In the residual kriging procedure, instead of kriging Z (x) directly, a regression analysis is first carried out between Z (x) and some external variables. Then, the residuals r (x) and the spatial field Z * (x) can be estimated for each point x generated from the regression results. The new variable r (x) retains the spatial variability of Z (x), but some of the variability has been removed, as a result of external information used in the regression model.
After this analysis, a kriging procedure is used for the residuals r(x) . As a results, a map of r(x), representing the corrections to apply to the regression model, is obtained. The final estimates Z(x) are obtained by combining both Z * (x) and r(x) estimates separately on the kriging grid:
Z( x) = Z * (x) + r( x).