## Kriging with Surface III

Universal kriging is a procedure that can be used to estimate values of a surface at the nodes of a regular grid from irregularly spaced data points. Kriging, developed by Prof. Georges Matheron and his associates at the Institute for Mathematical Morphology in Fontainebleau, France, is unlike other gridding methods because it makes explicit use of the specific autocorrelation between observations on the surface being mapped. If the surface is second-order stationary, or can be made stationary by some transformation, the spatial autocorrelation will express the degree of dependence between all locations on the surface, and most particularly between observations and grid nodes.
Under the statistical theory which includes universal kriging, a single-valued, continuous, mappable property is called a "regionalized variable" and is considered to consist of two parts--a drift, or expected value, and a residual, or deviation from the drift. The drift may be modeled by a local polynomial function within a neighborhood that is analogous to a local trend surface. If the drift is removed, the residual surface can be regarded as first-order stationary in a statistical sense.

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