Scaling and the Palaeogeographical Distribution of Stratigraphic Events
265
2
Correlation and Standard-Error Calculation (CASC)
In CASC, which is a companion program of RASC, all individual sections are
compared to the standard. This is accomplished by fitting a curve (line of correlation) in an XY plot where X represents the composite standard value (sum of
interevent distances measured from origin set at first event) and Y the relative
stratigraphic order value of an event in the section. Deviations between the observed position of an event and its average position in the standard (its probable
location on the line of correlation) can be random or indicative of palaeoecological trends. Events with relatively small standard deviations and widespread geographic distribution are useful as stratigraphic time markers. Events with large
standard deviations are either poor markers because of significant biostratigraphic uncertainty, or indicate time-transgressive behavior in which the event
becomes systematically younger or older according to a geographic trend.
The probable locations of events can be used to correlate sections with one
another. Good markers yield good correlations with few if any cross-overs of
lines connecting either their observed or their estimated positions in the wells.
This type of uncertainty can be expressed by means of error bars. The standard
deviation of the probable value of an event on the line of correlation can be estimated and projected along the depth scale (in meters). Probable values and observed values have different standard deviations. Both can be multiplied by 2.0
to obtain approximate 95% confidence intervals.
For each section an YZ plot is obtained where Y, as before, represents relative
stratigraphic order of an event and Z its depth (in meters). In general, there is
relatively little scatter in this plot and an interpolation spline curve (line of observation) can be used for the relationship between Y and Z. Contrary to the line
of correlation which normally is fitted to scattered points falling within a relatively broad zone, and is often approximately straight or only moderately
curved, the line of observation can be constructed through all observed points.
It tends to be wiggly and reflects local facies and sedimentation rates. An error
bar initially estimated along the Y-axis can be transformed into a generally
asymmetrical error bar along the depth axis of a section. The resulting error bars
have different widths, not only for different events in the same section, but also
for the same event in different sections. They provide 95% confidence intervals
for the observed and the estimated average locations of the events in the sections.
Figure 2 provides an example of CASC using three events in four wells from
the data set used to obtain Fig. 1. In the top part, the observed positions of two
events (205: last occurrence of Heterosphaeridium difficile, and 212: last common occurrence of Hedbergella delrioensis) are connected by lines, and accompanied by their estimated 95% confidence intervals which have been constructed around the probable positions for these events. In Well No.3, the observed
position of event 205 is slightly above the upper limit of its 95% confidence interval. This does not necessarily mean that event 205 is anomalous in this well,
265
2
Correlation and Standard-Error Calculation (CASC)
In CASC, which is a companion program of RASC, all individual sections are
compared to the standard. This is accomplished by fitting a curve (line of correlation) in an XY plot where X represents the composite standard value (sum of
interevent distances measured from origin set at first event) and Y the relative
stratigraphic order value of an event in the section. Deviations between the observed position of an event and its average position in the standard (its probable
location on the line of correlation) can be random or indicative of palaeoecological trends. Events with relatively small standard deviations and widespread geographic distribution are useful as stratigraphic time markers. Events with large
standard deviations are either poor markers because of significant biostratigraphic uncertainty, or indicate time-transgressive behavior in which the event
becomes systematically younger or older according to a geographic trend.
The probable locations of events can be used to correlate sections with one
another. Good markers yield good correlations with few if any cross-overs of
lines connecting either their observed or their estimated positions in the wells.
This type of uncertainty can be expressed by means of error bars. The standard
deviation of the probable value of an event on the line of correlation can be estimated and projected along the depth scale (in meters). Probable values and observed values have different standard deviations. Both can be multiplied by 2.0
to obtain approximate 95% confidence intervals.
For each section an YZ plot is obtained where Y, as before, represents relative
stratigraphic order of an event and Z its depth (in meters). In general, there is
relatively little scatter in this plot and an interpolation spline curve (line of observation) can be used for the relationship between Y and Z. Contrary to the line
of correlation which normally is fitted to scattered points falling within a relatively broad zone, and is often approximately straight or only moderately
curved, the line of observation can be constructed through all observed points.
It tends to be wiggly and reflects local facies and sedimentation rates. An error
bar initially estimated along the Y-axis can be transformed into a generally
asymmetrical error bar along the depth axis of a section. The resulting error bars
have different widths, not only for different events in the same section, but also
for the same event in different sections. They provide 95% confidence intervals
for the observed and the estimated average locations of the events in the sections.
Figure 2 provides an example of CASC using three events in four wells from
the data set used to obtain Fig. 1. In the top part, the observed positions of two
events (205: last occurrence of Heterosphaeridium difficile, and 212: last common occurrence of Hedbergella delrioensis) are connected by lines, and accompanied by their estimated 95% confidence intervals which have been constructed around the probable positions for these events. In Well No.3, the observed
position of event 205 is slightly above the upper limit of its 95% confidence interval. This does not necessarily mean that event 205 is anomalous in this well,