Principles of Probabilistic Regional Mineral Resource Estimation

Five principal sources of uncertainty in quantitative mineral resource estimation are listed and illustrated by means of a simple example (mosaic model) and a case history study for large copper deposits in the Abitibi area of the Canadian Shield. Abitibi copper potential originally was estimated on the basis of 1968 estimates of production and reserves totalling 3.12 Mt Cu. This prognostication now could be evaluated on the basis of 2008 copper production and reserves totalling 9.50 Mt Cu. An earlier hindsight study performed on the basis of 1977 data (totalling 5.23 Mt Cu) showed seven new discoveries occurring either in the immediate vicinities of known deposits or on broad regional copper anomalies predicted from the 1968 inputs. By 1977, the global geographic distribution pattern of large copper deposits in the Abitibi area had stabilized. During the next 30 years, new copper was essentially found close to existing deposits, much of it deeper down in the Earth's crust. In this paper, uncertainties associated with copper ore tonnage are analyzed by comparison of 2008 data with 1968 data using (a) log-log plots of size versus rank, and (b) lognormal QQ-plots. Straight lines fitted by least squares on these plots show that 1968 slopes provide good estimates of 2008 slopes but 1968 intercepts are much less than 2008 intercepts. In each linear log-weight versus log-rank plot, the slope is related to fractal dimension of a Pareto frequency distribution, and in a lognormal QQ-plot it is determined by logarithmic variance. The difference between 2008 and 1968 intercepts represents the increase in copper ore production and reserves from 1968 to 2008. The Pareto model fits actual copper and massive sulphides increase over the past 40 years better than the lognormal frequency distribution model for 10 km×10 km cells on favorable environments in the Abitibi area.