Special Issue

Mathematical Geosciences

, Volume 41, Issue 6, pp 643-659

First online:

Wavelet Analysis and Filtering to Identify Dominant Orientations of Permeability Anisotropy

  • Loring WatkinsAffiliated withUniversity of Colorado at Boulder
  • , Roseanna M. NeupauerAffiliated withDepartment of Civil, Environmental, and Architectural Engineering, University of Colorado at Boulder Email author 
  • , Gilbert P. CompoAffiliated withCIRES/Climate Diagnostics Center, and NOAA Earth System Research Laboratory/Physical Sciences Division, University of Colorado at Boulder

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An accurate representation of permeability anisotropy is needed to model the rate and direction of groundwater flow correctly. We develop a wavelet analysis technique that can be used to characterize principal directions of anisotropy in both stationary and non-stationary permeability fields. Wavelet analysis involves the integral transform of a field using a wavelet as a kernel. The wavelet is shifted, scaled, and rotated to analyze different locations, sizes, and orientations of the field. The wavelet variance is used to identify scales and orientations that dominate the field. If the field is non-stationary, such that different zones of the field are characterized by different dominant scales or orientations, the wavelet variance can identify all dominant scales and orientations if they are distinct. If the dominant scales and orientations of different zones are similar, the wavelet variance identifies only the dominant scale and orientation of the primary zone. In this paper, we present a combined wavelet analysis and filtering approach to identify all dominant scales and orientations in a non-stationary permeability field. We apply the method to permeability data obtained in the laboratory from the Massillon sandstone.


Heterogeneity Non-stationary Morlet wavelet Permeability Anisotropy Wavelet analysis