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Fig. 6.16 (continued)
2
(
X
)
This yields new estimates of
1,183,972. In this application,
the new estimates are probably better than those obtained from the original gold
values without use of an appropriate transformation.
The comparison of the Pulacayo zinc example with the Whalesback copper and
Witwatersrand gold examples illustrates that there are similarities in that the frequency
distributions of channel samples in all three examples are positively skew and
approximately lognormal. Also, in all three cases, the autocorrelation function can
be approximated by a negative exponential function with value less than unity at the
origin indicating existence of a noise component superimposed on the spatial random
variable representing more continuous variability at larger distances. Negative expo-
nential autocorrelation functions are closely related to Markov chain analysis and to
scaling properties of sequences of mineral grains in igneous rocks. For example, Xu
et al. (
2007
) demonstrated existence of small-scale scaling in “ideal granite” grain
sequences previously modeled as Markov chains (Vistelius et al.
1983
). Wang
et al. (
2008
) applied multifractal and Markov chain analysis to sphalerite banding at
the microscopic scale in the Jinding lead-zinc deposit, Yunnan Province, China.
In Fig.
2.10
for the Pulacayo zinc example, the noise component was filtered out
to retain a “signal” with approximately unity autocorrelation function value at the
origin (
cf
. Agterberg
1974
). The nugget effect can be modeled as random noise at
lag distances greater than 2 m. Existence of a sill is not obvious in the Pulacayo zinc
example. However, as originally realized by Matheron (
1971
), a nugget effect of
this type may reflect strong autocorrelation so close to the origin that it cannot be
seen in semivariograms or correlograms because its spatial extent is less than the
sampling interval used in practice. The frequency distribution of the Pulacayo zinc
example has less positive skewness than those of copper and gold in the other
examples.
μ
(
X
)
¼
879.1;
˃
¼
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