Fractal and multifractal analyses of sphalerite banding at the Zhaishang gold deposit, western Qinling, China

Abstract

Sphalerite from Carlin–type gold deposits in Zhaishang, western Qinling, China, exhibits colour banding ranging from light to dark brown. Scanning electron microscopy (SEM) and electron-probe microanalysis show that such sphalerite banding is caused by variable Fe incorporation. A linear relationship exists between grey-scale level in photomicrographs and Fe content, thus allowing the extraction of Fe compositional length scales from high spatial resolution banding. Hurst exponents and Lyaponov exponents were measured using this technique. In the outer banding region, the measured Hurst exponents range from 0.20 to 0.41 with an average of 0.32, indicating fractal scaling and anti-persistent behaviour. The values of the Lyaponov exponent range from 0.0254 to 0.0757, with an average of 0.0468, revealing weakly chaotic behaviour in the oscillatory banding pattern. Analysis of the multifractal spectrum from the inner to outer bandings indicates that, compared with the inner and outer areas in the bandings of sphalerite crystals, the middle area exhibits a greater degree of fractal behaviour. The fractal dimensions can be taken as a quantitative indicator of temperature. Furthermore, zoning patterns may reflect chaotic behaviour in a nonlinear non-equilibrium system.