Variogram

Summary

The variogram of a spatial random field measures how different the values at two locations are expected to be. It is a function of the displacement between the two locations. It is defined as the variance of the increment $Z(s + h) - Z(s)$, and half of it is called the semivariogram. It exists under weaker assumptions than a covariance function, so it also describes fields without a constant variance, such as the Wiener process. The variogram is the basic input of kriging and of most of geostatistics.