2-D and 3-D Trend Analysis - Geomathematics: Theoretical Foundations, Applications and Future Developments - page 261

Fig. 7.21 Same as Fig. 7.20 using Model 2. It is assumed that the trend is according to pattern
shown in Fig. 7.23 and that residuals from this trend are autocorrelated according to pattern shown
in Fig. 7.22 (Source: Agterberg and Chung 1973 , Fig. 3)
Sect. 7.1.3 . The quadratic exponential trend surface for the Harbour Seam is shown
in Fig. 7.23 . Next the kriging method of Model 1 was applied to the residuals to
complete the computations required for Model 2. For the autocorrelation function
for residuals from the surface of Fig. 7.23 , see Agterberg and Chung ( 1973 ).
The basic concepts behind the two models are illustrated by a hypothetical
example in Fig. 7.24 . Extrapolations by Model 1 are based on known data at points
in the immediate vicinity. Every predicted value (crosses) in Fig. 7.20 is based on
all known values (dots) within a circle of 9,000 ft. radius, unless there occur ten or
more values within a smaller circle of 7,000 ft. radius; then, the smaller circle was
used. The mean of the known data is used for prediction in the unknown area. This
is called the (kriging) mean in Fig. 7.24 . Separate values for blocks anywhere in the
unknown area are estimated next. Uncertainty increases with distance from the
worked area, and the predicted values converge to the kriging mean which provides
the best estimate when the distance is great. In the more immediate area, close to the
shoreline, the estimates are more precise than this mean value.
A basic assumption for Model 1 is that the mean value remains constant. It is
known, however, that average sulphur content of Cape Breton coal, even for a