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Fig. 7.25 Trend surface analysis of occurrence of massive sulphide deposits in cells measuring
10 km on a side, Island of Newfoundland. Calculated values for cells were subjected to the
transformations 9*(Value
MIN) where MIN and MAX represent smallest and
largest calculated value. Transformed values were contoured (M
MIN)/(MAX
8.5); (a) Contours of quadratic
trend surface; MIN ¼ 0.0733, MAX ¼ 0.0741; (b) Contours of logistic quadratic trend surface.
Solution obtained after 13 iterations for level of convergence equal to 0.001 ( cf . Chung 1978 );
MIN ¼ 0.000; MAX ¼ 0.2188 (Source: Agterberg 1984 , Fig. 11)
¼
can be used to estimate probabilities. However, in the example of Fig. 7.25 , the
pattern for the logistic model is obviously more meaningful than the pattern for the
corresponding linear model, if the contours are to be interpreted as indicative of the
chances that a cell contains one or more massive sulphide deposits.
The main reason that that S ( u , v )ismoresuitablethan T ( u , v )inthistypeof
application is related to the fact that T ( u , v ) in Fig. 7.25 (left side) is an elliptic
paraboloid. It means that any vertical intersection of it is a parabola without inflection
points at either side of its maximum value. The many 0 values for empty cells then
result in small positive values for area where there are known deposits and small
negative values for areas without known deposits. The pattern on the right side of
Fig. 7.25 , on the other hand, is positive everywhere, with small positive values in the
areas without known deposits. This is because the logistic trend surface is more
flexible than the corresponding ordinary polynomial trend surface.
7.4 Harmonic Trend Surface Analysis
Many features in the Earth's crust tend to be periodic in that they repeat themselves
at more or less the same intervals. Examples are anticlines and synclines and fault
systems. In these situations harmonic trend analysis may produce better results than
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