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 Z _V (x₀)=1/V∫Z(x)dx. The data comprises a set of grade values Z(x _i ), in short x _i’ i=1 to N. The grades are defined either on point supports, core supports, etc. They could also be mean grades Z _Vi (x _i ) defined on the supports V _i centered on the points x _i . 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(Z _i )=m.