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environments in the Canadian Shield. In total, his study area constituted approxi-
mately 9 % of the shield. Next he tted the so-called exponential distribution. Later,
Grifths (
1966
) showed that it is better to apply the negative binomial model to
Slichter's data.
Suppose that the “control” area in Ontario is representative for the entire shield.
Because there occur 147 mines in Slichter's area, the total number of mines for the
entire shield would be approximately (100/9)
1,600 mines. Of course, this
estimate will be too low if not all mines in the control area were discovered. On the
other hand, it will be too large, if the control area is richer in mines (and larger
deposits) than the remainder of the Precambrian Shield.
The problem of predicting total value of all orebodies in the Canadian Shield
was discussed by De Geoffroy and Wu (
1970
) who argued as follows. The Cana-
dian Shield occupies an area of about 2,146, 000 sq. miles. Nearly 90 % of
commercial mineral deposits known in 1968 occur in volcanic belts and Lower
Proterozoic sedimentary belts. These relatively favorable environments, which
alternate with other rock types, occupy approximately 341,220 sq. miles or
15.9 % of the total area. An area of 50,000 sq. miles (Timmins-Kirkland Lake
area, Ontario; Noranda-Val-d'Or area, Qu´bec) for the favorable environments was
treated in detail by De Geoffroy and Wu (
1970
) with the following results:
147
Size of area: 50,000 sq. miles
Total number of deposits: 254 orebodies
Average number of deposits per 10
10 sq. miles: Ave (
k
)
¼
0.508
Variance:
s
2
(
k
)
2.016
Average value of deposits: Ave (
x
)
¼
60.5 · 10
6
US dollars (based on 1968 prices)
Logarithmic mean (base e): Ave (log
e
x
)
¼
2.858 (unit of value is 10
6
dollars)
¼
Variance:
s
2
(log
e
x
)
¼
3.103
These statistics can be used for a preliminary prediction of number of deposits
and their value in the 341,220
¼
291,220 sq. miles of territory that, for the
larger part, has not been explored in the same detail as the 50,000 sq. miles of
favorable environment in the control area. Variances of these estimates can be
computed to express their uncertainties. According to the statistics compiled by De
Geoffroy and Wu (
1970
), 0.508
50,000
1,733 mines are predicted to exist
on the Canadian Shield. This number is fairly close to that based on Slichter's data.
However, 129 of 254 orebodies of De Geoffroy and Wu fall in Slichter's area, and
the control area underlying the two estimated values overlap in part. Also, for the
second estimate, deposits outside the more favorable environments were not
considered.
De Geoffroy and Wu (
1970
) tted the negative binomial to number of orebodies
per unit area with satisfactory results. They also tted a normal distribution to the
logarithms of values in dollars for mines. The chi-square test discussed in Sect.
2.4.1
gave a chi-square value of 12.51 for six degrees of freedom (nine classes),
which may be compared to
P
{
341,220/100
¼
2
(6)
94.8 %. This result indicates that the
lognormal model provides a degree of t that is only moderately good. In fact, the
histogram for logarithmically transformed data shows a positive skewness that is
ˇ
<
12.5}
¼
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