The Hurst exponent as a tool for the description of magma field heterogeneity reflected in the geochemistry of growing crystals

Andrzej Domonik, Ewa Slaby, Michal Smigielski


Trace element behaviour during crystallization of three alkali feldspar crystals of mixed origin was investigated. The first crystal (gm1) was growing under an intensive magma mixing regime in an active region of an inhomogeneous magmatic field. The second crystal (ref) was growing in a coherent region of this field and the third one (gm2) was growing under moderate progress in magma mixing, with the process being close to completion. The Hurst exponent (H) was used as a tool for the description of the local heterogeneities of the magma field during the mixing process. Values of H were calculated for compatible trace element patterns along each traverse for each crystal. The gm1 crystal is strongly zoned. The value of the Hurst exponent (H) for zones reflecting intensive chemical mixing varies between 0.06 and 0.47. it emphasizes strong anti-persistent behaviour of elements during crystallization. The zones that grew in a slightly contaminated felsic magma exhibit H > 0.5. it means that the process goes over a longer path than a random walk and shows increasing persistence in element behaviour with decreasing hybridization. Similarly, zones crystallized in magma regions compositionally located close to coherent characteristic or in active domains featuring a high homogenization (crystals gm2, ref) show higher H values.


Fractals; Hurst exponent; magma mixing; geochemistry; Persistent element behaviour; Anti-persistent element behavior

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