Geoscience Reference
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in Fig.
5.7
, the ternary pattern for geochemical signature has parts of the area for
which no data were available (Fig.
5.4
). Uncertainty due to missing data becomes
zero in places where all patterns including the geochemical signature are available.
The term
˃
1
2
is only added to the variance in places where presence or absence of
the feature could not be determined.
The weights
W
+
1.0047 and
W
¼
¼
0.1037 for geochemical signature
were calculated from likelihood ratios for the entire area. For example,
W
þ
¼
log
e
0047 was based on (1)
pb
d
¼
pb
jðÞ
pbjd
pb
ðÞ
pd
ðÞ
¼
1
:
ðÞ
¼
nbd
ð =
nd
ðÞ
with
n
(
bd
)
¼
10 and
d
¼
nbd
=
n d
with
nbd
¼
ðÞ
p d
p
bd
n
(
d
)
¼
68; and (2)
pb
j
ðÞ
¼
164
:
9
10
¼
154
:
9
and
n d
¼
0. The weight
W
+
canberegardedasindepen-
dent of the prior probability. For this example, approximately the same value of
W
+
is
obtained when (1) the calculation is based on the subarea (
2, 945
:
0
68
¼
2, 877
:
1,765.8 km
2
)withknown
geochemical signature, and (2) the prior probability within the area with known
geochemical signature is set equal to the prior probability for the total study area
(
¼
2,945 km
2
). The second condition would imply that there are 41 deposits within
the area with known geochemical signature. In reality, this subarea contains only
24 known gold occurrences. Revised weight based on the subarea only would amount
to 1.5444 which is greater than
W
+
¼
1.0047, because the subarea would contain a
larger proportion of the deposits. The lesser weight (
W
+
¼
¼
1.0047) was used in
˃
1
2
.
For this example, the modified prior probability, which is based on all patterns
except geochemical signature, will be set equal to 0.05 and 0.10 within the area
without definable geochemical signature. The logits of these values are
Fig.
5.7
and will now be employed for estimating
2.9444
and
2.1972, respectiv
e
ly. Addition of
W
+
and
W
provides the required esti-
mates of
p
(
d
|
b
)and
pd
b
.For
p
(
d
)
0.05, the conditional probabilities are equal
to 0.1257 and 0.0453, respectively. For
p
(
b
), which also is necessary to determine
˃
1
2
, the ratio of favorable area (
¼
16
4.9 km
2
) to known area (
1,765.8 km
2
)can
¼
¼
p b
¼
be used. This gives
pb
ðÞ
¼
1
0
:
9066. Consequently,
˃
1
(0.05)
¼
0.024.
By the same method, it follows that
0.042. In a previous example, it
was pointed out that a unit cell in the Goldenville Formation with unknown
geochemical signature in the proximity of the linear features except granite
contact has posterior probability of 0.070 with standard deviation equal to
0.028. Addition of the uncertainty due to missing pattern results in the larger
standard deviation of 0.042.
A question that is often asked when WofE is used to define target areas
representing areas with relatively high posterior probabilities but with no or
few known deposits is related to bias arising when undiscovered deposits prob-
ably exist in the study area. All posterior probabilities in a study area systemat-
ically underestimate the “true” posterior probabilities if there are undiscovered
deposits in the study area. Such bias could be eliminated only if it would be
˃
1
(0.10)
¼
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