Application of Zipf’s law to estimate undiscovered Gold endowment in the Quadrilátero Ferrífero Province, Brazil

Abstract

Ore-forming processes act as self-organizing critical systems. These systems exist in an unbalanced nature, such that energy-release can occur as a scale-invariant power-law behavior when a certain threshold is exceeded. In ore-forming systems, the energy released from multiple transient pulses of over-pressured fluid appears to follow a power-law, since the distribution of mineral deposits in mature provinces have been shown to obey Zipf’s law. Zipf’s law represents a statistical relationship between the size and rank of a discrete phenomenon. In this work, we present the application of Zipf’s law in estimating the undiscovered gold endowment of the Quadrilátero Ferrífero Province in Brazil. In addition, we conducted several statistical tests to validate the application of Zipf’s law and discussed its limitations regarding smaller deposits. The Kolmogorov-Smirnov’s minimum distance was presented as an alternative to defining the lower boundary of the Zipf’s law’s domain, rather than using an economic cut-off. Our results estimate the maturity of the Quadrilátero Ferrífero Province to be 65%, with potential for the discovery of at least 749 t of gold, comprising 28 deposits larger than 8 t (totaling 519 t), and 2 deposits larger than 40 t (totaling 122 t).