a) Introduction
Representative samples from each of the major inliers in
the vicinity of Moffat have been grouped together to form the
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study, where more than one sample has been analysed at a given
locality, the results have been combined and a mean value for each
element computed for that locality. The discussion of the areal
variation for most of the elements is based on the results at 32
regional points but that for the trace elements Rb, Sr, Y and Zr,
and also C is based on only 30 and 27 points respectively. A summary
of the univariate statistics for the elemental composition of the
grid samples is given in Table 3-4.
b) Application of trend surface analysis
Many authors have pointed to the dangers of plotting
areally distributed data using contours determined by human
judgement, e.g. Whitten (1963). In this study an objective
contouring method is used, which is a modification of the genex*al
trend surface analytical technique. This involves the iterative
modification of a polynomial surface and is known as iterative
trend surface analysis (Cole 1969). The merits of this technique
will be discussed in more detail in Appendix C»
Linear, quadratic and cubic surfaces have been calculated
for each element. In every case it was found that the cubic surface
explained more ’sums of squares’. This was taken to indicate that
the cubic surfaces approximated the data distribution most closely.
Iterative surfaces have also been computed. These are a result of
10 iterations over the chosen cubic surface.
c) The cubic surfaces
elements are given in Table 3-5, The surface computed for Cu
accounts for 78 per cent of the variance whereas those quoted for
Si, Fe and Y account for more than 40 per cent and those computed
for Mn, Na, Zn, Sr and Zr account for more than 30 per cent. The
cubic surfaces which have been computed for the remaining elements
only account for less than 30 per cent of the variance and are
therefore not considered to be significant.
The boundary between significance and non-significance has
been arbitrarily fixed at the 30 per cent degree-of-fit level. This
was necessary because the measure of reliability of the fitted
surface is based on a sums of squares test. This test does not
define confidence limits. It has been demonstrated that if for a
100 points, a sums of squares test produces values that fall below
6.0, 12.0 and 16.2 per cent for the linear, quadratic and cubic
surfaces respectively, the distribution of data points is not
significantly different from random at the 0.05 level (Howarth 1967),
Critical sums of squares values have not as yet been proposed for
surfaces defined on less than 100 points but intuition suggests
that they must be higher than those quoted for 100 points.
The cubic surfaces for each of the elements are illustrated
in Figs 30-47. It is interesting that all eight significant
surfaces are centred around the Hartfell and Carrifran Burn exposures.
All surfaces, except for those for Si and Na which take the form of
elongate domes, conform to a general pattern of elongate basins. The
basins computed for Cu and Mn are aligned in a north-west to south
east direction and as such they are orientated across the regional
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Y are orientated parallel to the Caledonian strike. The structural
dome for Si follows the same NW-SE trend as displayed by both Cu
and Mn, The Na surface is unique in that it is orientated east to
west.
d) The iterative surfaces
The cubic surfaces are highly smoothed expressions of the
main geographic trend in the data. The iterative surface for an
element begins with the chosen cubic surface and progressively
modifies it until after a specified number of iterations, ten in
this work, it has improved the fit of the data but has lost much
of the original form (Table 3-5). It is therefore not possible to
generalise as much for the iterative map patterns as it was for the
cubic surfaces.
It was noted above that the peak of the dome or the lowest
part of the basin was located in the same general area over most of
the cubic surfaces. This is to some extent still true for the
iterative surfaces, Figs. 30 to 47, but the accurate position of the
’lows’ and ’highs’ is more difficult to define because of small-
scale fluctuations in the computed trends.
e) Conclusion
The irregular nature of the geographic orientations of the
trend surfaces is taken to imply that the distribution of the
elements is not governed by areal processes. In this study no
attempt has been made, nor would it have been possible, to sample a
vertical thickness of sediments between samples is less than 100 m
there is a large time difference. This is attributable to an
exceptionally slow overall rate of deposition. The points of
inflection in the surfaces coincide with those localities which are
predominantly composed of Ordovician sediments. Perhaps therefore,
the trend-surface maps are depicting stratigraphic time variations
in the chemical abundances.