Multifractal analyses of hydraulic conductivity distributions

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Abstract
The concept of a universal multifractal, a generalization of a monofractal, is a recently developed scaling model for natural phenomena characterized by irregularity. Presented herein is an effort to use universal multifractal concepts to deal with spatial variations of hydraulic conductivity K, which have a significant effect on contaminant transport in the subsurface. Structure function analyses of four K data sets show that some vertical variations of K display multifractal structures, while others are consistent with monofractal behavior. In order to make multifractal concepts more useful, multifractal noise is introduced and defined as the increments of a multifractal. It is concluded that the multifractal formalism of Schertzer and Lovejoy [1987] has provided a rather general approach for modeling In K variations in the vertical. With the exception of horizontal variations of the Borden data, all results fell within the domain of universal multifractal behavior, which includes the monofractal case. Parameters were well‐defined in an empirical sense and easy to calculate, indicating a robust formalism. Results were consistent with the recent finding of Liu and Molz [1997, also Non‐Gaussian and scale‐variant behavior in hydraulic conductivity distributions, submitted to Water Resources Research, 1997, hereinafter referred to as submitted paper] that K variations display increasing heterogeneity at decreasing scales.