Anisotropic Scaling of Berea Sandstone Log Air Permeability Statistics

We analyze directional dependence and scaling of air log permeability statistics characterizing minipermeameter measurements by Tidwell and Wilson on the faces of a 30 by 30 by 30 cm(3) size unsaturated block of Berea sandstone. We find distinct differences between the statistics and scaling behaviors of data measured on faces parallel and normal to bedding, and of incremental measurements in three orthogonal directions along these faces. Whereas the distribution on of data and their increments parallel to bedding are heavy tailed, those of increments normal to bedding are Gaussian. Order q sample structure functions of increments parallel to bedding scale as powers xi(q) of directional lag, s(d), over limited ranges of s(d). Using moment and extended self-similarity methods of analysis we find xi(q) to be generally nonlinear in q, tending to be concave in q on faces normal to bedding and convex on faces parallel to bedding. Whereas the literature attributes nonlinear scaling of xi(q) with q to multifractals or fractional Laplace motions, we find the data to be consistent with sub-Gaussian random fields subordinated to truncated (monofractal, self-affine) fractional Gaussian noise. The increments exhibit negative statistical dependence (antipersistence) that varies with direction parallel to bedding and is more pronounced on faces parallel than normal to bedding.