Predicting Facies Size, Shape, and Complexity Using Quantitative Relationships Derived from a Modern Carbonate Depositional System

There is growing evidence that the size and geometry of facies bodies within modern shallow water carbonate environments are predictable through quantitatively derived relationships. The most well-established premise is that the distribution of facies area by frequency of occurrence for many sediment types adheres to a power-law. Shape and shape-complexity of individual facies units are similarly predictable through mathematical rule sets. These relationships specify the distribution of size, shape, and complexity of facies in an artificial landscape. The utility of studying modern carbonate depositional environments is that high-resolution digital datasets can be assembled to understand the system at scales irresolvable in the sub-surface. Using a particularly comprehensive dataset that exists for the island of Vieques (Puerto Rico), a case study is accomplished to investigate the feasibility of incorporating size and shape statistics as rules for predicting facies geomorphic attributes. We meld field observations with airborne bathymetric LiDAR and satellite datasets to map the spatial configuration of modern carbonate facies in this setting. We demonstrate that the system is predictable with regard to size, complexity, and shape. Using these relations, we construct a synthetic realization that is statistically similar to the real-world environment on which it is based. This model honors size, shape, and complexity properties in such a way that it is both visually plausible and mathematically rigorous. Furthermore, we confirm that satellite remote sensing is a powerful and appropriate technology for generating rule sets relevant to the prediction and modeling of carbonate facies size, shape, and shape complexity.