Quantitative Stratigraphy, Splining and Geologic Time Scales - Geomathematics: Theoretical Foundations, Applications and Future Developments - page 320

.8750
.9922 .9922 .9688 .9844 .9961

.8750 .7500 .8750 .8750 .8750 .5000 .0000 .0000

.8750

.9375 .8750

.0000

.5000 .5000 .5000 .0000 .5000 .5000

.9375 .9375 .8750 .8750 .9375 .3750

.3750
ʴ

.0000 .6250 .7500 .0000

.0000

.3750 .0000 .3750

.3750 .6250 .3125

.0000 .0000

.6250

Fig. 9.8 Values of (1 P ) where P represents the probability that the sequential relation between

two events is non-random according to Hay ( 1972 ) (Source: Agterberg 1990 , Fig. 5.2)

Fig. 9.9 Diagrams to illustrate superpositional relations between (a) three events and (b) four
events in the Hay example. Although both occur only in four sections, their

superpositional relation is probably non-random because of their relations with other events
(Source: Agterberg 1990 , Fig. 5.3)

ʔ and Φ

As mentioned in Sect. 9.1.3 , it usually is not possible to obtain a unique optimum
sequence in practice because of cycling events. This problem is illustrated for a
three-event cycle in Fig. 9.10 . More than three events can be involved in cycling
(Agterberg 1990 ) In the RASC computer program, a ranking solution is obtained by
first identifying all subgroups of events involved in cycling and then followed by
“breaking” the cycles using sample size considerations. Scaling is not subject to
cycling problems and has the additional advantage that it quantifies the strengths of
all superpositional relationships. Ranked and scaled optimum sequences for the Hay
example are shown in Fig. 9.11 . Intermediate steps before the final scaling solution
of Fig. 9.11b was obtained are illustrated in Tables 9.9 , 9.10 , 9.11 , and 9.12 .