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 Quadrilatero Ferrifero 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 Quadrilatero Ferrifero 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).
Highlights
The modern mineral systems concept comprises all geological factors that combine to form an ore deposit, including assembly, transportation, and ore accumulation (Wyborn et al 1994)
Energy release follows a scale-invariant power-law behavior, with spatial fractal geometry (Bak 1996). This behavior can be seen in mature mineral provinces, where the distribution of mineral deposits follows a power-law distribution when deposits are ranked in order of decreasing size (Hronsky and Groves 2008)
The Rio das Velhas Supergroup hosts the majority of the largest gold deposits in the Quadrilátero Ferrífero Province (Figure 1)
Summary
The modern mineral systems concept comprises all geological factors that combine to form an ore deposit, including assembly, transportation, and ore accumulation (Wyborn et al 1994) Even when these factors are well understood, ore-forming systems occur in unpredictable, complex patterns, focused on maximizing entropy, i.e., ore-formation represents a self-organized critical system (Hronsky 2011). In such systems, energy release follows a scale-invariant power-law behavior, with spatial fractal geometry (Bak 1996). Similar distributions are present where a free and natural competition mechanism exists, such as economics, finance, social sciences and physics (Buchanan 2008; Haldar 2018; Newman 2005) Since these events, ranked by their frequency in descending order, follow a power-law, we can say that they obey Zipf’s law (Zipf 1949). We discuss some premises and limitations of Zipf’s law, as applied to estimate the residual gold endowment of Quadrilátero Ferrífero Province
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