Scaling laws of karst dissolution features; evidence from three-dimensional unmanned aerial vehicle imaging and ground-penetrating radar analyses

The discovery of karst dissolution features in boreholes or well logs serves as a key indicator of the presence of significant karst porosity and high permeability zones in carbonate reservoirs. This insight is crucial for the development of such reservoirs. Our research demonstrated that the dimensions of karst dissolution features adhere to power laws, providing a practical method for scaling the measured dimensions of these features. This conclusion is the result of a comprehensive study of two outcrops of the Jandaira Formation (Potiguar Basin, northeastern Brazil), and deposited within an early Turonian-early Campanian carbonate platform setting that offers a well-preserved exposure of an epigenetic karstic system. Our methodology involved estimating the geometric dimensions of karst dissolution features on the surface and underground, using three-dimensional unmanned aerial vehicle and ground-penetrating radar data sets. We first confirmed that ellipsoids can effectively approximate karst dissolution features. Subsequently, we demonstrated that the dimensions of the semiaxes, cross-sectional areas, and volumes of the ellipsoids conform to power laws. By applying the power law derived for the occurrence of volumes, we generated a statistically equivalent three-dimensional stochastic model for karst features that closely replicates the distribution of actual karst features.