Among broadly different types of sedimentary successions, those that accumulate in nearshore settings are perhaps unique in that a very wide range of rock types recurs with high frequency over relatively short stratigraphic intervals. This vertical lithofacies heterogeneity suggests that deposition of any sedimentary unit at any site was short-lived, that many different sediment types existed within a complex mosaic over the depositional surface, and that this facies montage repeatedly moved across surfaces of accumulation in response to eustatic, sedimentologic, and/or tectonic forcing.

Data on numbers and thicknesses of lithofacies units from several dozen such sequences define the size frequency distribution expected if horizons of lithologic change occur randomly within sedimentary successions. Walther's law suggests that the amount of vertical lithologic heterogeneity manifest in a sedimentary sequence should reflect the degree of lateral heterogeneity in sediment composition that existed across depositional surfaces. If so, this repetition should also be manifest in sizes and areal distributions of sediment patches constituting the depositional mosaic. In order to examine size frequency relations of sediment bodies across surfaces of sediment accumulation, we tabulated numbers and areal extents of lithotopes across two rather dissimilar settings, across the Persian Gulf and around the Caribbean island of Antigua.

Although compositions and lateral extents of different sediment types exhibit broad lateral variation across interior to margin transects in either area, lithotope abundances and areal extents define frequency distributions that are in excellent agreement with those anticipated for a facies mosaic of elements whose mean linear widths constitute an exponential frequency distribution. These are the size frequency distributions one would expect if mosaic element boundaries occur randomly across regions of sediment accumulation, and suggest that distributions of lithotope areas from Holocene surfaces are directly analogous to lithofacies thickness frequencies from ancient successions. In addition to the fact that both of the size frequency distributions attest to the importance of stochastic processes during sediment deposition, they also afford numerical descriptors of abundances and areal extents of Holocene lithosomes that can then be used as controlling parameters in computational models of sediment accumulation. Importantly, results derived from such simulations are based not on inference of water depth varying in response to change in subsidence, sea level, and rate of sediment accumulation but on statistical attributes intrinsic to modern and ancient marginal marine successions.

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