Cokriging for optimal mineral resource estimates in mining operations
RCA Minnitt, CV Deutsch
Cokriging uses a sparsely sampled, but accurate and precise primary dataset,
together with a more abundant secondary data-set, for example grades
in a polymetallic orebody, containing both error and bias, to provide
improved results compared to estimation with the primary data alone, as
well as filtering the error and mitigating the effects of conditional bias. The
method described here may also be applied in polymetallic orebodies and in
other cases where the primary and secondary data could be collocated, and
one of the data-sets need not be biased, unreliable, etc. An artificially
created reference data-set of 512 lognormally distributed precious metal
grades sampled at 25×25 m intervals constitutes the primary data-set. A
secondary data-set on a 10×10 m grid comprising 3200 samples drawn from
the reference data-set includes 30 per cent error and 1.5 multiplicative bias
on each measurement. The primary and secondary non-collocated data-sets
are statistically described and compared to the reference data-set.
Variograms based on the primary data-set are modelled and used in the
kriging of 10×10 m blocks using the 25×25 m and 50×50 m data grids for
comparison against the results of the cokriged estimation. A linear model
of coregionalization (LMC) is established using the primary and secondary
data-sets and cokriging using both data-sets is shown to be a significant
improvement over kriging with the primary data-set alone. The effects of
the error and bias are filtered and removed during the cokriging estimation
procedure. Thus cokriging using the more abundant secondary data, even
though it contains error and bias, significantly improves the estimation of
recoverable reserves.
Keywords
Cokriging, primary data-set, secondary data-set, linear model of coregionalization
(LMC), ordinary kriging, optimal resource estimates.