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fossil taxa. Biostratigraphic events commonly used for this purpose are the
observed first and last occurrence (abbreviated to FO and LO) of each fossil
taxon considered. Co-occurrences of fossil taxa in the biostratigraphic record can
be used as well. The RASC method for ranking and scaling of the FOs and LOs
(also known as “rascing”) was first published 30 years ago (Agterberg and Nel
1982a
,
b
). This method has become well-established. In paleontological textbooks
by Benton and Harper (
2009
), Foote and Miller (
2007
) and Hammer and Harper
(
2005
) it is listed as one of several methods described to construct regional
biostratigraphic zonations. The main difference between RASC and the other
methods is that it estimates the relative positions of average fossil events instead
of maximal time-stratigraphic ranges, although maximal ranges also can be
obtained by RASC, as will be seen in the next two sections. Zhou (
2008
) has
reviewed RASC/CASC in the context of quantitative stratigraphy and presents
interesting novel applications.
Quantitative biostratigraphy methods are statistical because of the large uncer-
tainties commonly associated with the positioning of biostratigraphic events.
Land-based biostratigraphic sections are more continuous and normally more
complete than km-deep exploratory wells drilled in sedimentary basins that usually
are sampled by collecting pieces of drill-core at discrete, regular intervals. RASC
can be applied to both kinds of data. It is based on a statistical model in which
averages are computed from samples of biostratigraphic events supposedly drawn
at random from an infinitely large population. Here the term “sample” is used for a
set of observations such as biostratigraphic events. Computationally, RASC is very
fast and can deal with up to 1,000 biostratigraphic events observed in dozens of
wells or land-based sections.
An early statistical method in quantitative stratigraphy was developed by Shaw
(
1964
) for use in hydrocarbon exploration. In this topic, Shaw illustrates his
technique of “graphic correlation” on first and last occurrences of trilobites in the
Cambrian Riley Formation of Texas for which range charts had been published by
Palmer (
1954
). RASC/CASC results for this dataset will be briefly discussed in this
section for method comparison. Shaw's method consists of constructing a “line of
correlation” on a scatter plot showing the locations of LOs and FOs of taxa in two
sections. If quality of information is better in one section, its distance scale is made
horizontal. LOs stratigraphically below and FOs above the line of correlation are
moved horizontally or vertically toward the line of correlation in such a way that
the ranges of the taxa become longer. The reason for this procedure is that it can be
assumed that observed highest occurrences of fossil taxa generally occur below
truly highest occurrences and the opposite rule applies to lowest occurrences.
Consequently, if the range of a taxon is observed to be longer in one section than
in the other, the longer observed range is accepted as the better approximation.
The objective is to find approximate locations of what are truly the First Appear-
ance Datum (or FAD) and Last Appearance Datum (LAD) for each of the taxa
considered. True FADs and LADs probably remain unknown but, by combining
FOs and LOs from many stratigraphic sections, approximate FADs and LADs
are obtained and the intervals between them can be plotted on a range chart.
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