KRIGING IN A FINITE DOMAIN

Adopting a random function model {Z(u), u is-an-element-of study area A} and using the normal equations (kriging) for estimation amounts to assume that the study area A is embedded within a infinite domain. At first glance, this assumption has no inherent limitations since all locations outside A are of no interest and simply not considered. However, there is an interesting and practically important consequence that is reflected in the kriging weights assigned to data contiguously aligned along finite strings; the weights assigned to the endpoints of a string are large since the endpoints inform the infinite half-space beyond the string. These large weights are inappropriate when the finite string has been created by either stratigraphic/geological limits or a finite search neighborhood. This problem will be demonstrated with numerical examples and some partial solutions will be proposed.