My question is regarding the following statement given in this paper on page 51. It reads,

Fundamental to both anisotropy and heterogeneity is the concept of scale. Whether anisotropy and heterogeneity are perceived depends on sample size and sampling resolution. In fact, to say "this rock is anisotropic" is almost meaningless unless scale is also defined-that is, both the size of the sample and the resolution of the sampling method.

Can you help me understand? A concrete example would help me. Say a rock core 7 inches (177.8 mm) in diameter and 12 inches (304.8 mm) in length. It has visible bedding on the mm to cm scale running parallel to its length. Several plugs (20 say) are cut from about the core’s diameter. Let’s say the plug dimension is 1-inch (25.4 mm) diameter x 2-inch (50.8 mm) length. The plugs’ permeabilities are measured, from which the 2x2 permeability tensor for the diametral plane of the parent core is characterized. Let’s say the max-to-min ratio of the two principal values of this 2x2 tensor is 3. How should the size of the sample and the resolution of the sampling method for this result be stated? (If more information is needed, what information is needed?)

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