Wavelet analysis of dominant scales of heterogeneous porous media

Abstract

Heterogeneity of aquifer permeability has a significant influence on the transport of solutes; therefore characterization of aquifer heterogeneity is needed to accurately predict the behavior of solutes. A critical characteristic of heterogeneity is a characteristic length scale that is a measure of the distance over which property values are correlated. We show that the characteristic length scale of a statistically homogeneous permeability field can be identified through wavelet analysis using the global wavelet energy spectrum (GWES). The relationship between the wavelet scale and the characteristic length scale of a random field is investigated for the Mexican hat and Morlet wavelets and different covariance structures. The ability of the GWES to identify multiple characteristic length scales in a random field with nested covariance structures is also investigated. We use the technique to identify the characteristic length scales of a laboratory‐collected permeability transect from Massillon sandstone.