Geoscience Reference
In-Depth Information
1 initially coincide but one of the two spheres is shifted in the
h
direction. Then the
amount of overlap of overlap of the two spheres then decreases from its maximum
value (
0) at lag
a
. The cubic semivariogram
function describes 1 minus the amount of overlap. This spherical model often
provides a good fit and is relatively easy to use in geometrical extrapolations.
In situations of asymmetry as frequently occur in Nature; the sphere can be replaced
by an ellipsoid. The spherical-ellipsoidal model of diminishing autocorrelation
formalizes the idea of a probable influence cell (“prince”; Agterberg
1965
)
according to which strong local spatial continuity diminishes with distance until
spatial variability becomes totally dominated by other, mainly deterministic,
genetic processes.
¼
1) at zero shift to its minimum (
¼
6.2.6 Short-Distance Nugget Effect Modeling
In Sect.
2.5.1
, it was pointed out that there is uncertainty associated with the
definition of effective length
L
0.5 m of the channel samples in the Pulacayo
Mine. This is because these samples were taken across the entire width (
¼
1.30 m)
of drift whereas the Tajo vein has (horizontally measured) thickness of 0.50 m on
the 446-m level. This thickness value was used by Matheron and earlier in this
chapter as a best estimate of
L
. It has been shown that the choice of
L
¼
0.5 results in
estimates of
A
that are satisfactory for lag distances greater than 2 m (up to 400 m).
For shorter lag distances, however, it is useful to generalize Matheron's concept of
absolute dispersion by defining
A
(
L
), which depends on the value of
L
. Conse-
quently,
A
¼
A
(0.5) for the applications described in Sect.
6.2.1
. Theoretically, the
method used to estimate
¼
(0.5) in Fig.
6.17
can be used to optimize our
choice of
L
. In Agterberg (
2012
, Fig. 10) estimates of
A
(
L
) are shown that would be
obtained for effective channel sample lengths less than 0.5 m. For
L
ʲ
(0.5)
¼
6
ʱ
>
3 cm,
A
(
L
)
increases slightly from about 0.01 to 0.0165 at
L
¼
0.5 m; for
L
<
0.03 m, there is
rapid decrease to
A
(
L
)
0. Sums of squared deviations from lines of best fit for
different values of
L
. showed that the optimum solution (
ʱ
(
L
) ¼0.021) is obtained
at
L
¼
13 cm (Agterberg
2012
, Fig. 12). The de Wijsian variogram model that best
fits the 10 observed values of Table
6.1
is for linear samples that are not only
shorter than the channel samples on which zinc concentration was measured
(
L
¼
0.5 m).
This result probably reflects small-scale clustering of the chalcopyrite crystals.
In Agterberg (
2012
) it was tentatively suggested that the very narrow optimum
effective vein width may reflect the fact that the Tajo vein was originally formed
along a fissure.
It should be kept in mind that the preceding conclusions remain subject to
uncertainty because of limited precision of the variogram values of Table
6.1
.
Also, anisotropy may have played a role because zinc concentration value varia-
bility perpendicular to the Tajo vein could well differ from variability parallel to the
vein. However, the best explanation is that over short lag distances
h
(e.g. within the
¼
1.3 m) but also shorter than the thickness of the Tajo vein (
L
¼
Search WWH ::
Custom Search