When are relative variograms useful in geostatistics?

Abstract

The relative variogram has been employed as a tool for correcting a simple kind of nonstationarity, namely that in which local variance is proportional to local mean squared. In the past, this has been linked in a vague way to the lognormal distribution, although if {Z_t; t ∈ D}is strongly stationary and normal over a domain D,then clearly {exp (Z_t); t ∈ D}will stillbe stationary, but lognormal. The appropriate link is made in this article through a universal transformation principle. More general situations are considered, leading to the use of a “scaled variogram.”