Including Multi-Scale Information in the Characterization of Hydraulic Conductivity Distributions

Abstract

Transport in heterogeneous porous media is highly dependent on the spatial variability of aquifer properties, particularly hydraulic conductivity. It is impractical, however, when modeling a real situation, to obtain aquifer properties at the scale of each grid block. Wavelet transforms are investigated as a tool to assess the movement of information between scales, and to incorporate the scale and location of hydraulic conductivity test data when interpolating to a fine grid. Wavelet transforms are particularly useful as they include parameters that define a spatial localization center that can be positioned in space, and changed in size. As a result, one can incorporate multiple measured hydraulic conductivity values in the wavelet transformation at a resolution matched to each measurement scale. A multi-scale reconstruction method is developed here which uses forward and inverse wavelet transforms in conjunction with a pseudo-fractal distribution to fill in missing information around sparse data. This wavelet reconstruction method is compared to several more traditional interpolation schemes with respect to accuracy of solute transport prediction. The wavelet reconstruction algorithm is then used to examine the issue of optimum sample size and density for stationary and fractal random fields.