Algorithms for the scaling of stratigraphic events

Abstract

The scaling algorithms presented in this paper form the second part of the RASC program for ranking and scaling of biostratigraphic events and other events which can be identified uniquely. An optimum sequence constructed by a ranking algorithm provides the starting point for estimating average “distances” between successive events. Frequency of crossover (mismatch) of events in sections is used for this purpose. Distances are clustered by constructing a dendrogram which can be used as a standard and permits definition of assemblage zones. Options of the second part of the RASC program include the following: (i) Normality test option: Each section is compared to the standard. This allows the detection of events which in a given section occur significantly above or below their average position in the standard. (ii) Marker horizon option: Each stratigraphic event is assumed to satisfy a normal probability curve with equal variance along the relative time axis. Chronostratigraphic (marker) horizons such as bentonite beds resulting from volcanic ash falls are assigned zero variance if the marker horizon option is used. (iii) Unique event option: After ranking and scaling the events for all more abundant fossil species, a rare (unique) event can be entered into the optimum sequence by comparing its position in a single or few sections to those of the more abundant taxa.