The growth and size of orogenic gold systems: probability and dynamical behaviour

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Every nonlinear system grows by increments, and the final probability distributions for components of that system emerge from an amalgamation of these increments. The resulting probability distribution depends on the constraints imposed on each increment by the physical and chemical processes that produce the system. Hence there is the potential that the observed probability distribution can reveal information on these processes. Complex systems that grow by competition between the supply and consumption of energy and mass have growth laws that are cumulative probability distributions for their component parts that reflect such competition. We show that the type of probability distribution is characteristic of the endowment of orogenic gold deposits with the sequence: Weibull → Fréchet → gamma → log normal representative of increasing endowment. Further, the differential entropy of the probability distribution is indicative of the quality of the deposit, with low-quality deposits represented by high entropy and high-quality deposits represented by low or negative entropy. The type of probability distribution gives an indication of the processes that operated to produce the deposit. These conclusions hold for mineralisation as well as for the associated alteration assemblages. We suggest that the probability distribution for the mineralisation or the alteration assemblage gives a good indication of the endowment and quality of a deposit from a single drill hole. KEY POINTS A single drill hole from a deposit can provide information on endowment and organisation. Weibull → Fréchet → gamma → log normal probability distributions are representative of increasing gold endowment. The differential entropies of these distributions characterise the organisation of the system.