Selected Topics for Further Research - Geomathematics: Theoretical Foundations, Applications and Future Developments - page 515

Fig. 12.44 Theoretical frequency distributions for amount of acidic volcanics per cell compared
with 64 10-km cell vales in Fig. 12.43 and 16 20-km cell values (Source: Agterberg and Fabbri
1978 , Fig. 11)

0.1973 and s 2

estimated from the 64 values are m ¼ ¼ 0.0919, respectively. The

variance of a square cell with side of length a satisfies

Z dx Z c

e p xy dy

C 0
a 4

C 0 a ðÞ ¼

where x and y denote vectors in the plane and the integrations are carried out over
the cell with side a ( cf . Agterberg 1978a ). This 2-D equation is in accordance with
basic 3-D geostatistical theory (Box 6.7 ).
Substitution of the coefficients c ¼ 0.87 and p ¼ 0.194 obtained previously and

m 2 0.0910 which is close to s 2

setting C 0 ¼ m ¼ 0.1584, yields C 0 ( a ) ¼ ¼ 0.0919

estimated from the 64 values for (10 10 km) cells. A further test of the model

consisted of dividing the (80 80 km) test area into 16 (20 20 km) cells. This

gave 16 percentage values for acidic volcanics in (20 20 km) cells with mean

0.1973 and s 2 m ¼ ¼ 0.0622. The corresponding theoretical variance is C 0 ( a ) ¼

0.0627 (Fig. 12.44 ).
The preceding results indicate that it is possible to model the variance of the
random variable X which represents the relative amount of acidic volcanics per