Quantification of uncertainties in geological modelling of kimberlite pipes

Future development of kimberlite mines is now focused on mining at deeper levels. The consequences are increased difficulty and costs of the mining operations. The decisions on investments require accurate resource evaluation and quantification of the risk. In the decision process the first step consists in choosing the number of boreholes sampling the pipe relative to the level of uncertainty that can be accepted. The uncertainty in the volumes of rocks of different types can be assessed as soon as we can estimate these volumes from a given borehole layout and calculate the error by means of its variance for instance. In theory this can be achieved by using geostatistical techniques (‘transitive theory’), but in practice the calculation of the error on volumes can be achieved in very particular cases, assuming some regular sampling patterns. A different approach has been chosen based on simulations, giving maximum flexibility to reproduce the reality of the sampling procedure. The idea is to simulate the geometry of several ‘possible’ pipes with their internal geology and estimate them by kriging. Several experimental errors are obtained on which risk analysis can be performed. The aim is to find a feasible method to perform the simulations with reasonable chance to correctly represent the reality, without data on the pipe extension. The methodology applied is based on some hypotheses that can be assessed by the geologist as well as by the geostatistician. The procedure assumes a geological model based on current knowledge including appropriate geostatistical variation. What make these simulations specific and powerful in this case comes from the fact that the boundaries between the different rock-types can be simulated using a transformation of the real 3D space into a 2D space defined by means of polar coordinates. Ultimate transformations to account for smoother variations with morphological transformations allow the generation of realistic pipe geometries on which sampling pattern can be used to evaluate the estimation errors. By estimating the simulated pipe geometries with different boreholes layouts a risk curve expressing the uncertainty in the volumes of the different rock-types versus the number of holes can be developed.