Some comments on the scale dependence of the hydraulic conductivity in the presence of nested heterogeneity

Under certain conditions, which are not particularly restrictive, the hydraulic and electrical conductivities of heterogeneous media can be proven to be non-increasing functions of system size. Measurements can suggest otherwise. This discrepancy may be related to scale-dependent definitions of the relevant medium (such as might be appropriate for a fractal structure), inadequate sampling, or to improper inference.