The use of Markov chains in the study of sedimentary cycles

Markov chains, applied to stratigraphic sections, are suitable for the description of geological cycles. Cyclicity is a property which ranges from completely damped to perfect periodic oscillations. A measurement of “cyclicity” is provided by the eigenvalues of the Markov matrix. At the same time, it was found that the method of Markov chains and discrete stochastic chains, in general, is a cumber-some tool when applied to stratigraphic analysis. Many sections require high-order chains and consequently larger transition probability matrices, which are difficult to interpret. Great care must be taken not to oversimplify these chains, because this results in a loss of cyclicity. By applying the methods to a composite section of Upper Pennsylvanian strata of northeastern Kansas, a 40- to 50-ft “cycle” was found. The oscillations are damped if directly measured data are used. Removal of a trend in sedimentation rates reduces damping to such an extent that the hypothesis of time cyclicity is at least feasible.