Stratal Thickness Frequencies and the Prevalence of Orderedness in Stratigraphic Sequences

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Abstract
Assuming the existence of discernable hierarchies in the thickness and/or temporal recurrence of stratal units within sedimentary sequences has become an increasingly important axiom of sequence and cyclostratigraphic studies, and multiple orders of stratigraphic cyclicity are now commonly associated with inferred durations and magnitudes of rhythmic variation in global sea level. Beyond the desire to establish an informal nomenclature relating stratigraphic thickness to periodicity of eustatic change, an assumption of stratigraphic orderedness also supports the inference that groups of sedimentary units with distinct modal dimensions in fact do occur with some generally distinct frequency in stratigraphic sequences. In contrast to such perceived patterns of stratigraphic order, many groupings of sedimentary units exhibit lognormal frequency distributions wherein most of the population has an exponentially increasing frequency of occurrence with linearly decreasing class size. Such thickness distributions typify a wide range of sedimentary entities, including individual lithofacies, formally named stratigraphic units, epoch-interval sedimentary sections, and cyclic peritidal lithofacies associations, as well as durations of unconformity-bounded stratigraphic sequences and the magnitudes and durations of presumed change in global sea level. These distributions indicate that most natural populations of sedimentary units comprise a non-modal series of increasing frequency with decreasing size. The importance of this statement lies in the fact that discrimination of stratigraphic hierarchies and their designation as nth-order cycles may constitute little more than the arbitrary subdivision of an uninterrupted stratigraphic continuum.

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