Fractal Scaling of Secondary Porosity in Karstic Exposures of the Edwards Aquifer

We used feeler gauges and image analysis to quickly characterize and interpret hundreds of fracture apertures and the cross-sectional area, aspect ratio, and perimeter of thousands of dissolution features in eight exposures of the Edwards aquifer in south-central Texas. Using frequency-size distribution plots, we showed that fracture aperture and the cross-sectional area and hydraulic diameter of dissolution features follow fractal scaling, with fractal dimensions ranging from 0.85 to 0.93 for aperture and from 0.62 to 1.15 for cross-sectional area of dissolution features. We used fractal scaling with the Riemann zeta function to estimate secondary porosity of the exposures. Estimates of secondary porosity using fractal scaling are two to five times higher for fractures and on average twice as high for dissolution features than those determined directly from the measured values.