[1] Wavelet analysis is an image analysis technique that can extract local information at multiple scales. Because of this capability, wavelet analysis can be used to identify dominant scales in statistically heterogeneous and anisotropic random fields. We develop and test a wavelet analysis method for identifying dominant scales and orientations in permeability fields and for identifying boundaries between regions with different dominant orientations. We evaluate three different wavelets (fully anisotropic Morlet wavelet, Mexican hat wavelet, and Cauchy wavelet) and show that the Morlet wavelet is the most effective of these three wavelets in identifying dominant orientations. We also investigate the use of several different quantitative wavelet measures in identifying dominant scales and orientations in permeability fields. The technique is demonstrated using both a synthetic data set with known characteristics and a laboratory-collected permeability data set from Massillon sandstone.

[1] 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.Citation: Qi, X., and R. M. Neupauer (2008), Wavelet analysis of dominant scales of heterogeneous porous media, Water Resour.

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