Geoscience Reference
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Fig. 10.21 First stages of
two-dimensional cascade
model of de Wijs. Overall
mean concentration value
was set equal to one;
d
¼
dispersion index.
Non-Random index matrix
corresponds to (4
4)
squares distribution of
concentration values
(Source: Agterberg
2007
,
Fig. 2a)
(1+
d
)
(1-
d
)
(1+
d
)
2
(1+
d
)(1-
d
)
(1-
d
)
2
(1+
d
)(1-
d
)
(1+
d
)
3
(1-
d
)
(1+
d
)
3
(1-
d
)
(1+
d
)
2
(1-
d
)
2
(1+
d
)
4
(1+
d
)
2
(1-
d
)
2
(1+
d
)
2
(1-
d
)
2
(1+
d
)
2
(1-
d
)
2
(1+
d
)(1-
d
)
3
(1+
d
)(1-
d
)
3
(1+
d
)
3
(1-
d
)
(1+
d
)
3
(1-
d
)
(1+
d
)
2
(1-
d
)
2
(1+
d
)
2
(1-
d
)
2
(1+
d
)(1-
d
)
3
(1+
d
)(1-
d
)
3
(1-
d
)
4
40
31
31
22
31
22
22
13
31
22
22
13
22
13
13
04
04
13
13
22
13
22
22
31
22
13
40
31
31
22
31
22
Fig. 10.22 Realization of
model of de Wijs (see
Fig.
10.21
in 2-D for
d
¼
0.4
and
N
¼
14). Overall
average value is equal to
1. Values greater than
4 were truncated (Source:
Agterberg
2007
, Fig. 3)
4
3
2
100
1
0
50
50
100
can be written as (1 +
d
)
for the other half so that
total mass is preserved. The coefficient of dispersion
d
is assumed to be independent
of block size. This approach can be modified by replacing
d
by a random variable
(random-cut model; Sect.
12.3.1
). Figure
10.21
illustrates the original model of de
Wijs: any cell containing a chemical element in 1-, 2-, or 3- dimensional space is
divided into two halves with element concentration values (1 +
d
)
ʾ
for one half and (1
d
)
ʾ
ʾ
and
(1
can be set equal
to unity. This implies that all concentration values are divided by their overall
regional average concentration value (
d
)
ʾ
. For the first cell at the beginning of the process,
ʾ
). The index of dispersion (
d
) is indepen-
dent of cell-size. In 2-D space, two successive subdivisions into quarters result in
ʼ
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