Selected Topics for Further Research - Geomathematics: Theoretical Foundations, Applications and Future Developments - page 481

Table 12.2 Gold and arsenic in till samples, Southern Saskatchewan: results of graphical
estimation of parameters for the model of de Wijs

Gold Arsenic

Straightline on Q-Q plot: intercept 0.8006 5.3035

Ditto, slope 0.4222 2.7611

Mean 2.48 7.29

Logarithmic variance 5.61 0.131

Cell data Q-Q plot: intercept 0.2121 12.399

Ditto, slope 0.8784 6.0591

Logarithmic variance of cell averages 1.296 0.0272

Straightline on Tau vs q plot: intercept 1.4232

Ditto, Slope 2.7611 1.8075
Dispersion index (Eq. 3) 0.433 0.069
Apparent number of subdivisions - till samples 26.12 27.5
Number of subdivisions, cell data 6.03 5.71
Gold concentration values in ppb; As concentration values in ppm (Source: Agterberg 2007a ,Table1)

5.3035

be mixtures of separate populations, and the exact nature of these mixtures can be
left undetermined.
If the model of de Wijs is satisfied, the mass exponents

( q ) become linearly
related to q when q is large. The parameter d then can be estimated from the slope of
the resulting straight line. Together with the estimate of logarithmic variance
provided by the original variance equation of de Wijs, this yields an estimate of
apparent maximum number of subdivisions N .

˄

12.4.2 Au and As in South Saskatchewan till Example

The approach is illustrated by application to gold and arsenic content of till samples
obtained during systematic ultra-low density (1 site per 800 km 2 ) geochemical
reconnaissance, Southern Saskatchewan. There are 389 observed gold concentra-
tion values ranging from below detection limit to 77 ppb. All Au values below
detection limit ( 2 ppb) were set equal to 1 ppb. The arithmetic mean gold

concentration value is 2.5 ppb. In total, only about one third of 389 observed values
exceed this average. Overall average gold value of 2.5 ppb slightly overestimates
true mean gold concentration value because most gold values below 2 ppb are
probably less than 1 ppb.
For arsenic, all observed values are above the detection limit with overall mean
of 7.9 ppm and ranging from about 2-44 ppm. The main difference between
frequency distributions of Au and As is that gold has positively skewed distribution
whereas arsenic shows approximately symmetric, normal distribution. Most dia-
grams in this section are for Au only. Similar results (not shown as diagrams) were
obtained for As. Estimates for both Au and As are listed in Table 12.2 .
The method used here resembles the one used by Brinck ( 1974 ). Lognormal Q-Q
plots for Au and As are shown in Fig. 12.10 . The first step in Brinck's approach

¼