Geoscience Reference
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Fig. 11.2 Logarithmic variance of gold values as a function of reef area sampled. The variance
increases linearly with log-area if the area for gold values is kept constant. The relationship
satisfies the model of de Wijs (Source: Agterberg
2012b
, Fig. 1)
constant terms are contained in the observed logarithmic variances plotted in Fig.
11.2
.
These additive terms are related to differences in the shapes of blocks. For example,
channel samples are approximately linear but gold fields are plate-shaped. This
constant term (called “sampling error” by Krige (
1966
), which equals 0.10 units
along the vertical scale in Fig.
11.2
) is independent of size of area. These two relatively
small refinements were discussed in more detail in Agterberg (
2012a
).
11.1.2 Worldwide Uranium Resources
The logbinomial model of de Wijs was used in mineral resource evaluation studies
by Brinck (
1971
,
1974
). A comprehensive review of Brinck's approach can be
found in Harris (
1984
). The original discrete model of de Wijs is assumed to apply
to a chemical element in a large block consisting of the upper part of the Earth's
crust with known average concentration value
ʾ
commonly set equal to the ele-
ment's crustal abundance.
According to Brinck (
1974
), chemical analysis is applied to blocks of rock that
are very small in comparison to the large block targeted for study. Let
n
N
represent the maximum number of subdivisions of the large block. Suppose that
the element concentration values available for study: (1) constitute a random
sample from the population of 2
N
very small blocks within the large block, and
(2) show an approximate straight line pattern on their lognormal
Q-Q
plot. The
slope of this line then provides an estimate of
¼
(and
d
) can be derived
by means of the variance formula of de Wijs. Brinck (
1974
) set 2
N
equal to the
average weight of the very small block used for chemical analysis divided by total
weight of the environment targeted for study. This model constitutes one of the
earliest applications of the model of de Wijs. It is likely that Brinck's approach
remains applicable. Estimation of the parameters of the model of de Wijs including
d
could be improved by adopting the multifractal modeling approach to be discussed
in Sect.
11.2
.
˃
from which
ʷ
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