On nonnegative weights of linear kriging estimation - by E.Y. Baafi, Y.C. Kim, and F. Szidarovszky Technical Papers, MINING ENGINEERING, Vol. 38, No. 6 June 1986, pp. 437-442

Philip, G. M. ; Watson, D. F.
Organization: Society for Mining, Metallurgy & Exploration
Pages: 1
Publication Date: Jan 1, 1988
The article cited above reflects the difficulty that is often encountered in interpreting different aspects of kriging. Baafi et al. write: "Due to negative kriging weights, negative block grades may be obtained in some extreme situations, which makes no practical sense." Their solution to this particular problem is to constrain the kriged estimates to data values that have positive weights, i.e., reduce the subset size contributing to the estimation. As Journel (1986, p. 133) has already observed, "Negative weights are no evil." Indeed, they are an ineluctable result of the Lagrangian multipliers in the system of simultaneous equations. The fact that data distant from the estimation point may be given negative weights simply means that the influence of such distant values must be negated because their influence is contradictory to closer values (as illustrated by Baafi et al. in their Figs. 3 and 4). Of course negative kriging weights applied to distant grade values will not in themselves induce negative grade at some central interpolation point. Negative grade values, rather, seem to be a particular artifact of automatic methods of estimation involving accumulations (Philip and Watson, 1985a, 1985b, 1987b). The elimination of negative weights, suggested by Baafi et al., is likely to exacerbate a quite different problem of kriging and piecewise spline interpolation discussed elsewhere (Philip and Watson, 1987a). In interpolating large data sets of scattered observations, changing local subsets or neighborhoods must be selected automatically. Because of the mathematical formulation of kriging and spline interpolation, discontinuities then occur between closely-spaced estimation points as the subset used in the estimation changes. If this subset is reduced in number and size, the discontinuities will be amplified and more common.
Full Article Download:
(70 kb)