Identifying ideal stratigraphic cycles using a quantitative optimization method

Abstract

The ideal cycle concept is poorly defined yet implicit and potentially useful in many stratigraphic analyses. A new method allows quantitative definition of ideal cycles and provides a simple but robust method to analyze stratal order and quantify stratigraphic interpretations. The method calculates transition probability (TP) matrices from a vertical succession of strata for all possible permutations of facies-class row numbering in the matrices. The ordering of facies classes that gives highest transition probabilities along diagonals of the TP matrix can be taken as a quantitative definition of an ideal cycle for the strata being analyzed. Application to a synthetic example shows how an ideal cycle can be identified, even in noisy strata, without any assumptions about or prior knowledge of cyclicity. Application to two outcrop examples shows how it can be useful to define the most optimal cycle and determine how much evidence is present for ordered and cyclical facies successions.