A fundamental assumption for geostatistical methods is that any two locations that are a similar distance and direction from each other should have a similar value difference squared. In a spatial setting, stationarity is used to obtain the necessary replication.
Note: with only one set of measured values, there is no hope of knowing the dependence rules without being told what they are. However, through contined observations of numerous samples, dependencies become apparent. In the process of replication, dependence rules or prediction rules can be derived and the variation and uncertainty of the predicted values can be understood from repeated observations.
see mean stationarity , second-order stationarity, intrinsic stationarity