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Oberst S, Niven RK, Lester DR, et al. Detection of unstable periodic orbits in mineralising geological systems. Chaos. 2018;28(8):085711doi: 10.1063/1.5024134.
Oberst, S., Niven, R. K., Lester, D. R., Ord, A., Hobbs, B., & Hoffmann, N. (2018). Detection of unstable periodic orbits in mineralising geological systems. Chaos (Woodbury, N.Y.), 28(8), 085711. https://doi.org/10.1063/1.5024134
Oberst, S, et al. "Detection of unstable periodic orbits in mineralising geological systems." Chaos (Woodbury, N.Y.) vol. 28,8 (2018): 085711. doi: https://doi.org/10.1063/1.5024134
Oberst S, Niven RK, Lester DR, Ord A, Hobbs B, Hoffmann N. Detection of unstable periodic orbits in mineralising geological systems. Chaos. 2018 Aug;28(8):085711. doi: 10.1063/1.5024134. PMID: 30180652.
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Chaos. 2018 Aug;28(8):085711. doi: 10.1063/1.5024134.

Detection of unstable periodic orbits in mineralising geological systems.

Chaos (Woodbury, N.Y.)

S Oberst, R K Niven, D R Lester, A Ord, B Hobbs, N Hoffmann

Affiliations

  1. Centre for Audio, Acoustics and Vibration, University of Technology Sydney, Broadway, Sydney, New South Wales 2007, Australia.
  2. School of Engineering and Information Technology, The University of New South Wales, Canberra, Northcott Drive, Campbell, Australian Capital Territory 2600, Australia.
  3. School of Engineering, Royal Melbourne Institute of Technology, GPO Box 2476, Melbourne, Victoria 3001, Australia.
  4. Centre for Exploration Targeting, The University of Western Australia, 35 Stirling Highway Crawley, Perth, Western Australia 6009, Australia.
  5. Commonwealth Scientific and Industrial Research Organisation, 26 Dick Perry Ave., Kensington, Western Australia 6152, Australia.
  6. Dynamics Group, Complex Systems, Mechanical Engineering, Technical University Hamburg, Schlossmühlendamm 30, 21073 Hamburg, Germany.

PMID: 30180652 DOI: 10.1063/1.5024134

Abstract

Worldwide, mineral exploration is suffering from rising capital costs, due to the depletion of readily recoverable reserves and the need to discover and assess more inaccessible or geologically complex deposits. For gold exploration, this problem is particularly acute. We propose an innovative approach to mineral exploration and orebody characterisation, based on the analysis of geological core data as a spatial dynamical system, using the mathematical tools of dynamical system analysis. This approach is highly relevant for orogenic gold deposits, which-in contrast to systems formed at chemical equilibrium-exhibit many features of nonlinear dynamical systems, including episodic fluctuations on various length and time scales. Feedback relationships between thermo-chemical and deformation processes produce recurrent fluid temperatures and pressures and the deposition of vein-filling minerals such as pyrite and gold. We therefore relax the typical assumption of chemical equilibrium and analyse the underlying processes as aseismic, non-adiabatic, and inherent to a hydrothermal, nonlinear dynamical open-flow chemical reactor. These processes are approximated using the Gray-Scott model of reaction-diffusion as a complex toy system, which captures some of the features of the underlying mineralisation processes, including the spatiotemporal Turing patterns of unsteady chemical reactions. By use of this analysis, we demonstrate the capability of recurrence plots, recurrence power spectra, and recurrence time probabilities to detect underlying unstable periodic orbits as one sign of deterministic dynamics and their robustness for the analysis of data contaminated by noise. Recurrence plot based quantification is then applied to three mineral concentrations in the core data from the Sunrise Dam gold deposit in the Yilgarn region of Western Australia. Using a moving window, we reveal the episodic recurring low-dimensional dynamic structures and the period doubling route to instability with depth, embedded in and originating from higher-dimensional processes of the complex mineralisation system.

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