Geoscience Reference
In-Depth Information
7.3.7
Probabilistic Estimation Methods
based on more local corrections, so that downstream
work, such as mine planning, takes its effect into account.
b. Forcing the overall resources to match the volume-vari-
ance corrected distribution implies ignoring all other di-
lution sources described above. Therefore, the reported
overall resources are known to be wrong, since they are
based on the incorporation of a single source of dilution.
The resource model should incorporate more dilution than
predicted by volume-variance correction to include geo-
logic contact dilution, the information effect, and planned
operational dilution.
Another application is correcting the drill hole data such
that an estimate of the expected SMU distribution is ob-
tained prior to estimating the resources. This provides a tar-
get distribution against which the resource model can be
compared.
The example shown in Fig.
7.9
corresponds to the Cerro
Vanguardia operation, which mines gold and silver vein de-
posits in the Patagonia Region in Southern Argentina. Fig-
ure
7.9
shows the distributions of the 2 m composites used
for estimation, as well as the DG-predicted and the Affine-
predicted SMU distributions. Note that in this case, the SMU
is a 5 × 10 × 5 m cube, to account for the open pit mining
method currently used. The example shown is from the Os-
valdo Diez vein, one of more than 40 Au-Ag bearing veins
identified in the district, and the source of most of the mine's
production through the late 1990's and early 2000's. It is in-
structive to note several points:
• The graph in Fig.
7.9
shows the Au cutoff grades applied
to the distribution on the X axis, the left Y-axis shows the
predicted proportion of tonnage above the corresponding
cutoff, while the right Y-axis shows the corresponding
grade above cutoff.
• The grade-tonnage curves allow an immediate analy-
sis for the cutoffs of interest, and how the distributions
change for different grade ranges.
• The volume-variance correction factor is estimated at
28 %, implying that there is a very significant change
in variance from the original 2 m composite to the
5 × 10 × 5 m SMU distributions.
• The Affine correction is not the appropriate method to use
in this case. It is presented here to highlight the differ-
ences in the resulting distributions. Among other reasons,
the artificial minimum generated by the Affine correc-
tion is quite high, and, although not shown here, the DG
model was proven by production data to be more robust.
• The difference between the tonnage and grades for any
given cutoff between the SMU distributions and the com-
posites distribution is an indication of the how severe the
predicted volume-variance correction is.
In the literature there are several other detailed examples and
comparisons of the different volume-variance corrections,
see for example Verly (
2000
) and Rossi and Parker (
1993
).
Several probabilistic estimation methods, described in detail
in Chap. 9, can be used to incorporate the volume-variance
effect into the resource estimation process.
One option is to modify the point probability distribu-
tions resulting from the multiple indicator kriging (MIK)
technique into block probability distributions using either an
affine, ILC, or DGM correction. A variant of is the procedure
has been used by Newmont Gold at its Gold Quarry mine in
Nevada (Hoerger
1992
), which, appears to work reasonably
well when there is sufficient production data for a correct
calibration.
A different option within the application of MIK is to
apply the volume-variance correction to a cumulative prob-
ability distribution, at the composite scale, resulting from
MIK. The compositing refers here to simply averaging the
MIK probability distribution values to larger panels. A dis-
cussion of this method can be found in Chap. 9 and in Jour-
nel and Kyriakidis (
2004
).
Methods used to estimate distributions that are based on
the Gaussian or Lognormal assumptions are also applied to
incorporate the volume-variance effect into the resource esti-
mation model. The available options include Multi-Gaussian
Kriging (Verly
1984
), Disjunctive Kriging (Matheron
1976
)
and its derivative, Uniform Conditioning (Roth and Deraisme
2000
), and the Lognormal Shortcut methods (David
1977
).
The change of support models afforded by these methods
is generally robust, as long as the corresponding underlying
Gaussian or Log-normal assumptions are reasonable.
The volume-variance correction methods described share
in the same limitations: they do not account for other types of
dilution and the information effect. They assume that every
block can be selected individually and independently from
any other (free selection), and that the selection itself is made
based on a known true grade (perfect selection).
7.3.8
Common Applications of Volume-Variance
Correction Methods
The methods for volume-variance correction described are
applied to ore resource modeling in several manners. The
traditional application has been the correction of the global
resource model to match the predicted grade-tonnage curve
according to the volume-variance effect predicted (David
1977
; Journel and Huijbregts
1978
). This application is now
less common for multiple reasons:
a. The volume-variance correction performed in such a way
is a global correction, and therefore of little practical use,
except for the overall assessment of resources from a
deposit; the mineralization's internal dilution should be
somehow incorporated into the resource block model
