Geoscience Reference
In-Depth Information
Fig. 12.24 United States uranium resources (unit
¼
10
6
t) versus cut-off grade (in percentage
U
3
O8) from Harris (
1984
) on log-log paper (logs base 10). Last eight values satisfy Pareto
distribution model. The decrease in slope toward the origin probably is caused by the fact that
lower grade deposits are underreported because it is not economic to mine them (Source:
Agterberg
1995
, Fig. 5)
12.5.2 Accelerated Dispersion Model
A common problem in mineral resource studies is that frequently the high-value tail
of the observed size-frequency distribution is thicker than lognormal which, in turn,
Fig.
12.24
for U.S. uranium resources. The high-value tail in this log-log diagram is
approximately according to a straight line indicating a Pareto distribution. The
following relatively simple modification of the model of de Wijs results in thicker
than lognormal frequency distribution tails (
cf
. Agterberg
2007b
). It could be
assumed that the coefficient of dispersion
d
increases as a function of element
concentration value
. For example, suppose that the first derivative of a chemical
element's dispersion coefficient is a linear function of
ʾ
ʾ
so that
d
¼
d
0
exp(
p
ʾ
)
where
p
is a constant. Setting
p
0.01 and re-running the 2-D experiment previ-
¼
+4)
shown in Fig.
12.25
where the vertical scale is logarithmic. The logarithmically
transformed concentration values of Fig.
12.25
are normally distributed except for
the largest values. Figure
12.26
is a comparison of the largest log-concentration
values with those arising when there would be no acceleration of dispersion. Values
with log
10
(
0.4;
N
¼
14) yielded the pattern for (
ʾ
ʾ
2 are larger than expected in comparison with patterns such as
Fig.
10.22
resulting from the model of de Wijs with
p
)
0. Only relatively few very
large values emerge from the approximately lognormal background if
p
is small.
¼
Search WWH ::
Custom Search