Poisson processes of carbonate accumulation on Paleozoic and Holocene platforms

ABSTRACT Cambro-Ordovician carbonate lithofacies units in the Elbrook and Conococheague formations exposed at Wytheville, Virginia, as well as those in many other Phanerozoic peritidal sequences, exhibit exponential thickness frequency distributions. That is, occurrence frequency decreases exponentially with linear increase in unit thickness. Such distributions are characteristic of waiting times between independent Poisson events. This relative frequency of spaces of different size between horizons of lithologic change is what one would expect if the horizons were distributed randomly throughout carbonate successions. Abundances of different lithologies, both as net stratigraphic thickness and as number of occurrences, also decreases exponentially among successively rare sediment types, with each lithology being about 60% as plentiful as the next more abundant rock type. Relations between net thickness and number of occurrences for each facies define a linear trend coincident with a mean thickness for all Wytheville units of 0.48 m, a relation indicating that thickness distribution is independent of facies type. Similar relations are apparent for the horizontal extent of carbonate sediment bodies from the Holocene Florida-Bahama platform. Areal extents of individual facies units (lithotopes) are described by a frequency distribution in agreement with that anticipated for a population of equidimensional facies elements whose diameter distribution follows an exponential frequency distribution. Although regional gradients in sediment texture and composition are also apparent along most transects from platform margin to interior, such frequency distributions indicate that lateral extents of individual sediment reflect a largely stochastic distribution of facies boundaries across this Holocene surface. Lithotope abundances also yield trends of exponentially decreasing dominance among successively subordinate facies, with each being about 70% as extensive the next more abundant sediment type. Relations between areas and abundances for all lithotopes define a covariant trend corresponding to a mean area of 2.2 103 km2 for all Florida-Bahamas lithotopes. We consider several numerical models of stochastic carbonate accumulation; although not demonstrably unique, scenarios incorporating the sequential superposition of randomly placed coniform lithotopes result in thickness and area frequency distributions that are the same as those observed in ancient and modern platform deposits. Such simulations of Poisson processes of sediment accumulation are in general agreement with stochastic models of lithologic heterogeneity that have been more widely applied to petroleum reservoirs and groundwater aquifers. To the as yet unknown degree that peritidal lithofacies area and thickness are correlated, data from Paleozoic and Holocene platforms suggest that carbonate units should exhibit length/height ratios of approximately 105. Given the decimeter scale over which facies are designated in most Paleozoic peritidal successions, these relations predict mean lateral extents on the order of several tens of kilometers, a value in general agreement with the few data that exist on spatial continuities of peritidal lithotopes in Paleozoic carbonate sequences.