Kriging Variance and Kriging Procedure

Abstract

In order to derive Kriging Variance, we proceed as follows: we assume that Z′ (x) — the random function is defined on a point support and is second order stationary. It follows that E[Z(x)]=m, and the covariance, defined as E[Z(x+h)Z(x)]−m2=C(h) exists. We know that E[{Z(x+h)−Z(x)}2]=2γ(h). We are interested in the mean ZV(x0)=1/V∫Z(x)dx. The data comprises a set of grade values Z(xi), in short xi’i=1 to N. The grades are defined either on point supports, core supports, etc. They could also be mean grades ZVi(xi) defined on the supports Vi centered on the points xi. It is possible that the N supports could be different from each other. Under the assumption of stationarity, the expectation of these data is m. That is, E(Zi)=m.