Evaluating uncertainty in kimberlite pipe volume by simulating geometry in cylindrical coordinates

A significant source of uncertainty in the diamond resource contained in kimberlite pipes is the volume of the pipes. Often the material within a pipe will be mined as ore, leaving the actual geometry of the pipe as a significant source of uncertainty. It is desirable to use stochastic techniques, rather than deterministic methods, to model pipe geometry because stochastic techniques generate multiple realizations that are reproducible and can be used to assess uncertainty in pipe geometry. The proposed methodology uses sequential Gaussian simulation of pierce point locations interpreted from drillholes through a kimberlite pipe. Kimberlite pipes are approximately cylindrical in shape; therefore, the data are transformed to cylindrical coordinates to facilitate the simulation of pipe geometry. Rather than using xyz coordinates to define the pierce points, z, ??and pipe radius are used. The radius variable can be simulated in z-??space to generate multiple realizations of pipe volume. Uncertainty in the volume of the pipe can then be evaluated. This methodology is demonstrated with a kimberlite pipe at BHP Billiton’s Ekati diamond mine.