Geoscience Reference
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Fig. 11.22 Spatial statistics
for Au mineral occurrences.
(a) Log-log plot of
relationship between
K
(
r
)
and distance
r
;
solid lines
are LS fits for
˄
(2)
¼
1.219
0.037. (b) Log-log
plot for relationship
between second-order
intensity
a
10.0
9.5
9.0
8.5
8.0
7.5
2
and
r
with
theoretical line for
ʻ
(2) ¼
1.219 (Source: Cheng and
Agterberg
1995
, Fig. 7)
˄
7.0
6.5
6.0
2.0
2.5
3.0
3.5
4.0
4.5
Log
r
b
2.50
2.25
2.00
1.75
1.50
1.25
1.00
0.75
0.50
2.0
2.5
3.0
3.5
4.0
4.5
Log
r
multifractal and geostatistical modeling of the largest and smallest geochemical
element concentration values in rocks and orebodies. These extreme values corre-
spond to local singularities with near-zero fractal dimensions that occur close to the
minimum and maximum singularity in the multifractal spectrum. These extremities
normally cannot be estimated by means of the method of moments because of
small-sample size problems that arise when the largest and smallest concentration
values are raised to very high powers
q
. This problem also will be investigated
by means of a computer simulation experiment and application to thousands of
copper determinations from along the 7-km deep KTB borehole in southeastern
Germany, for which local singularity analysis can be used to determine all singu-
larities including the extreme values. The singularities estimated by this method are
linearly related to logarithmically transformed element concentration values. This
simple relation also can be useful to measure the small-scale nugget effect, which
may be related to measurement error and microscopic randomness associated with
ore grain boundaries.
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