Spatial interpolation: an overview

The interpolation of spatial data has been considered in many different forms. The various forms of kriging are among the best known in the earth sciences although techniques such as inverse distance weighting were and are in use for spatially located data. In the numerical analysis literature various forms of splines and more recently radial basis functions have been developed and used. Because these techniques have been developed in very different contexts the relationship between them has not always been apparent. Various forms of kriging are considered as well as kernel estimators, splines and radial basis functions. By using the dual form of kriging and the positive definiteness property of the variogram connections are shown between splines, kriging and radial basis functions. One of the distinctions between kriging and other interpolators is the incorporation of the support of the samples and explicit estimation of linear functionals such as spatial integrals.