The quantification of uncertainty attached to selected sampling protocols in a kimberlite using a discrete simulation method
Date
1998
Authors
Thurston, Malcolm Lawrence
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Abstract
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.
Description
A thesis submitted to the Faculty of Engineering, University of the
Witwatersrand, Johannesburg, in fulfilment of the requirements for the
Doctor of Philosophy.
Keywords
Ores -- Sampling and estimation., Kimberlite., Diamonds -- Assaying., Diamond mines and mining -- South Africa.