The occurrence of power law relationships in the spatial distribution of sedimentary lithotopes has been identified in both modern and ancient carbonate depositional bodies. In this study, facies patterns and their spatial relationships are investigated quantitatively in an Arabian Gulf shallow subtidal carbonate ramp setting, using a synergy of IKONOS satellite imagery and vessel-based acoustic bathymetry survey. Three-dimensional reconstruction of the facies distribution on the seabed enabled quantification of relationships between eight dominant facies classes and the association of particular lithotopes to water depth. Fractal behavior was investigated using a combination of boundary- and patch-based metrics, and the spatial distribution of early diagenetically cemented hardgrounds and unconsolidated carbonate sand were shown to display strong fractal properties. In contrast, we show that landscape-scale processes can be treated as essentially deterministic and facies neighborhood patterns are strongly probabilistic. Identifying that the heterogeneity of shallow subtidal carbonate facies scales with a power law within certain thresholds has the potential to serve as a tool in environmental reconstruction in the ancient, where information on the lateral persistence of facies units is difficult to obtain. The findings are relevant to the interpretation of stratigraphic sequences and paleo-depth analysis.
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