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Fig. 11.6 Construction of multifractal spectrum of gold in Mitchell-Sulphurets mineral district
(see Fig.
10.4
)
. (a)
x(f)
represent s sum of gold values greater than 100 ppb averaged for cell s and
raised to the power
q
; cell edge
i n km; log base 10; lowest sets of solid triangles and squares are
E
for
q
equal to
(
q
) of best-fitting straight lines including
those shown in Fig.
1.6a
as function of
q
.(c and d) Multifractal spectra are for four different cut-off
values. It is noted that, contrary to a multifractal, a fractal is characterized by a single dimension
that would have a spectrum consisting of a spike (Source: Agterberg
1995
, Fig. 4)
7.45 and
9.15, respectively. (b) Slopes
˄
(
q
) were connected by straight-line segments
(Fig.
11.7b
) which, together, form an approximately differentiable curve. Values
of the singularity
Successive estimates of
˄
(Fig.
11.7c
) were estimated by applying the central difference
technique to successive sets of three consecutive values
α
˄
(
q
). The multifractal
spectrum
f
(
) (Fig.
11.7d
) was derived from the values shown in Fig.
11.7b, c
.
The results of Fig.
11.7
show that the Pulacayo zinc concentration values are
multifractal instead of monofractal because an ordinary fractal would have resulted
in a single straight line in Fig.
11.7b
, a horizontal line in Fig.
11.7c
, and a vertical
spike in Fig.
11.7d
. The straight lines in Fig.
11.7a
then would have had interrelated
slopes
α
˄
(
q
)/(
q
1)
¼
˄
(
p
)/(
p
1) for any pair of values
q
6
¼
p
in a monofractal
model; for example,
˄
(12)
¼
˄
(
10)
10 when
q
¼
12 and
p
¼
10. Linear
regression for
these values gave the estimates
˄
(12)
¼
9.8709
0.2192 and
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