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Fig. 5.2
Venn diagrams corresponding to areas of binary patterns of Fig.
5.1
;(
a
) is for Fig.
5.1b
;
(
b
) is for Fig.
5.1c
;(
c
) is for Fig.
5.1d
(Source: Agterberg et al.
1990
, Fig. 2)
a deposit. These probabilities are estimated by counting how many deposits occur
within the areas occupied by the polygons of their patterns. The relationships
between the two patterns (
B
and
C
), and the deposits (
D
) can be represented by
Venn diagrams as shown schematically in Fig.
5.2
.
Operations such as creating corridors around line segments on maps and
measuring areas can be performed by using Geographic Information Systems
(GIS's). The Spatial Data Modeller (SDM) (Sawatzky et al.
2009
) is an example
of a system that provides tools for weights of evidence, logistic regression, fuzzy
logic and neural networks. The availability of excellent software for WofE and
WLR has been a factor in promoting widespread usage of these methods. Examples
of applications to mapping mineral prospectivity can be found in Carranza (
2004
),
Cassard et al. (
2008
), Porwal et al. (
2010
), Coolbaugh et al. (
2007
) and Lindsay et al.
(
2014
). Applications of these techniques in other fields include Cervi et al. (
2010
),
Cho et al. (
2008
), Gorney et al. (
2011
), Neuh
¨
user and Terhorst (
2007
), Ozdemir
and Altural (
2013
), Regmi et al. (
2010
) Romero-Calcerrada et al. (
2010
)and
Song et al. (
2008
).
Box 5.1: Bayes' Rule for Single Map Layer
When there is a single pattern
B
, the odds
O
(
D
|
B
) for occurrence of mineral-
ization if
B
is present is given by the ratio of the following two e
x
pressions of
B
¼
ðÞ
ðÞ
PðÞ
PB
j
D
P D
PBjD
ð
ÞPðÞ
PðÞ
where
the set
D
represents the complement of
D
. Consequently, ln
O
(
D
|
B
) ¼ ln
O
(
D
)
+
W
+
where the positive weight for presence of
B
is:
W
þ
¼
ð
j
B
Þ
¼
;
P D
j
ln
PB
j
D
ð
Þ
. The
ðÞ
PBjD
ðÞ
P BjD
ln
P
B
j
D
negative weight for absence of
B
is:
W
¼
.
ðÞ
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