Pareto-Lognormal Modeling of Known and Unknown Metal Resources. II. Method Refinement and Further Applications

Pareto-lognormal modeling of worldwide metal deposit size–frequency distributions was proposed in an earlier paper (Agterberg in Nat Resour 26:3–20, 2017). In the current paper, the approach is applied to four metals (Cu, Zn, Au and Ag) and a number of model improvements are described and illustrated in detail for copper and gold. The new approach has become possible because of the very large inventory of worldwide metal deposit data recently published by Patino Douce (Nat Resour 25:97–124, 2016c). Worldwide metal deposits for Cu, Zn and Ag follow basic lognormal size–frequency distributions that form straight lines on lognormal Q–Q plots. Au deposits show a departure from the straight-line model in the vicinity of their median size. Both largest and smallest deposits for the four metals taken as examples exhibit hyperbolic size–frequency relations and their Pareto coefficients are determined by fitting straight lines on log rank–log size plots. As originally pointed out by Patino Douce (Nat Resour Res 25:365–387, 2016d), the upper Pareto tail cannot be distinguished clearly from the tail of what would be a secondary lognormal distribution. The method previously used in Agterberg (2017) for fitting the bridge function separating the largest deposit size–frequency Pareto tail from the basic lognormal is significantly improved in this paper. A new method is presented for estimating the approximate deposit size value at which the upper tail Pareto comes into effect. Although a theoretical explanation of the proposed Pareto-lognormal distribution model is not a required condition for its applicability, it is shown that existing double Pareto-lognormal models based on Brownian motion generalizations of the multiplicative central limit theorem are not applicable to worldwide metal deposits. Neither are various upper tail frequency amplification models in their present form. Although a physicochemical explanation remains possible, it is argued that preferential mining of the largest and smallest orebodies can have economic historical reasons. The size–frequency distribution of uranium can be regarded as lognormal without Pareto tails. At the end of the paper, it is shown that original copper deposit size data can be used for forward projection of discovery trends toward the end of this century.