Fractals - Geomathematics: Theoretical Foundations, Applications and Future Developments - page 374

Au>=1 Au>=10 Au>=20 Au>=40 Cu>=10 Cu>=20 Cu>=30 Cu>=40

Au>=60 Au>=80 Au>=100 Au>=200

Cu>=50 Cu>=60 Cu>=70 Cu>=80

Au>=300 Au>=500 Au>=700 Au>=1000

Cu>=400 Cu>=600 Cu>=800 Cu>=1000

Fig. 10.5 Successive binary patterns for separate contours of Au and Cu, Mitchell-Sulphurets
area. (Source: Cheng et al. 1994 , Fig. 5)

at the boundary or outside the moving window, and 1 for samples located at the
center) and maximum of ten samples per window. (If more than ten samples occur
within the window for a given location, only the ten nearest points were used to
evaluate the surface at that location.)
Suppose A(

ˁ

) denotes the area with concentration values greater than the

ˁ ˁ ˁ ʽ

contour value represents

the threshold, the following empirical model generally provides a good fit to the
data for different elements in the study area:

. This implies that A( ) is a decreasing function of .If

Þ/ˁ ʱ 1 Þ/ˁ ʱ 2

A ð ˁ ʽ A ð ˁ > ʽ

;

ʱ 2 are different exponents.
Figure 10.6 shows log-log plots satisfying the preceding two power-law relations
for Au, Cu, As, Ag, Sb and Pb. All areas were computed from separate contour
maps such as those shown in Fig. 10.5 for Au and Cu. Pairs of estimated exponents
and corresponding optimum thresholds for these 6 elements and 22 other elements
or oxides were presented by Cheng ( 1994 , Table 1). These thresholds delineate
anomalous areas. Comparison of the areas above and below the threshold of
200 ppb Au on the contour map (Fig. 10.5 ) with the geological map shows
significant spatial correlation between the areas with Au concentration above
200 ppb and Au-associated alteration zones (Cheng et al. 1994 , Fig. 2). The same
type of correlation with alteration zones applies to Cu (400 ppm threshold; see
Fig. 10.5 ). Note, however, that the Au anomalies are more prominent than the Cu
anomalies in the southeastern part of the area. It may be concluded that the log-log
plots for the element concentration-area relation provide an excellent method for
separating anomalies from background in the Mitchell- Sulphurets area. This
empirical result will be explained by fractal modeling in Sect. 10.3.1 .
Cheng ( 1994 ) also subjected element concentration maps as shown for Au and
Cu in Fig. 10.5 to perimeter-area analysis as follows. Theoretically, for a group

/ ʱ 1 and

where denotes proportionality;