Multifractals and Local Singularity Analysis - Geomathematics: Theoretical Foundations, Applications and Future Developments - page 436

0 20 km

5620

130 30

N

5610
13000

Fig. 11.19 Gold mineral occurrences in Iskut River map sheet, northwestern British Columbia
(from B.C. Minfile Map 104B, 1989) (Source: Cheng and Agterberg 1995 , Fig. 4)

For spatial analysis, values of K ( r ) shown as circles in Fig. 11.21 were estimated
by using Ripley's edge effect correction that satisfies

X

I i r ij

^ Kr

n 2 A w 1

ij

ðÞ ¼ jj

i6 ¼ j

as discussed in Sect. 1.5.3 and also used in Sect. 10.2.2 . The values shown in
Fig. 11.21 were estimated using the program CLUST (Agterberg 1994b ) to correct
for edge effects in a study area bounded by a polygon. Figure 11.21 is a special kind
of diagram with the property that a Poisson model for complete spatial randomness
(CSR) of points would plot as a straight line through the origin that dips 45 .
Ripley's ( 1981 , p. 316) approximate 95 % confidence interval for the largest
difference between ðÞ=ˀ 0 : 5 and r (CSR null hypothesis) is shown as well in

Fig. 11.21 . Clearly, the CSR model should be rejected.
Cheng ( 1994 ) and Cheng and Agterberg ( 1995 ) have developed a theoretical
multifractal model for 2-D point processes that is equivalent to the multifractal

^ Kr