The effect of the variogram estimation on pit-limit design

In transitional mineralization, the sill of the underlying variogram is relatively easily estimated, but the estimation of the nugget effect may be more difficult. This study aims to determine for massive copper deposits just how sensitive the estimations of ore reserve, economic copper content, total net value, and ultimate pit limits are to the errors of estimation in the nugget effect of the spherical variogram model. A massive copper deposit which has a log-normal distribution and a spherical variogram was simulated on a rectangular grid using the turning bands method. By using the three dimensional random kriging method, the mean block grades were estimated at four different sampling densities. The ultimate pit-limits were determined by using the two-dimensional dynamic programming algorithm. To calculate the estimation errors, the values obtained by using the actual nugget effect and structured component values were deducted from the estimations obtained using the incorrect nugget effect and structured component values. For isotropic massive copper deposits, it was found that the ratio of the nugget effect to the structured component of the spherical variogram has no significant effect on either the block grades estimated by the kriging method or on the ultimate pit limits.