Mononodal indicator variography—Part I: Theory

Abstract

For any distribution of grades, a particular cutoff grade is shown here to exist at which the indicator covariance is proportional to the grade covariance to a very high degree of accuracy. The name “mononodal cutoff” is chosen to denote this grade. Its importance for robust grade variography in the presence of a large coefficient of variation—typical of precious metals—derives from the fact that the mononodal indicator variogram is then linearly related to the grade variogram yet is immune to outlier data and is found to be particularly robust under data information reduction. Thus, it is an excellent substitute to model in lieu of a difficult grade variogram. A theoretical expression for the indicator covariance is given as a double series of orthogonal polynomials that have the grade density function as weight function. Leading terms of this series suggest that indicator and grade covariances are first-order proportional, with cutoff grade dependence being carried by the proportionality factor. Kriging equations associated with this indicator covariance lead to cutoff-free kriging weights that are identical to grade kriging weights. This circumstance simplifies indicator kriging used to estimate local point-grade histograms, while at the same time obviating order relations problems.