{title2=$\gamma(h)$}

For an <intrinsically stationary random field>, the <semivariogram> is $\gamma(h)=\tfrac12\operatorname{Var}[Z(s+h)-Z(s)]$. It is even and vanishes at zero. With constant mean, a second-order stationary field has $\gamma(h)=C(0)-C(h)$. An isotropic model writes it as a function of nonnegative distance.


Semivariogram

An intrinsically stationary random field has constant mean and finite increment <variances> depending only on displacement. Its <semivariogram> is $\gamma(h)=\tfrac12\operatorname{Var}[Z(s+h)-Z(s)]$. Second-order stationarity implies this property, but the converse can fail: subtracting the value at a fixed origin from a stationary field preserves increments and makes marginal <variance> vary with location.


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 Incoming links: Intrinsically stationary random field