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

[摘要] The prime objective of this thesis is to understand, in a quantitative way, howthe uncertainty in local and global grade estimates change with differentsampling configurations, both in terms of the size of a sample and in termsof the number of samples taken.A second objective, and necessary in order to achieve the first, is topractically apply a new simulation method that takes into account thestatistical, spatial and discrete nature of the diamond distribution in akimberlite.A limited number of practical, sampling protocols were considered.For global grade estimates, and for the situations tested, it was shown thatthe number of holes required to place the global estimate within '10% of thetrue global mean (at a lower 90% confidence interval) ranged from 12holestor a high nugget effect semi-variogram model to 16 holes for a low nuggeteffect seml-varlogram model.For larger samples the results showed very little improvement in the globalconfidence limits for the low nugget semi-variogram model while the highnugget semi-variogram model improved significantly.For local grade estimates, and for the situations tested, it was shown that90% of the blocks estimated were within 25% of their true value for both thelow and high nugget semi-variogram models. Moving to a larger sample sizeimproved the confidence in the local estimates for the low and high nuggeteffect models.The effect of bottom cut-off on local and global grade confidence limits wasinvestigated and found to be, for the situations tested, minimal in the caseof global grade estimates but played a role when local estimates wererequired.The possibility of estimating diamond grade across part of the diamond sizedistribution was explored and shown to be a promising technique incircumstances where the full diamond size distribution is known. Theadvantage of this approach is that the grade of the restricted size range canbe estimated using a smaller sample size.

[发布机构] University of the Witwatersrand