Order, disorder, alternations, and cycles: robust analysis of patterns in vertical facies successions using a moving-window method

ABSTRACT Identification of cyclic facies successions is fundamental in many sedimentological and sequence-stratigraphic interpretations to accurately reconstruct paleoenvironment and paleoclimate, and to make useful predictions of stratal heterogeneity. However, quantitative identification of cyclical strata to provide sufficiently strong evidence for such interpretation and prediction is challenging. A new method evaluates the order present in any stratigraphic section consisting of at least four lithofacies. Transition-probability matrices are calculated over a range of window sizes up the vertical succession to calculate a Markov-order metric, which is then compared with multiple randomly shuffled versions of the same facies units to calculate the probabilities of the observed succession occurring by chance. Applying the method to eight synthetic sections demonstrates that this method can successfully distinguish cyclical sections from disordered and alternating strata. Two summary metrics are tested on the progressively shuffled versions of the eight synthetic sections and are demonstrated to be useful to quantify order and to distinguish cyclical and alternating strata. Application to one siliciclastic and one carbonate outcrop succession demonstrates that the method can identify order in strata at various length scales. Application to a global dataset of 47 vertical carbonate sections demonstrates mostly disordered strata, suggesting that common interpretations of stratal order related to climate settings might represent conceptual bias. Analysis of eight coeval fluvial–deltaic sections suggests that application of the method can reveal potential characteristic length scales of cyclicity, allow more rigorous correlation, and inform more robust interpretations of autocyclic and allocyclic processes.