Grade estimation of Zu2 Jajarm deposit by considering imprecise variogram model parameters based on the extension principle

Abstract

Nowadays, kriging has been accepted as the most common method of grade estimation in mineral resource evaluation stage. Access to the crisp assay data and a variogram model are the necessary means for the utilization of this method. Since fitting a crisp variogram model is generally difficult, if not impossible, the fitted theoretical model is usually tainted with uncertainty due to various reasons especially limitation of drill holes number. Although the geostatistical kriging model is incapable of taking into account the uncertainties, the fuzzy kriging method (presented based on the fuzzy concept) is capable of calculating the effects of uncertainties on the fitted model (and even on the assay data). To evaluate the Zu2 Jajarm mineral resource, effort was made to use Bardossy’s fuzzy kriging method (proposed based on the extension principle) instead of ordinary kriging because of high uncertainties tainted with fitted variogram model. Since no comprehensive software existed to be used for this method, the “FuzzyKrig” was developed for the required calculations. A key merit of the fuzzy kriging method compared with the general, simple, ordinary, and log- kriging is that it presents, as a parameter, the width of the fuzzy number of every block as a criterion for the evaluation of the uncertainties in the estimation process. The advantage of this parameter is that, unlike the estimation variance, it depends not only on the data arrangement, but also on the grade data and can, therefore, play a key role in risk management studies.