Autocorrelation and Geostatistics - Geomathematics: Theoretical Foundations, Applications and Future Developments - page 223

Fig. 6.20 Relative power spectrum for autocorrelation function of Fig. 6.19 . Decrease in slope at
higher frequency side is caused by the superimposed nugget effect (Source: Agterberg 2012 ,
Fig. 24)

6.2.7 Spectral Analysis: Pulacayo Mine Example

The normalized power spectrum corresponding to the nested design of Fig. 6.19 is:

" #

X

2

c i =ˀ f ci

Pf ðÞ ¼ 1 c i þ

2

1 þ ð f = f ci Þ

i ¼1

where f ci ¼ . A log-log plot of this spectrum is shown in Fig. 6.20 adopting the

coefficients previously used for the nested design plotted in Fig. 6.19 . The curve in
Fig. 6.20 is approximately a straight line for lower frequencies but for high
frequencies there is a marked decrease of slope reflecting the nugget effect.

a i /2 ˀ

Box 6.8: Periodograms
If n is even and the origin is chosen in the center of a series y k ( k ¼ 1, 2, , n ), it

...

þ 2 P ½ n 1

i ¼1

ˀ ik

n

ˀ ik

n

2 2

can be written as: y k ¼ a 0 þ a i cos b i sin þ a ½ n

R i cos

2 P ½ n 1
i ¼1

cos ˀ k ; its amplitude and phase representation is: y k ¼ R 0 þ

.Also:

q

a i þ

2 ˀ ik

n þ ˆ i

b i
a i

b i ; þ R ½ n cos ˀ k where R i ¼ ˆ i ¼ arctan

(continued)