Further evidence of fractal structure in hydraulic conductivity distributions

Abstract

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 fractional Gaussian noise and fractional Brownian motion [Hewett, 1986; Molz and Boman, 1993]. New K data analyzed herein lend further support to this notion. Horizontal processes that mimic fBm will display a power‐law variogram. The Mandelbrot‐Weierstrass random fractal function is introduced as an analytical model for fBm and used to illustrate several concepts. With the exception of the Hurst coefficient value (H), our 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.