Correlation, Method of Least Squares, Linear Regression and the General Linear Model - Geomathematics: Theoretical Foundations, Applications and Future Developments - page 131

frequency distribution of amount of copper per control cell could be used for this
purpose. A relatively recent development is that increasingly it is realized that ore
deposits, like earthquakes and several other types of natural phenomena, have
fractal characteristics and resulted from non-linear processes. Mandelbrot ( 1983 ,
p. 263) posed a challenge to geoscientists by stating that oil and other natural
resources have Pareto distributions and “this finding disagrees with the dominant
opinion, that the quantities in question are lognormally distributed. The difference
is extremely significant, the reserves being much higher under the hyperbolic than
under the lognormal law.” This topic will now be investigated in more detail for
copper in the Abitibi area. Later, it will be discussed again in the context of fractals
(Chap. 10 ) .

4.4.2 Comparison of Weight Frequency Distributions
for Copper Metal and Ore

Size frequency distribution studies usually are carried out on populations of mineral
deposits of the same type. In this study, it is applied to total amount of copper in the
one or more copper deposits per (10 km 10 km) cell. This procedure has advan-

tages as well as drawbacks. An advantage is that the effect of strong localized
clustering of deposits is curtailed, and total number of observations (27 in 1971
versus 35 in the combined data set) is stabilized. A disadvantage is that copper
deposits of different types are being combined with one other although frequency
distributions for different types of deposits can be different, especially if two or
more metals are considered.
Nearly all (86 % of 66) large copper deposits in the combined data set are volcanic
massive sulphide type (VMS). There are relatively few (six) magmatic Ni-Cu
deposits (and five of these are small), plus three porphyry-type copper deposits.
Preliminary statistical analysis was performed on various subsets such as using
copper deposits instead of copper cells, VMS deposits only, Lydon's statistics only,
but these exercises produced results similar to those to be presented here. However,
explicit consideration of average copper grade ( amount of copper/amount of ore)

generates somewhat different results. For this reason, the following analysis is for two
variables per copper cell: (1) total weight (amount) of copper, and (2) total weight of
ore. A comparison will be made between the 2008 and 1968 data.
Figure 4.12 shows log-log plots of copper and ore weight versus rank. A Pareto
distribution plots approximately as a straight line on this type of plot as also shown
for gold tonnages in lode gold deposits in the Superior Province of the Canadian
Shield (Agterberg 1995 ; cf . Fig. 10.10 ). In each plot of Fig. 4.12 , a straight line was
fitted by least squares to most data points excluding the smallest copper or copper
ore cells for which information is probably incomplete. Also, it can be expected that
the Pareto distribution does not provide a good fit for low weight cells because it has
the property that frequency of occurrence continues to increase with decreasing

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