Characterization of permeability anisotropy using wavelet analysis

Abstract

[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.

Wavelet analysis of dominant scales of heterogeneous porous media

“…This pattern is consistent with the relationship between wavelet scales and periods for a periodic function [see Neupauer et al, 2006].…”

“…[22] In some prior applications of wavelet analysis [e.g., Li and Loehle, 1995;Neupauer et al, 2006], the GWS was found to be useful for identifying characteristic length scales. In these applications, the data were approximately …”

“…Kumar [1995] and Neupauer et al [2006] used a similar measure to identify scale-space anisotropy of a rainfall event and of a nonstationary permeability field, respectively. Farge [1992] analyzed turbulent flows using a measure similar to the global wavelet energy spectrum (GWES), which is defined as Frantziskonis [2002] identified dominant length scales in a two-dimensional binary random field representing the pore and matrix structure of a porous material using the energy of wavelet transform (EWT), defined as…”

Wavelet analysis of characteristic length scales and orientation of two-dimensional heterogeneous porous media

“…In two dimensions, analyses have also been conducted to identify anisotropic spatial variations of rainfall [19,20], rock composition [14,15], soil thickness, surface slope, and direct solar radiation [24], and permeability [29,42]. Wavelets have also been applied to upscaling of porous medium properties [7][8][9]28,[32][33][34]36].…”

“…For example, for a property that displays periodic fluctuations, such as seasonal fluctuations in ice extent [17], the global wavelet spectrum (GWS), r 2 W ðaÞ ¼ A À1 R X jW f ða; bÞj 2 db, where A is the area of the domain, can be used to identify the period, T, of the fluctuations. The scale a max at which r 2 W ðaÞ attains its maximum value is related to the period T through the relationship T ¼ 2pa max = ffiffiffi 3 p [29]. The GWS has been used to identify characteristic length scales in some prior applications (e.g., [26,29]).…”