Geoscience Reference
In-Depth Information
Abitibi copper potential map (see Sect.
4.4.1
) and cell 17/59 contains the Kidd
Creek Mine with the largest volcanogenic massive sulphide deposit in the Abitibi
area. All 1,086 probabilities for (10
10 km) cells obtained by the original appli-
cation were multiplied by the factor
F
1.828 representing the number of control
cells known to contain one or more massive sulphide deposits in the control area
constructed around the mining districts divided by the sum of originally estimated
probabilities in this control area. For the ten cells in Table
12.1
the jackknife
probabilities are all close to the original probabilities multiplied by 1.828. It is
noted that one of the estimated probabilities in Table
12.1
is negative. This is
because the general linear model was used that does not constrain probabilities to
could be replaced by zeros but in the applications to Abitibi copper deposits a
correction of this type would not affect final results.
The jackknife method has two significant advantages with respect to the original
solution: (1) it provides estimates of the standard deviations of cell probabilities
(shown for ten cells in Table
12.1
) which are larger than estimates based on
ordinary regression (not shown), which are probably significantly biased; and
(2) it does not require the construction of a control area; which in the original
applications was a somewhat arbitrary, subjective undertaking.
¼
12.2 Compositional Data Analysis
Geological variables, especially for rock composition data often are subject to
various constraints that affect the shapes of their frequency distributions and their
relations with other variables. Closed-number systems such as the major oxides
measured on rock samples provide a primary example (Chayes
1971
). Some very
simple examples are as follows: (1) in Sect.
2.5.1
it was pointed out that, if a
Pulacayo ore sample would consist of pure sphalerite, its maximum possible zinc
value would be about 66 %. This upper limit constrains possible shapes of zinc
which Mg and Fe can interchange positions in the silicate lattice. It means that if
different olivine crystals are analyzed for Mg and Fe, these two elements would
show perfect negative correlation (
r
1.00) because increase in content of one
element implies decrease in content of the other.
Chayes (
1971
) pointed out that silica (SiO
2
) content generally is negatively
correlated with other major oxides in collections of rock samples, simply because
it usually is the major rock constituent, and increases in other major oxides must be
accompanied by decreases in silica. Pearson (
1897
) already had pointed out that
spurious correlations between variables can arise if they are functions of random
variables. His reasoning was as follows: “If
x
1
¼
¼
f
2
(
w
2
,
w
3
)be
two functions of the three variables
w
1
,
w
2
,
w
3
, and these variables be selected at
random so that there exists no correlation between
w
1
,
w
2
or
w
1
,
w
3
or
w
2
,
w
3
, there
will still found to exist correlation between
x
1
, and
x
2
.”
f
1
(
w
1
,
w
2
) and
x
2
¼
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