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Fig. 12.39 Relationship between estimates of mean (
x
), and variance (
s
2
) of proportion of cell
area underlain by the rock type considered, for various values of
r
(Source: Agterberg
1981
, Fig. 3)
The preceding measurements on the Quantimet 720 were amplified by analysis
of binary images obtained on the Flying Spot Scanner with results shown in
Fig.
12.42
. This two-dimensional geometrical covariance function is isotropic by
good approximation. Geometrical covariances for the east-west direction were
converted into autocorrelation coefficients as before and are close to the estimates
based on Quantimet 720 readings and the fitted signal-plus- noise model of
Fig.
12.41
. Therefore, the semi-exponential autocorrelation function with
c
¼
0.87
and
p
0.194 can be used for further computations. However, there was a discrep-
ancy in the estimate of mes
A
(1,319 km
2
on the Quantimet 720 vs 1,264 km
2
on the
Flying Spot Scanner). Because the Quantimet reading is less satisfactory in this
instance (
cf
. Agterberg
1978a
), the Flying Spot Scanner reading was adopted. It is
close to an estimate of mes
A
¼
1,262.5 km
2
originally obtained by point-counting
the original geological maps at points on a grid with 500 m spacing in the north-
south and east-west directions. The study area
T
0
of 80
¼
80 km consists of
64 (10
10 km) cells belonging to Zone 19 of the Universal Transverse Mercator
grid shown on 1:250,000 topographic maps. These 64 cells were point-counted
separately (400 counts per cell) and a histogram of the 64 values for acidic
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