ABSTRACT
A fractal-based function, whether self-similar or self-affme, is a natural candidate for representing a hierarchical structure in either time or space. The chapter reviews the origin of fractional Brownian motion (fBm) and fractional Gaussian noise (fGn) and the methodology for using such functions to represent three-dimensional porosity function and hydraulic conductivity function distributions in saturated porous media. Many of the existing algorithms for generating fBm or fGn were motivated by the desire to construct synthetic landscapes and other random fractal forgeries. If further experimental study verifies that fBm/fGn or related functions may be used widely to represent the hydraulic properties of porous media, then this will imply that autocorrelation between properties will extend over very large distances. In a practical sense, it is probably accurate to say that correlation length, like apparent dispersivity, will be scale-dependent. Earth science applications of fBm/fGn are presented within a conditional simulation-stochastic realization framework.
