Geoscience Reference
In-Depth Information
6.2.3 Other Applications to Ore Deposits
The question can be asked of how representative the relatively small, historical data set
of 118 Pulacayo zinc values is of ore deposits in general. Matheron (
1962
)usedseveral
other mineral deposits exemplifying his extension of the model of the Wijs that
resulted in linear variograms. His primary examples were from the Mounana uranium
deposit, Gabon, and the Mehengui bauxite deposit, Guyana. These two deposits occur
relatively close to the Earth's surface and were explored by means of subvertical
boreholes drilled on regular grids. His other examples included the Bou-Kiama,
Montbelleux, Laouni, Mpassa, and Brugeaud orebodies. In all these situations, the
model of de Wijs proved to be satisfactory. Some of these examples and others also
were discussed in geostatistical textbooks including David (
1977
) and Journel and
Huijbregts (
1978
). Later, however, this type of modeling became de-emphasized,
probably because the model of deWijs does not allow for sills that occur generally and
problems associated with working with logarithmically transformed concentration
values instead of original data. However, as pointed out by Matheron (
1974
), lognor-
mality is an issue that must be considered generally. Multifractal modeling (
e.g
., use of
multiplicative cascades, see Chap.
12
) confirms the validity of several aspects of
Matheron's original approach. The multifractal autocorrelation function of Cheng and
Agterberg (
1996
) has a sill as well as a nugget effect with exceptionally strong
Agterberg (
1965
) estimated autocorrelation coefficients for the original deWijs zinc
data and obtained similar results for titanium data from adjoining borehole samples in a
magnetite deposit, Los Angeles County, California, originally described by Benson
et al. (
1962
). Figure
6.16a
(modified from Agterberg
1974
, Fig. 56) shows average
autocorrelation coefficients and best-fitting negative exponential function derived from
logarithmically transformed element concentration values for copper from the
Whalesback copper deposit, Newfoundland, and Fig.
6.16b, c
are for two relatively
long series of gold assays from the Orange Free State Mine, Witwatersrand goldfields,
South Africa (data from Krige et al.
1969
). In these three examples, the negative
exponential function with significant noise component provides a good fit. In each
situation, there is finite variance (existence of sill) and a de Wijsian variogram can only
be fitted for the copper and gold examples over relatively short distances (over
approximately the first six values from the origin in the three examples of Fig.
6.16
).
A typical sample of 1,090 copper concentration values from the Whalesback
deposit (
cf
. Agterberg
1974
, p. 301) had mean value of 1.57 % Cu and logarithmic
variance of 1.21. Converting these values back into copper concentration values
2
43.84. The positive
skewness of the copper concentration is so large that it is not possible to obtain
reliable statistics from original data without use of a more efficient estimation
method involving logarithmic transformation (Aitchison and Brown
1957
; Sichel
1966
). The logarithmic variance of the gold values in the other example is approxi-
mately 1.03. Krige et al. (1960) did not report the corresponding mean value but the
following statistics can be derived from the relatively small data set of 61 gold
values in Table
2.6
:
(
X
)
¼
2
(
X
)
2
μ
(
X
)
¼
906.6;
˃
¼
1,470,410;
μ
¼
6.144; and
˃
¼
0.929.
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