Selected Topics for Further Research - Geomathematics: Theoretical Foundations, Applications and Future Developments - page 487

Fig. 12.16 Lognormal Q-Q plots for discrete binomial frequency distributions of (a) gold and
(b) arsenic concentration values resulting from the model of the Wijs. (a) For Au: overall average
element concentration value ʾ ¼1.82 ppb, dispersion index d ¼0.433, and apparent number of

subdivisions of the environment N ¼26; (b) For As: ʾ ¼7.05 ppm, d ¼0.069, and N ¼28 (Source:

Agterberg 2007a , Fig. 13)

12.5.1 Random Cut Model

In the original model of de Wijs illustrated in Fig. 12.16 , the dispersion index d is a
constant. The lower and higher values generated at successive iterations were assigned
random spatial locations with respect to one another by introducing the random
variable B with P ( B

¼ d ) ¼ P ( B ¼ d ) ¼

1/2 ( d

>

0). A different way of formulating
this type of randomness is to introduce a new random variable D*

1+ D that
assumes either the value d or the value - d with equal probabilities. Consequently, E
( D* )

¼

0. In the variant of the model of de Wijs resulting in Figs. 12.17
and 12.18 , D* is bimodal. Its two separate peaks, which satisfy normal distributions
with standard deviations equal to 0.1, are centered about 0.4 and 1.4, respectively.
It is more realistic to replace this bimodal model by a unimodal frequency density
model centered about E ( D* )

¼ 1and E ( D ) ¼

¼ 1 (see later).