 Intrinsically stationary random field

An intrinsically stationary random field has constant mean and finite increment variances depending only on displacement. Its semivariogram is $\gamma (h)=\frac{1}{2}\mathrm{Var}[Z(s+h)-Z(s)]$. 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.