Statistical Modeling of Regional and Worldwide Size-Frequency Distributions of Metal Deposits

Publicly available large metal deposit size data bases allow new kinds of statistical modeling of regional and worldwide metal resources. The two models most frequently used are lognormal size-grade and Pareto upper tail modeling. These two approaches can be combined with one another in applications of the Pareto-lognormal size-frequency distribution model. The six metals considered in this chapter are copper, zinc, lead, nickel, molybdenum and silver. The worldwide metal size-frequency distributions for these metals are similar indicating that a central, basic lognormal distribution is flanked by two Pareto distributions from which it is separated by upper and lower tail bridge functions. The lower tail Pareto distribution shows an excess of small deposits which are not economically important. Number frequencies of the upper tail Pareto are mostly less than those of the basic lognormal. Parameters of regional metal size-frequency distributions are probably less than those of the worldwide distributions. Uranium differs from other metals in that its worldwide size-frequency distribution is approximately lognormal. This may indicate that the lognormal model remains valid as a standard model of size-frequency distribution not only for uranium but also for the metals considered in this chapter, which are predominantly mined from hydrothermal and porphyry-type orebodies. A new version of the model of de Wijs may provide a framework for explaining differences between regional and worldwide distributions. The Pareto tails may reflect history of mining methods with bulk mining taking over from earlier methods in the 20th century. A new method of estimating the Pareto coefficients of the economically important upper tails of the metal size-frequency distributions is presented. A non-parametric method for long-term projection of future metal resource on the basis of past discovery trend is illustrated for copper.