Selected Topics for Further Research - Geomathematics: Theoretical Foundations, Applications and Future Developments - page 503

Log 10 M

1.2

1

0.8

0.6

0.4

0.2

Log 10 Δx

0.5 1 1.5 2

Fig. 12.34 Log-Log plot of first order structure function for Pulacayo zinc values for q ¼ 0.25,
0.5, , 3. Fourth line from top ( q ¼ 2) is variogram; first point on fourth line from bottom ( q ¼ 1)

represents de Wijs dispersion index d (Source: Lovejoy and Schertzer 2007 , Fig. 26a)

...

x (q)

0.25

0.2

0.15

0.1

0.05

q

0.5 1 1.5 2 2.5 3

Fig. 12.35 Slopes ʾ ( q ). Slope and value near q ¼ 1 yield H ¼ 0.090, C 1 ¼ 0.018, because H ¼ ʾ

(1) and C 1 ¼ H ' (1); H represents deviation from conservation of pure multiplicative process

for which H ¼ 0 (Source: Lovejoy and Schertzer 2007 , Fig. 26b)

ʾ

q ( ¼ 0.25, 0.5, ... , 3 for the 118 zinc values). The resulting pattern for q ¼ 2

represents the variogram and the first point on the pattern for q 0 is the de Wijs

index of dispersion d . Straight lines are fitted to all patterns and a new diagram is
constructed with the slopes of the lines (

¼

ʾ q ) plotted against q . Slope and value of this

new line near q ¼ 1 yielded H ¼ 0.090 and C 1 ¼ 0.02 for the Pulacayo orebody

because H ¼ ʾ 1 and C 1 ¼ H ʾ ' 1 where ʾ ' 1 is the first derivative of ʾ q with respect

to q (Fig. 12.35 ).