Quantitative Stratigraphy, Splining and Geologic Time Scales - Geomathematics: Theoretical Foundations, Applications and Future Developments - page 332

distributions for all possible pairs of events, which are subject to many further
occurrences of missing data.

9.3.1 Sample Size Considerations

Because of the prevalence of missing data, an important input parameter in any
RASC run is the Minimum Number of Sections (MNS) in which an event should
occur (in RASCW program documentation, MNS is called k c ). From a statistical
point of view, RASC results rapidly improve when MNS is increased because of
greater precision of the relative frequencies ( p ij ). The downside of large MNS is that
low-frequency but biostratigraphically important events could become excluded from
the RASC standard zonation. This problem is circumvented as follows: Commonly,
the user chooses a value of MNS together with up to 20 “unique events” that occur in
fewer than MNS wells. Unique events are biostratigraphically significant (e.g. they
may be for index fossils) although they occur rarely, perhaps in a single well. They
are added to the ranked optimum sequence and also incorporated in the RASC
zonation after scaling. Figure 9.18 shows an output example of scaling for dataset
(A) with MNS 6 and ten unique events. The method by which RASC distances

involving unique events are estimated is shown in Fig. 9.19 .
Figure 9.18 is an example of a RASC scaling dendrogram in which the estimated
interevent distances between successive events in the scaled optimum sequence are
plotted to the left in the horizontal direction and connected by lines dropped in the
stratigraphically downward direction. In the original RASC dictionary for any
dataset, all events have a name and an event number (last two columns of
Fig. 9.18 ). Names of unique events are preceded by double asterisks. The North
Sea (NS) log events with single asterisks in Fig. 9.18 are marker events that
received more weight during the scaling because they are without biostratigraphic
uncertainty. The method by which RASC distances involving marker horizons are
estimated is graphically illustrated in Fig. 9.20 . Successive clusters in the dendro-
gram represent RASC zones consisting of events that are relatively close together
along the RASC scale. Further biostratigraphic interpretation of RASC clusters will
be given in the next section for another practical example.

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9.3.2 Cenozoic Microfossils Example

Table 9.13 shows ranked biostratigraphic events observed in part of a single
exploratory North Sea well taken from dataset (A). Sequence numbers in columns
1 and 2 are based on depth (column 3) in the well and position of event (columns
4 and 5) in the ranked optimum sequence for MNS 6. Figure 9.21 is a scattergram

showing relative sample position versus ranked optimum sequence number for all
events observed in this well together with a best-fitting quadratic PPL curve. Use of

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