I was always puzzled by the definition of pseudo-cross-variograms in the presence of physical units.

Given Zi and Zj two variables representing permeability and thermal conductivity for example, the quantity Zi - Zj is not well defined, yet it is what pseudo-cross-variograms rely on.

Many papers discuss the advantanges of pseudo-cross-variograms over cross-variograms, but none seem to give an explanation to why it is reasonable to consider this quantity to start with. Is there an implicit normalization assumption Zi* = Zi / ki and Zj* = Zj / kj with ki and kj characteristic values in the support of Zi and Zj?

I appreciate if someone can clarify the hidden assumptions in the theory. A good paper to start the discussion is Myers 1991, Pseudo-Cross Variograms, Positive Definiteness, and Cokriging. Mathematical Geology, Vol 23, No. 6.