Abstract: 

Identifying order or pattern in strata on the basis of qualitative interpretation forms the basis for much current sedimentological and sequence stratigraphic analysis. Order can be usefully defined as some arrangement of facies or unit thickness that has a discernable trend or pattern that is unlikely to occur by chance because it requires some particular systematic process to form. Coarsening, fining, thickening, or thinning-upward trends, and arrangement of strata into cycles are examples of order. Qualitative interpretations of order often demonstrate little more than an implicit assumption of order. This paper defines a robust yet simple-to-apply quantitative method to identify order in strata and to indicate when order cannot be reliably demonstrated. The method is based on two calculated metrics, the Markov metric m derived from analysis of a vertical facies succession, and the runs metric r derived from analysis of observed thicknesses of stratal units. Most importantly, both metrics can be compared with equivalent metrics calculated for disordered strata composed of many randomly shuffled versions of the same lithological units. Probability values can then be calculated from the comparison between observed and randomly shuffled cases, and these p values indicate the degree of evidence present for order in the observed strata. Several test examples using synthetic strata show that the m and r values can define and identify different degrees and types of stratal order, and that the metrics are robust for both stationary and non-stationary successions with a range of different lengths and numbers of distinct facies. Analysis of four outcrop examples, two siliciclastic and two carbonate, demonstrate that ordered facies successions and thickness trends may be less common than typically assumed; none of the four examples analyzed show trends in thickness, and only the examples from the Book Cliffs, which represent a bedset scale composite of observations, show evidence for facies order. The examples demonstrate how a quantitative analysis can lead to better understanding of strata, either ordered or disordered, and can provide better insight into the validity of current stratigraphic interpretations and models. Absence of order in many of the analyzed 1D vertical successions may also indicate that we need to focus more on longer-term trends and analysis of 2D and 3D stratal geometries.

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