Regionalized Variable Theory

Abstract

Many physical, chemical and biological processes have acted to create the current environment with the result that the variation appears to be random. Practical geostatistics treats the results as if they were the outcomes of correlated random processes and is underpinned by assumptions of stationarity. Variation may be treated as second-order stationary and represented by covariance functions. The somewhat weaker assumption of intrinsic stationarity leads to a more general analysis based on the variogram as a description of the variation. Quasi-stationarity limits stationarity to local areas, and with sufficient data the assumptions can be applied locally. If there is trend then more complex assumptions are needed; these usually comprise a combination of deterministic spatially smooth trend plus random residuals that are spatially correlated and stationary to some degree.