed results as a result of the decorrelation algorithm in both log-ratio transformed and oxide data, which in some instances caused impossible negative values to be returned for some variables in the final results. In a comparison of net profit calculations for each method, the distortions introduced from both log-ratio transformation, and decorrelation become evident in either overly optimistic or conservative profit distributions for methods in which they were used. Of the results presented, only BOK, CS and LUC of non-decorrelated oxide data appear to show results similar to those which would be used at the operation during final selection (based on ordinary kriging of a complete dataset). Based on the comparison of spatial grade distributions and both net profit spatial distribution and summary, the decision to employ a non-linear method of recoverable resource calculation at the operation under question would be questionable in terms of its reward for effort, given that the current method of BOK appears to produce equivalent results.

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