FURTHER EVIDENCE OF FRACTAL STRUCTURE IN HYDRAULIC CONDUCTIVITY DISTRIBUTIONS

Past rescaled range analyses of porosity and hydraulic conductivity (K ) distributions have indicated the presence of long-range correlations in the data typical of the related stochastic functions known as frac tional Gaussian noise and fractional Brownian motion [Hewett, 1986; Mo lt and Boman, 1993]. New K data analyzed herein lend further support t o this notion. Horizontal processes that mimic fBm will display a powe r-law variogram. The Mandelbrot-Weierstrass random fractal function is introduced as an analytical model for fBm and used to illustrate seve ral concepts. With the exception of the Hurst coefficient value (H), o ur analysis supports the existence of fractal-like K fields similar to those visualized by Neuman [1990, 1994]. Past studies which produced H values greater than or less than 0.5 appear to differ mainly because of the underlying model, fractional motion or fractional noise, that was assumed in the respective analyses.