Ranking-Scaling (Agterberg & Gradstein 1999) is a method for quantitative biostratigraphy based on events in a number of wells or sections. The data input consists of wells in rows with one well per row, and events (e.g. FADs and/or LADs) in columns. The values in the matrix are depths of each event in each well, increasing upwards (you may want to use negative values to achieve this). Absences are coded as zero. If only the order of events is known, this can be coded as increasing whole numbers (ranks, with possible ties for co-occurring events) within each well.
The implementation of ranking-scaling in PAST is not comprehensive, and advanced users are referred to the RASC and CASC programs of Agterberg and Gradstein.
Overview of the method
The method of Ranking-Scaling proceeds in two steps:
1. Ranking
The first step of Ranking-Scaling is to produce a single, comprehensive stratigraphic ordering of events, even if the data contains contradictions (event A over B in one well, but B over A in another), or longer cycles (A over B over C over A). This is done by 'majority vote', counting the number of times each event occurs above, below or together with all others. Technically, this is achieved by Presorting followed by the Modified Hay Method (Agterberg & Gradstein 1999).
2. Scaling
The biostratigraphic analysis may end with ranking, but additional insight may be gained by estimating stratigraphic distances between the consecutive events. This is done by counting the number of observed superpositional relationships (A above or below B) between each pair (A,B) of consecutive events. A low number of contradictions implies long distance.
Some computed distances may turn out to be negative, indicating that the ordering given by the ranking step was not optimal. If this happens, the events are re-ordered and the distances re-computed in order to ensure only positive inter-event distances.
RASC in PAST
Parameters
- Well threshold: The minimum number of wells in which an event must occur in order to be included in the analysis
- Pair threshold: The minimum number of times a relationship between events A and B must be observed in order for the pair (A,B) to be included in the ranking step
- Scaling threshold: Pair threshold for the scaling step
- Tolerance: Used in the ranking step (see Agterberg & Gradstein)
Ranking
The ordering of events after the ranking step is given, with the first event at the bottom of the list. The "Range" column indicates uncertainty in the position.
Scaling
The ordering of the events after the scaling step is given, with the first event at the bottom of the list. For an explanation of all the columns, see Agterberg & Gradstein (1999).
Event distribution
A plot showing the number of events in each well, with the wells ordered according to number of events.
Scattergrams
For each well, the depth of each event in the well is plotted against the optimum sequence (after scaling). Ideally, the events should plot in an ascending sequence.
Dendrogram
Plot of the distances between events in the scaled sequence, including a dendrogram which may aid in zonation.
Variance analysis
For each event, this function plots the deviations from the line of correlation (see above) across all the wells. This gives a graphical representation of the biostratigraphic quality of each event.
Reference
Agterberg, F.P. & F.M. Gradstein. 1999. The RASC method for Ranking and Scaling of Biostratigraphic Events. In: Proceedings Conference 75th Birthday C.W. Drooger, Utrecht, November 1997. Earth Science Review 46(1-4):1-25.