Geoscience Reference
In-Depth Information
stringers, and occur in well-defined narrow veins with maximum width of 1.2 m.
The deposit coincides with a shear zone. It is about 400 m long at the surface.
Average width of the central copper zone which averages more than 1 % copper is
approximately 20 m, and vertical depth is 270 m. The copper zone is enveloped by a
rather strongly altered chlorite zone with 0.35 % Cu on the average. The plate-
shaped mineralized zone dips about 70
south-southwest. Before mining (by the
British Newfoundland Exploration Company) commenced in 1965, ore reserves
were estimated at four million short tons averaging 1.48 % copper.
Trend surface analysis (Agterberg
1974
) was applied to copper concentration
values from the 425 ft. level that occurs 425 ft. below the surface. The core for
underground drill-holes, which were 50 ft. apart, was divided into pieces of 5 ft. length
and assay values (percentages copper) were determined from these. About 15 vol.%of
the rocks in the deposit consist of dikes that do not contain copper. This yields zero
assay values which were omitted from the data to be used for statistical analysis and
trends will be projected across the dikes. Therefore, if average grade values are to be
determined for larger blocks of ore, these values, after calculation, should be reduced
by 15 % for dilution caused by barren dikes. Of course, more precise corrections can
be made in places where the precise location of dikes is known.
Because trend surfaces are imprecise at the edges of clusters of observation
points, overlapping sets of six drill-holes, or cross-cuts which has been sampled in
the same manner, were used and quadratic and cubic trend surfaces
S
(
u
,
v
) were
fitted to logarithmically transformed copper values. The fitted values were
converted back to ordinary copper values by using the transformation
T
(
u
,
v
)
ΒΌ
exp[
S
(
u
,
v
)+
s
2
/2] where
s
2
is the residual variance for the
S
(
u
,
v
) surfaces. The
central part for each converted surface
T
(
u
,
v
) for a 150 ft. wide zone situated
between the second and fifth hole in each situation, is shown in the mosaics of
Figs.
7.8
and
7.9
. This transformation is equivalent to the one applied to lognor-
are lognormally distributed with mean
T
(
u
,
v
) and logarithmic variance
s
2
.
Autocorrelation of residuals affects the results of trend surface analysis. This
topic will be discussed in more detail in the next section. Here it can be assumed
that the autocorrelation function of the residuals is approximately as shown in
Fig.
6.15a
which is an average correlogram based on 24 separate correlograms
for series of logarithmically transformed copper values (8 ft. apart) along drifts at
various levels of the mine that were approximately within the mineralized zone.
Watson (
1971
) has shown that if the residuals satisfy a weakly stationary process
with an autocorrelation function that is independent of geographic location, then the
best fitting trend surfaces are unbiased (
cf
. Cressie
1991
, p. 164). However, analysis
of variance to help decide on the optimum degree of a trend surface then are not
applicable because a set of
n
autocorrelated data does not contain the same amount
of information as
n
uncorrelated (iid) data. Some authors including Matalas (
1963
)
have developed methods to determine
n
0
representing a hypothetical sample of
uncorrelated (iid) values containing the same amount of information as
n
autocorrelated data (see Box
7.1
). It is usually assumed that the underlying
autocorrelation function is exponential. The topic is fraught with difficulties and,
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