Quantitative Stratigraphy, Splining and Geologic Time Scales - Geomathematics: Theoretical Foundations, Applications and Future Developments - page 322

Fig. 9.11 RASC results for Hay example of Fig. 9.6 (After Agterberg and Gradstein 1988 );
(a) ranked optimum sequence; (b) scaled optimum sequence. Clustering of events 1 to 7 in the
dendrogram (b) reflects the relatively large number of two-event inconsistencies and many
coincident events near the base of most sections used (Source: Agterberg 1990 , Fig. 6.3)
timescale (Agterberg et al. 2013 ). Accuracy and precision are both important when
geologic timescales are constructed. The use of significance tests and confidence
intervals can be illustrated by comparing different geologic time scales with one
another. As pointed out by Gradstein et al. ( 2012 ), the time scale is the tool “par
excellence” of the geological trade. Insight into its construction, strengths and
limitations greatly enhances its function and its utility. The calibration to linear
time of the succession of events recorded in the rocks of the Earth has three
components: (1) the international stratigraphic divisions and their correlation in
the global rock record; (2) methods of measuring linear time or elapsed durations
from the rock record; and (3) methods of joining the stratigraphic scale and the
linear scale to assign numerical ages (measured in millions of years ago, or Ma) to
the boundaries between the stratigraphic divisions ( cf . Gradstein et al. 2012 , p. 1).
9.2.1 Smoothing Splines
The interpolation spline curve passes through all ( n ) observed values. Along the
curve there are a number of knots where various derivatives of the spline function
are forced to be continuous. In the example of Fig. 9.12 , the knots coincide with the