Geoscience Reference
In-Depth Information
Consequently, the data matrix X used for the Abitibi area consists of 644 rows
and 56 columns. The matrix D
X(X 0 X) 1 X 0 for the relation between estimated
and observed values of the dependent variable ( Y
¼
¼
DY ) has 644 rows and
644 columns. Observed values for the dependent variable were based on logarith-
mically transformed amount of copper in (1968) production and reserves per cell
(Fig. 4.5a ). Only 27 cells contained one or more large copper deposits (with more
than 1,000 short tons of copper in past production and estimated reserves; 1 short
ton
) 617 cells had zeros for the dependent
variable. Rock type variables assume values that are either 0 or positive. Suppose
that all explanatory variables are subjected to a Heaviside transformation changing
their values that are greater than 0 into 1. Negative values for variables, that involve
one of the two geophysical variables, were changed into zeros. Transforming all
55 variables in this manner and correlating them individually with the copper
pattern of Fig. 4.5a showed that the single yes-no explanatory variable most
strongly correlated with copper is acid volcanics present in a cell and Bouguer
anomaly above average. This explanatory variable is shown in Fig. 4.5b . Clearly,
there is positive spatial correlation between the patterns of Fig. 4.5a, b . The
explanation of this association is that nearly all large copper deposits in the Abitibi
area are volcanogenic massive sulphide deposits that are genetically associated with
acidic volcanics. Relatively high Bouguer anomaly in this area indicates under-
ground presence of a relatively thick pile of mafic volcanics with above average
specific gravity.
Another simplified illustration of use of the general linear model for correlating
occurrence of large copper deposits with the geological framework can be based
of the D matrix. The Kidd Creek Mine near Timmins, Ontario, is the largest
volcanogenic massive sulphide deposit in the Abitibi area. Suppose that the depen-
dent variable that is related to all 56 explanatory variables by multiple regression
has zero values in all cells except in the cell that contains the Kidd Creek Mine.
This means that the 643 other cells are being compared with this single cell. If a full
regression is carried out using all values of the dependent variable and the explan-
atory variables, the estimated values of the dependent variable are related to the
corresponding observed values through the D matrix that consists of 644 rows of
644 values. The experiment of comparing all cells with the Kidd Creek cell then is
equivalent to restricting the input for the dependent variable to the 644 values of the
56 explanatory variables in this single cell only. Figure 4.6 shows the corresponding
estimated values for the dependent variable. These predicted values were classified
according to three classes: very similar, more similar than average, and less similar
than average. This map graphically represents the row of the D matrix that corre-
sponds to the Kidd Creek Mine. From Fig. 4.6 it can be seen that comparing all
(10 km
¼
0.907 t). The remaining (644-27
¼
10 km) cells in the Abitibi with the cell that contains the Kidd Creek
deposit produces a pattern that has predictive potency.
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