In order to assess the uncertainty or variability of geostatistical estimates based on incomplete data, it is now usual to adopt a probabilistic model of a spatially correlated random field. The fact that geographically close measurements resemble one another on the average, more than widely separated measurements, may be modelled in at least two different ways. In the first model we suppose that the greater resemblance of nearby measurements is due mainly to the greater resemblance of their mean values. The emphasis in this approach is usually on obtaining an estimate of the mean function (drift, trend surface) in a class of simply described, e.g., polynomial, mean functions. The secondary emphasis is placed on estimation of the statistical behavior of the residuals from the mean function. In the second model we suppose a priori that the mean is constant and that the greater resemblance of nearby measurements is due mainly to the strong correlation of their residuals. The practical consequences of choosing between these two basic approaches will be examined in the context of geographic interpolation between observations.