Geoscience Reference
In-Depth Information
1.8
1.6
Series 3
1.4
1.2
Series 2
1
Series 1
0.8
0.6
0.4
0
50
100
150
200
250
Distance, m
Fig. 11.31 Estimated singularities for iterative process with k ¼ 1 and k ¼ 1,000. Full conver-
gence singularities ( k ¼1,000) differ significantly from results for k ¼1 (and k ¼5) in two
neighborhoods along the Tajo vein (approximately from sampling point locations 60-75 and
90-100) (Source: Agterberg 2012a , Fig. 20)
component is 0.02079. This is only about 4 % of the variance of the noise
component previously used to construct the signal of Fig. 2.10 . The new sampling
error is probably a measurement error associated with the original chemical deter-
minations for zinc and incorporates the crystal boundary effect (Sect. 2.5.1 ) .
Incorporation of the nugget effect to estimate zinc content (e.g., by using the
theoretical values on the curve previously fitted in Fig. 2.10), approximately
reproduces the observed values. This in itself is a trivial result. However, the
importance of this application is that it illustrates that the Chen algorithm provides
a new method to estimate the nugget effect.
For the Pulacayo Mine example, the c k ( x ) values in the Chen algorithm converge
to a straight line with very small dip. After 1,000 steps they are all approximately
equal to the average Zn value of 15.61 % (Fig. 12.30 ). This explains why there is an
approximate logarithmic relationship between the singularities and the original zinc
concentration values (Fig. 11.32 ).
As explained in Chap. 6 , local singularity and this new type of nugget effect are
associated with variability over very short distances. Singularities less than 1 signify
local Zn enrichment whereas singularities greater than 1 indicate depletion. Minimum
and maximum singularities are
α min ¼
0.547 and
α max ¼
1.719, respectively. These
values are only slightly different from
1.693 obtained by
means of the original local singularity approach, without application of the Chen
α min ¼
0.591 and
α max ¼
 
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