Modal variation of quartz, color index, (potash feldspar/plagioclase), and total feldspar within a 25 square mile area of the ‘older granite’ of Donegal was analyzed on the basia of 71 specimens. Non‐orthogonal polynomial analysis was used to compute linear and quadratic trend surfaces and deviations for each variable. The IBM 650 was used for all computations.
Each variable behaved differently. Single modes gave excellent trend surfaces for color index, whereas averaging data within each square mile sometimes masked important residuals. Realistic trend surfaces for quartz or total feldspar were only derived from averaged data. With averaged data the four linear trend surfaces have almost parallel strikes, and such uniform regional trends have significance in the interpretation of geological gradients in relation to the petrogenesis of the granite.
Some deviations have been linked to observed geologic factors. Other deviations are consistent for all variables. These deviations reflect ghost stratigraphy; the latter group indicate ghost stratigraphy previously unsuspected in this area which is harmonious with the well‐known regional picture.
The advantages of using orthogonal rather than nonorthogonal polynomials for trend-surface analysis are discussed briefly. A method for calculating orthogonal polynomial trend surfaces of any degree on the basis of irregularly spaced data is described. The method is illustrated with subsurface data for the elevation on top of the Devonian Dundee Limestone, Michigan.
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