7.9 Geostatistics (by R. Gebbers)

Geostatistics is used to describe the autocorrelation of one or more variables in the 1D, 2D, and 3D space or even in 4D space-time, to make predictions at unobserved locations, to give information about the accuracy of prediction and to reproduce spatial variability and uncertainty. The shape, the range, and the direction of the spatial autocorrelation is described by the variogram, which is the main tool in linear geostatistics. The origins of geostatistics can be dated back to the early 50 s when the South African mining engineer Daniel G. Krige first published an interpolation method based on spatial dependency of samples. In the 60,s and 70,s, the French mathematician George Matheron developed the theory of regionalized variables which provides the theoretical foundations of Kriges's more practical methods. This theory forms the basis of several procedures for the analysis and estimation of spatially dependent variables, which Matheron called geostatistics. Matheron as well coined the term kriging for spatial interpolation by geostatistical methods.