Selected Topics for Further Research - Geomathematics: Theoretical Foundations, Applications and Future Developments - page 524

Fig. 12.53 Experimental frequency distributions for nine samples of cell values plotted along
axes with two normal probability scales (from Agterberg 1981 ). The values of b and r were
obtained from the means and variances of the cell values using Fig. 12.53. They determine the
positions and slopes of the lines for probnormal distributions (Source: Agterberg 1984 , Fig. 9)

Table 12.3 Estimation of the
values ˈ 1 i (Source: Agterberg
1984 , Table 2)

i 0 1 2 3

N C i q N i
1

p i 1 15 q 1 1 p 1 105 q 1 1 p 1 455 q 1 1 p 1

q 1 1

f i ( z 1 ) 0.66667 0.27400 0.05255 0.00624

F i ( z 1 )

0.66667 0.94066 0.99322 0.99946

x 1 ( F i ) 0 0.0282 0.0540 0.0765

ˈ 1 i 0 0.0141 0.0411 0.06525

that, in general, the relationship between variance and cell size can be determined
independently by geostatistical methods of 2-D integration such as the one
explained in Sect. 12.8.3 for acidic volcanics in the Bathurst area. There are
512 empty cells in Fig. 12.49 . Therefore, the frequency of zero values satisfies
q 1 N

¼ 512/786 ¼ 0.66667. Several values of N 5 were tried yielding nearly the

same results. Setting N ¼ 15 gives q 1 ¼ 0.97333 and p 1 ¼ 1 q 1 ¼ 0.02667. A

q N 1
1

N
i

sequence of values f i zðÞ ¼

p 1 ˈ 1 i is

the corresponding values of

shown in Table 12.3 .
The cumulative frequency F i ( z 1 ) in Table 12.3 is close to 1.0 for i ¼3. The

cumulative frequency distribution for 10-km cells was plotted and the
corresponding values of x 1 ( F 2 ) were read from the resulting graph. The ˈ 1 i values