2-D and 3-D Trend Analysis - Geomathematics: Theoretical Foundations, Applications and Future Developments - page 260

Fig. 7.20 Predicted sulphur variation (in percent) for (2,000 ft. 2,000 ft.) cells (Model 1),

Harbour seam, Lingan Mine area. Top diagram : average values in worked areas and predicted
values in target areas. Bottom diagram : standard deviations on predicted values in target areas.
Contours at regular 0.25 % intervals in A are used for pattern enhancement (Source: Agterberg and
Chung 1973 , Fig. 2)

Mine site by using the compound water cyclone (Walsh et al. 1969 ). By the end of
the last century, nearly all coal mining had been discontinued on Cape Breton
Island. This included closure of the Lingan Mine.
Two statistical methods were used for offshore prediction (Agterberg and Chung
1973 ). Results for (2,000 ft. 2,000 ft.) blocks in the Harbour Seam are shown in

Figs. 7.20 and 7.21 . Model 1 is based on kriging and Model 2 on universal kriging.
Details of the underlying mathematics and the computer algorithms used are given
in Agterberg and Chung ( 1973 ). Kriging (Model 1) was not based on the arithmetic
mean but on the Best Linear Unbiased Estimator (BLUE) which is efficient and,
theoretically, gives slightly better results than the arithmetic mean that is unbiased
only. It involves using a Lagrangian multiplier. The autocorrelation function used
for Fig. 7.20 is shown in Fig. 7.22 . The BLUE for the universal kriging (Model 2)
application could not be estimated but was approximated by an asymptotically
efficient estimator. Use was made of exponential trends similar to those used in