Conditional simulation of a placer gold deposit using sequential Gaussian, histogram-matching and simulated annealing algorithms - SME Transactions 2009

Ore grade modeling of a placer gold deposit is considered a challenging problem even today. Typically, gold-bearing deposits show extremely erratic and unpredictable grade variation. This is principally because of isolated occurrences of gold metal within a few high-grade pockets. Because of sporadic fluctuation of high-gold-grade distribution, the overall spatial continuity of the deposit becomes poor. This type of variation is often described by a lognormal or highly skewed frequency distribution, and the spatial continuity of the deposit is characteristically represented by a variogram model that exhibits a high nugget component. Further complicating the matter is the sparse availability of drillholes to capture such erratic variation. Due to the prohibitive cost of drilling, gold grade and reserve estimations are typically carried out using insufficient exploratory data. Use of a traditional estimation technique on limited data often produces an unreliable ore grade model. Kriging and its nonlinear variation, lognormal kriging, are frequently used in gold deposit modeling (Rendu, 1979; Journel, 1980); however, kriging is flawed by the smoothing effect. Moreover, though kriging is known to be globally unbiased, it is not free from conditional bias. As a result, if a deposit is modeled using the traditional kriging technique, a high-grade zone can be predicted to be a low-grade zone and vice versa. Predicting high grade as low grade results in a missed opportunity to exploit profitable ore. On the other hand, prediction of low-grade ore as high-grade ore might result in financial loss for a mining operation. Thus, the use of kriging for ore grade mapping of a gold deposit may not be recommended. Estimation techniques (including kriging) can produce an estimate with minimum error in a minimum-error variance sense. However, no matter which estimation technique is used for grade modeling of a highly erratic deposit like gold, the error margin is bound to be high. Therefore, any grade prediction made for an unknown location is associated with high uncertainty. Since various mine-planning operations, including derivation of grade tonnage curve, pit design and economic analysis of the deposit, are based on estimated grade rather than true grade, a mining project evaluation that depends upon estimation will be subject to considerable risk. Thus, the successful design of a mining project not only depends upon accurate grade estimates, but also upon accurate assessment of uncertainty, for predictive grade is equally important. Although the kriging standard deviation is used as an indicator of uncertainty for prediction, it is flawed by characteristics related to a data-independence property. This study, therefore, investigates the stochastic simulation technique of conditional simulation for ore grade modeling of a placer gold deposit at Nome, Alaska. It is expected that the research will provide a better solution to ore-grade deposit modeling than the kriging technique because (1) conditional simulation preserves spatial continuity as well as reproduces the data histogram, thus avoiding the smoothing problem; and (2) generation of multiple realizations helps to accurately quantify the uncertainty about grade values in the deposit.