Geoscience Reference
In-Depth Information
Fig. 8.1
The sketches to the left show the data configuration and a
central block being estimated (10 m on a side) in a high and low-grade
case. The histograms show the distributions of true grades conditional
to the 20 m spaced sample data. The heavy vertical line is the kriged
grade and the light vertical line is the mean true grade. The kriged grade
is too high in the high-grade case and too low in the low-grade case
Figure
8.1
shows a small example of conditional bias.
Consider mineralization with a lognormal histogram with a
mean of 1.0 and a variance of 4.0. The variogram has a rela-
tive nugget effect of 20 % and an isotropic range of 40 m.
Consider four samples on a regular 20 m grid to estimate a
central 10 m square block in a high and low-grade case. This
is a favorable estimation scheme since the nugget effect is
relatively low and the range is large relative to the sample
spacing. Nevertheless, there is conditional bias, that is, the
kriged grade is too high in the high-grade case and too low
in the low-grade case.
Conditional bias is largely (but not completely) removed
by using many samples in the estimation. This may be a
good idea when making
final
estimates, because it would not
be reasonable to accept estimates that are known to be wrong
in expected value. Large search routines retaining many data
are implemented to minimize conditional bias and provide
the best estimate. However, in mining, final estimates are
obtained using closely spaced data, which means that there
is seldom a good application for large searches and many
samples. Typical blast hole spacing in an open pit can vary
from 5 × 5 to 10 × 10 m patterns. The price of large searches
