A The estimates a = 1.287 and B = 0.096 will be treated in what follows as though they were true values. It is shown in the next section that 8 plays no role in estimating the error variance of kriging estimates. A BRIEF OUTLINE OF KRIGING THEORY We now relate our model to the given field procedure outlined above. As a general rule, let us denote by F(v) the mean value of F(x) over a volume (or area) v. We are interested in P_ (v) where v is chosen here to be a 100- x 100-foot cell. As the effect of errors or microstructures averages out over an area, we have Po™ = P(v) and FU) = F(v). Hence, from Equation 4, P(v) = aF(v) + B + TC) and we choose an estimator of the form * x * P (v) = aF (v) +B +T (Vv) > (6) * * where aF (v) + 8 is the Pu guess field and T (v) is the block correction * * term. F (v) and T (v) can be estimated independently from F(x) and T(x) * * * data, respectively. If F (v) and T (v) are unbiased, then so is P (v), and by the independence of T and F, the mean squared errors (MSE) just add up: E[P(v) - P(v)]2 = a2B[F\(v) - F(v)]2 + EIT (wv) - T(v)]? The MSE is a minimum when both terms on the right-hand side are a minimum. The estimation procedure can indeed be decomposed into two independent phases. Specifically, F* (vy) and T*(v) may be constructed by the kriging method (Matheron, 1963, 1965, 1969, 1971, 1973; Delfiner and Delhomme, 1973; Delfiner, 1973). A brief outline of the theory of kriging (which gives minimum mean square error unbiased estimates) is given below. For further details, the reader is referred to the references. Suppose we want to estimate the mean value over v, say Z(v), of a given variable Z. The kriging estimator Z*(v) is a moving average predictor N Z¥(v) = > ry 2(x,) i=l > where the weights a are chosen so as to achieve 376