Application of Markov Mean First-Passage Time Statistics to Sedimentary Successions: A Pennsylvanian Case-Study from the Illinois Basin

Abstract

Markov chains have been widely used in the statistical analysis of sedimentary successions for the discrimination of non-random transitions between lithologies and the examination of potential cyclic patterns. A lithologic transition probability matrix can also be transformed to a matrix of mean first-passage times that represent the expected number of steps for first occurrences between lithologies or facies. These passage times capture the statistics of multiple transition paths and provide a metric of distances that can be used for comparisons between sections separated stratigraphically or geographically. In addition, systematic long-term elements can be differentiated from the short-term model provided by the limited memory contained within a transition probability matrix. A case-study example is described that demonstrates the use of mean first-passage times to show changes in the interplay of deltaic and marine facies, based on transition matrices from type sections of Pennsylvanian formations in the Illinois Basin.