The quantification of uncertainty attached to selected sampling protocols in a kimberlite using a discrete simulation method

Thurston, Malcolm Lawrence
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The prime objective of this thesis is to understand, in a quantitative way, how the uncertainty in local and global grade estimates change with different sampling configurations, both in terms of the size of a sample and in terms of the number of samples taken. A second objective, and necessary in order to achieve the first, is to practically apply a new simulation method that takes into account the statistical, spatial and discrete nature of the diamond distribution in a kimberlite. A limited number of practical, sampling protocols were considered. For global grade estimates, and for the situations tested, it was shown that the number of holes required to place the global estimate within '10% of the "true" global mean (at a lower 90% confidence interval) ranged from 12holes tor a high nugget effect semi-variogram model to 16 holes for a low nugget effect seml-varlogram model. For larger samples the results showed very little improvement in the global confidence limits for the low nugget semi-variogram model while the high nugget semi-variogram model improved significantly. For local grade estimates, and for the situations tested, it was shown that 90% of the blocks estimated were within 25% of their true value for both the low and high nugget semi-variogram models. Moving to a larger sample size improved the confidence in the local estimates for the low and high nugget effect models. The effect of bottom cut-off on local and global grade confidence limits was investigated and found to be, for the situations tested, minimal in the case of global grade estimates but played a role when local estimates were required. The possibility of estimating diamond grade across part of the diamond size distribution was explored and shown to be a promising technique in circumstances where the full diamond size distribution is known. The advantage of this approach is that the grade of the restricted size range can be estimated using a smaller sample size.
A thesis submitted to the Faculty of Engineering, University of the Witwatersrand, Johannesburg, in fulfilment of the requirements for the Doctor of Philosophy.
Ores -- Sampling and estimation., Kimberlite., Diamonds -- Assaying., Diamond mines and mining -- South Africa.