Semivariogram

In spatial statistics the theoretical variogram ${\displaystyle 2\gamma (x,y)}$ is a function describing the degree of spatial dependence of a spatial random field or ${\displaystyle Z(x)}$.

As a concrete example from the field of gold mining, a variogram will give a measure of how much two samples taken from the mining area will vary in gold percentage depending on the distance between those samples. Samples taken far apart will vary more than samples taken close to each other.

The variogram is defined as the variance of the difference between field values at two locations (${\displaystyle x}$ and ${\displaystyle y}$) across realizations of the field (Cressie 1993):

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