Geoscience Reference
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Fig. 3.12 Graphical construction of F ( x ) which is proportional to the tangent of the slope of
x ¼ G ( z ) representing the theoretical lognormal distribution plotted on arithmetic probability paper
(Source: Agterberg 1974 , Fig. 33)
x
¼
G ( z ). The slope of G ( z ) is measured at a number of points giving the angle
ˆ
.
For example, if z
¼
x
¼
20 in Fig. 3.12a ,
ˆ ¼ ˆ 1 , and:
dG z
ðÞ
dZ ¼
tan
ˆ
is plotted against x, we obtain a function
F ( x ) that represents g ( X i ) except for a multiplicative constant that remains
unknown. This procedure is based on the general solution of the generating process
which can be formulated as:
If, in a new diagram (Fig. 3.12b ), tan
ˆ
Z 1
X 0
dX 1
gXðÞ ¼
Z
¼
ʵ i
0
This procedure is based on the assumption that Z is normally distributed.
The function g ( X i ) derived in Fig. 3.12b for the lognormal curve of Fig. 3.13a is
simply a straight line through the origin. This result is in accordance with the origin
theory of proportional effect. However, the method can produce interesting results
in situations that the frequency distribution is not lognormal. Two examples are
given in Fig. 3.13 . The original curves for these two examples (Fig. 3.13a ) are on
logarithmic probability paper. They are for the 1,000 Merriespruit gold values
shown in histogram form in Fig. 3.11 , and a set of 84 copper concentration values
for rock samples from sulphide deposits that surround the Muskox intrusion as a
rim. The results obtained by the graphical method are shown in Fig. 3.13b .
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