Selected Topics for Further Research - Geomathematics: Theoretical Foundations, Applications and Future Developments - page 484

Fig. 12.13 Straight line
fitted to part of lognormal
Q-Q plot for 64 average
gold concentration values
for cells (Source: Agterberg
2007a , Fig. 10)

The square arrays of Au and As cell average concentration values were subjected to
multifractal analysis using themethod of moments. Figure 12.14 shows mass-partition
function results for gold. For relatively large values of q there is approximate linear
relationship between the mass exponent

( q )and q for Au (Fig. 12.15 ). The slopes of
the best-fitting straight lines are 0.962 for Au and 1.808 for As, respectively
(Table 11.1). These slopes were converted into dispersion index estimates of
d

˄

0.069 for As. Straight line fitting to lognormal Q - Q
plots for the 64 cell average concentration values gave logarithmic variances of
1.292 for Au, and 0.029 for As, respectively. Using the original variance equation of
de Wijs then yields estimates of n equal to 6.0 for Au, and 5.7 for As, respectively.
Both estimates are nearly equal to 6 representing their expected value for the model
of de Wijs because 2 6

¼

0.433 for Au, and d

¼

64. This agreement between results indicates that the
model of de Wijs is approximately satisfied on a regional scale for both gold and
arsenic.
Logarithmic variances estimated from the 379 original till samples were 2.369
for Au and 0.362 for As, respectively. Using the variance equation of de Wijs, this
yields estimates of N equal to 26.1 for Au, and 27.5 for As, respectively. These
apparent maximum numbers of subdivisions of the environment would correspond
to square cells measuring approximately 75 m, and 40 m on a side, respectively.
Clearly, these cells are much larger than the very small areas where the till was
actually sampled for the purpose of chemical analysis. It shows that, for both Au
and As, the regional model of de Wijs does not apply at the local sampling scale.

¼