Modeling 3-D anisotropic fractal media

Published as SEP report, 80, 603-616 (1994)

Modeling 3-D anisotropic fractal media

Nizar Chemingui

Abstract:

This paper presents stochastic descriptions of anisotropic fractal media. Second order statistics are used to represent the continuous random field as a stationary zero-mean process completely specified by its two-point covariance function. In analogy to the two-dimensional Goff and Jordan model for seafloor morphology, I present the von Karman functions as a generalization to media with exponential correlation functions. I also compute a two-state model by mapping the random field from continuous realizations to a binary field. The method can find application in modeling impedances from fractal media and in fluid flow problems.