Geoscience Reference
In-Depth Information
Table 9.4 Statistics derived
from vertical deviations
between the six events and the
section PPLs in Fig.
9.2a-c
Taxon
s
(1)
s
(2)
Min
Max
Range
A
0.61
1.19
0.05
0.56
0.61
B
2.18
1.71
0.59
0.80
1.39
C
1.82
1.66
0.08
0.38
0.46
Source: Agterberg et al. (
2013
, Table 4)
Each standard deviation is computed from three observations
only;
s
(1) and
s
(2) are for FOs and LOs, respectively. Standard
deviations of this type are used in RASC variance analysis and for
estimation of error bars in CASC. Max and Min are for largest LO
and lowest FO. The RASC “range” (
Min) is comparable
to ranges for taxa derived by graphic correlation methods
¼
Max
depth scale that is different for each section. PPL values are later used in CASC for
correlation of average event occurrences between sections.
The residuals, which are the differences between observed event locations and
corresponding PPL values in Fig.
9.2a-c
, can provide useful information as illus-
trated in Table
9.4
for the artificial example. The rows in this table are for the three
taxa;
s
(1) and
s
(2) are standard deviations for FOs and LOs estimated from the three
residuals for each taxon. The next two columns in Table
9.4
represent lowest FO
and highest LO of each taxon. The “range” in the last column is the difference
between maximum LO and minimum FO. It has its largest value for Taxon B,
mainly because, according to the optimum sequence, B is out of place with respect
to A and C in Section 2. Table
9.4
illustrates how RASC, like other methods of
quantitative biostratigraphy, can be used for FAD/LAD approximation.
9.1.3 Scaling
The optimum sequence obtained by ranking (or “ranked optimum sequence”) often
can be refined by “scaling”, which consists of estimating intervals between succes-
sive optimum sequence events along a relative time scale. The ranked optimum
sequence serves as input for scaling. As the first step in scaling, each frequency
f
ij
is
converted into a relative frequency
p
ij
¼
f
ij
/
n
ij
where
n
ij
is sample size. Next, the
values of
p
ij
are converted into intervals (interevent distances) along a relative time
scale. Unlike ranking, scaling is not subject to problems of cyclical inconsistencies
involving three or more events. The final order of events after scaling usually differs
slightly from the order of events in the ranked optimum sequence.
Basically, scaling was introduced to circumvent the following problem associ-
ated with ranking. Events in a ranked optimum sequence can be regarded as
equidistant along a linear scale such as the horizontal scales in Fig.
9.2a-c
.
However, along a relative time scale, the events generally should not be equidistant.
For example, if two events are coeval on the average, their interevent distance along
a relative time scale should be zero. Events that occurred at approximately the same
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