**Abstract: Scalar Dependence of Deterministic and Random Variation in
Peritidal Carbonates**

WILKINSON, BRUCE H., Department of Geological Sciences, University of Michigan Ann Arbor, Michigan 48109-1063; and CARL N. DRUMMOND, Department of Geosciences, Indiana-Purdue University Fort Wayne, Fort Wayne, Indiana 46805-1499

Speculation on the depositional origins and geological significance of cyclic lithofacies associations in epicratonic successions has become an increasingly prominent facet of sequence stratigraphic theory, the understanding of which bears directly on their appropriateness as chronostratigraphic entities for global stratigraphic correlation, as well as their usefulness as records of periodic extrabasinal forcing during sediment accumulation. With relatively few exceptions, sequences of shallow water terrigenous and (especially) carbonate rocks have been widely interpreted as recording the influence of Milankovitch band periodic climate change on global sealevel and attendant patterns of carbonate accumulation. Many recent studies have also suggested an intrinsic relation between “hierarchies” of stratigraphic cyclicity, ranging from meter scale parasequences to longer term hierarchies of the sequence stratigraphic infrastructure inferred from terrigenous passive margin siliciclastic sequences, with each driven by some range of periodic glacio- to tectono-eustatic processes.

In contrast to assertions of inherent order, sequence scale
patterns of lithologic thickness and recurrence from epicratonic
Phanerozoic sequences, as well as patterns of facies mosaic area
and occurrence * frequency* from Holocene platforms, strongly suggest
that any effect of cyclic intra- and/or extra-basinal forcing is
commonly overwhelmed by the inherently stochastic nature of
sediment accumulation. With respect to Phanerozoic successions,
exponential thickness frequencies of peritidal carbonate units such
as those in the Elbrook and Conococheague formations at Wytheville,
Virginia, and in the Lower Ordovician Kindblade and West Spring
Creek formations at Ardmore, Oklahoma, are readily interpreted in a
context of probabilities of upsection transition from one lithology
to another. These largely reflect Poisson (random) processes of
suspended load, traction load, and microbialitic accumulation
wherein regression slopes of exponential thickness/recurrence

*distributions define probabilities of upsection recurrence of a particular sediment type. Thicknesses of individual lithofacies elements and stratigraphic intervals between recurrences of like lithofacies are only dependent on number of elements present and on net stratigraphic length. Such distributions require a significant component of haphazard variation in the type and amount of accumulated carbonate sediment. If deposition was influenced by extrabasinal forcing, such control must have been nearly random in both secular and spatial dimensions of water depth change.*

**frequency**Trends in data on abundances and sizes of individual facies areas from the modern Florida/Bahamas platform are indistinguishable from those that would result from the random segmentation of the platform surface into a number of subregions, each with a generally homogeneous sediment cover. Over this region, frequencies of occurrence of different peritidal facies areas are largely dependent on the number of facies elements present and the total area of Holocene carbonate accumulation. Like thicknesses and abundances of Phanerozioc carbonate units, areas and occurrences of peritidal facies on the Florida/Bahamas platform largely record the importance of random processes during sediment accumulation. If sediment accumulation were more or less constant, then transects across such a platform will comprise exponential distributions of chords across each facies type and, by inference, exponential distributions of thicknesses of individual lithofacies elements. This is exactly the pattern of variation observed in peritidal carbonate sequences.

However, it is also true that most longer sequences of peritidal
carbonate also display some degree of statistical nonstationarity
manifest as low * frequency* “third order” bundling among
stratigraphic waiting intervals. Conceptually, then, the recurrence
and/or intensity of carbonate accumulation on carbonate platforms
is perhaps best perceived as the embodiment of both high

*stochastic and low*

**frequency***deterministic attributes, with amount of predictability across any platform surface or within any particular peritidal sequence being dependent on temporal/spatial scales of stochastic versus deterministic variation.*

**frequency**At scales of individual peritidal lithologies or the several lithofacies elements that make up most “cyclic meter scale parasequences”, Poisson processes almost completely subjugate any influence of longer term change in sedimentation/subsidence rate or sealevel. At these scales of consideration, stratigraphic durations and recurrences more closely reflect the inherently stochastic nature of carbonate accumulation in epicratonic platformal settings than any influence of rhythmic eustatic forcing. Only at scales in excess of perhaps several dozen stratal elements do processes of glacio- to tectono-eustatic forcing of sediment accumulation begin to exert any important observable control on patterns of lithologic variation in most Phanerozoic stratigraphic sequences.

AAPG Search and Discovery Article #90937©1998 AAPG Annual Convention and Exhibition, Salt Lake City, Utah