Hydrothermal mineralising systems as chemical reactors: Wavelet analysis, multifractals and correlations

• Hydrothermal systems are non-equilibrium chemical reactors that exhibit chaos.
• The resulting irregularity can be quantified using wavelet transforms.
• Chaotic behaviour leads to multifractal geometries for alteration and mineralisation.
• Long range correlations are developed at scales of about 1 m and above.
• High and low grade ore bodies are characterised by distinct multifractal spectra.

Hydrothermal mineralising systems are discussed as large, open flow chemical reactors held far from equilibrium during their life-time by deformation and the influx of heat, fluid and dissolved chemical species. As such they are nonlinear dynamical systems and need to be analysed using the tools that have been developed for such systems. Hydrothermal systems undergo a number of phase transitions during their evolution and this paper focuses on methods for characterising these transitions in a quantitative manner and establishing whether they resemble either abrupt or continuous (critical) phase transitions or whether they have some other kind of nature. Critical phase transitions are characterised by long range correlations for some parameter characteristic of the system, power-law probability distributions, so that there is no characteristic length scale, and a high sensitivity to perturbations. The transitions undergone in mineralised hydrothermal systems are: (i) widespread, non-localised mineral alteration involving exothermic mineral reactions that produce hydrous silicate phases, carbonates and iron-oxides, (ii) strongly localised veining, brecciation and/or stock-work formation, (iii) a series of localised endothermic mineral reactions involving the formation of non-hydrous silicates, sulphides and metals such as gold, (iv) multiple overprinting repetitions of transitions (ii) and (iii). We quantify aspects of these transitions in some gold deposits from the Yilgarn craton of Western Australia using wavelet transforms. This technique is convenient and fast. It enables one to establish if the transition is multifractal (and if so, quantify the multifractal, or singularity, spectrum) and to determine the scale dependence of long range correlations or anti-correlations. Other aspects of the spectrum enable quantitative distinctions between sub-critical, critical and super-critical systems. The availability of long drill holes with detailed chemical analyses and mineral abundances derived from hyperspectral data enables individual ore bodies to be characterised rapidly in a quantitative manner and constraints placed on whether the various transitions are possibly critical or of some other form. We also present some simple nonlinear models, including numerical simulation, self-organised branching and multiplicative cascade processes that produce the multifractal character and correlation scaling relations observed in these data sets. Distinctions between systems that are strongly and weakly mineralised are discussed.

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