[1] We analyzed the scaling properties of the hydraulic conductivity K at three sites in Northern America: MADE, Borden, and Cape Cod. We found that K at all sites exhibits multifractality (fractal and multiscaling) in both the vertical and horizontal directions, though the multiscaling was within a range smaller than that of the maximum distance between measurements. In the vertical direction, the K data for MADE, Borden, and Cape Cod were multiscaling from 0.15 to 1.35 m, 0.05 to 0.5 m, and 0.15 to 0.9 m, respectively. They were multiscaling in the horizontal direction from 9 to 45 m, 1 to 10 m, and 1 to 17 m, respectively. The multiscaling was also anisotropic. Evidence of scaling was poorest for the horizontal direction of the MADE site, and it spanned half an order of magnitude. Such results compel one to treat multifractality in the horizontal direction of MADE as supported by heuristic arguments, rather than by pure statistical evaluation. We fitted a multifractal model to the data and estimated its parameters. We found the underlying statistics of all data to be non-Gaussian, and the model capable of reproducing the probability distribution of K data, especially the negative skewness of log K. We also generated two-dimensional isotropic multifractal fields illustrating the role of the parameters of the selected multifractal model.

Scaling analyses on geophysical measurements of electrical conductivity, gamma radiation, and magnetic fields, at the Oak Ridge Reservation were conducted. The electrical conductivity and magnetic data exhibited multifractality in the north-south and eastwest directions. The radiation data were observed to be non-scaling; a variogram with a sill was found to be more appropriate. The scaling of the EC and magnetic was generally within a range smaller than the maximum distance selected, as periodicity dominated at the larger distances. The electrical conductivity had anisotropy in the scaling of their variograms. But the magnetic data appear to have an isotropic scaling. The underlying statistics of the fields were near Gaussian for the electrical conductivity, but essentially Gaussian for the magnetic data. In environmental hydrogeology, knowledge of the spatial distribution of the intrinsic permeability, K, is very helpful in understanding the transport and spreading of contaminant plumes. Our previous studies have shown that the subsurface permeability, K, is multifractal. Detailed measurement of K is costly. Hence, large data sets of value collected both on a fine scale and over large distances are rare. In this study, we hypothesize that geophysical data could be used indirectly as a surrogate measurement for K, for obtaining statistical information on scale limited K data, and perhaps, directly at sites where K and electrical conductivity are correlated.

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