Automated Correlation Based On Markov Analysis Of Vertical Successions And Walther's Law

Abstract

Walther's Law of Facies (1894) states that facies overlying one another comformably were formed in geographically contiguous environments. This vertical-lateral linkage is the basis for our automated method of stratigraphic correlation. The probabilities of vertical adjacency of different lithologies are estimated by embedded Markov chain analysis of sequences to be correlated. These probabilities are transformed to dissimilarities and used as elements within a dynamic programming sequence comparison. Trajectory tracking of cumulative thicknesses between the two sequences provides an auxiliary criterion to incorporate factors of sedimentation rate and compaction. Stratigraphic correlation is simultaneously simple and complex. The operation is fundamentally one of pattern recognition, whose principles can be grasped easily by any geology student. One source of complexity is caused by the fact that most successions are composed of a relatively small number of distinctive rock types. Within each succession, they are ordered as a linear chain in which loosely repetitive sequences are often perceived as "cycles" or "rhythms." As a result, the correlation between two adjacent successions may be ambiguous, so that several competing alternatives may be equally valid candidates for the "true" correlation. The situation is made still more disma! by the knowledge that erosional events may have removed entire stratigraphic segments and that periods of non-deposition may have caused gaps. In the opinion of Ager (1973), the gap is more important than the record. Even if a "complete" lithology record were available, it is unlikely that the successions in two separate locations would be identical. Lateral facies changes result in differences of lithology within correlative intervals. Equivalence or "similarity" of rock type is not the only criterion used in correlation. Thicknesses are a secondary source of information for correlation decisions. Similarity in thickness of equivalent lithologies between successions often implies a greater likelihood of their correlation. However, exceptions to this rule commonly are observed in the lateral thinnings and thickenings caused by both lateral facies changes and differential compaction. The simpler aspects of correlation suggest that practical automated correlation procedures are both feasible and desirable. Even if programmed decisions cannot be characterized absolutely as "objective," they can at least be made consistent.