Quantitative Stratigraphy, Splining and Geologic Time Scales - Geomathematics: Theoretical Foundations, Applications and Future Developments - page 306

Two sections usually produce a crude approximation but a third section can be
plotted against the combination of the first two, and new inconsistencies can be
eliminated as before. The process is repeated until all sections have been used.
The final result or “composite standard” contains extended ranges for all taxa.
Software packages in which graphic correlation has been implemented include
GraphCor (Hood 1995 ) and STRATCOR (Gradstein 1996 ). The method can be
adapted for constructing lines of correlation between sections (Shaw 1964 ). Various
modifications of Shaw's graphic correlation technique with applications in hydro-
carbon exploration and to land-based sections can be found in Mann and Lane
(eds., 1995 ).
Instead of attempting to statistically maximize the ranges of taxa in relative time
by successively adding sections, RASC estimates average positions of biostrati-
graphic events by simultaneously combining events from all sections that contain
them. Often, such average values are more precise than estimates of FADs and
LADs that are based on single event occurrences, because these can be anomalous
for various reasons including possible local reworking. Because average or “prob-
able” event positions are used, RASC-ranges generally are much shorter than
ranges obtained by graphic correlation. In later versions of RASC, approximate
LADs (and FADs) are estimated by outward projection from every estimated
average event position by adding (or subtracting) the single largest deviation for
each event. Consequently, RASC can be used for FAD and LAD estimation as well.
CASC correlations, however, remain based on average event occurrences and not
on estimates of FADs and LADs. A simple example of construction of RASC lines
of correlation followed by FAD/LAD estimation will be provided in the next
section.
In their chapter on quantitative biostratigraphy, Hammer and Harper ( 2005 )
present separate sections on five methods of quantitative biostratigraphy: (1) graphic
correlation, (2) constrained optimization, (3) ranking and scaling, (4) unitary asso-
ciations and (5) biostratigraphy by ordination. Theory underlying each method is
summarized by these authors and worked-out examples are provided. Their topic on
paleontological data analysis is accompanied by the free software package PAST
(available through www.blackwellpublishing.com/hammer ) that has been under
continuous development since 1998. It contains simplified versions of CONOP
for CONstrained OPtimization (Sadler 2004 ) and RASC, as well as a comprehen-
sive version for Unitary Associations (Guex 1991 ), a method that puts much weight
on observed co-occurrences of fossil taxa in time. For comparison of RASC and
Unitary Associations output for a practical example, see Agterberg ( 1990 ). Multi-
variate statistical methods also can make useful contributions to the spatial and
temporal analysis of biostratigraphic events. These include principal component
analysis (Hohn 1993 ), correspondence analysis (Agterberg and Gradstein 1999 ) and
archeological seriation (Brower 1985 ).
CONOP was originally developed as a biostratigraphic adaptation of simulated
annealing by Kemple et al. ( 1989 ). Like RASC, it works on all sections simulta-
neously. A single line of correlation is constructed in N -dimensional space where
N is the number of sections. Biostratigraphic positions of all events are ranked