Multifractal Modeling of Worldwide and Canadian Metal Size-Frequency Distributions

Abstract

The Pareto-lognormal frequency distribution, which can result from multifractal cascade modeling, previously was shown to be useful to describe the worldwide size-frequency distributions of metals including copper, zinc, gold and silver in ore deposits. In this paper, it is shown that the model also can be used for the size-frequency distributions of these metals in Canada which covers 6.6% of the continental crust. Like their worldwide equivalents, these Canadian deposits show two significant departures from the Pareto-lognormal model: (1) there are too many small deposits, and (2) there are too few deposits in the transition zone between the central lognormal and the upper tail Pareto describing the size-frequency distribution of the largest deposits. Probable causes of these departures are: (1) historically, relatively many small ore deposits were mined before bulk mining methods became available in the twentieth century, and (2) economically, giant and supergiant deposits are preferred for mining and these have strongest geophysical and geochemical anomalies. It is shown that there probably exist many large deposits that have not been discovered or mined. Although overall the samples of the size-frequency distributions are very large, frequencies uncertainties associated with the largest deposits are relatively small and it remains difficult to estimate more precisely how many undiscovered mineral deposits there are in the upper tails of the size-frequency distributions of the metals considered.