OSCILLATORY ZONING IN AN AGATE FROM KAZAKHSTAN: AUTOCORRELATION FUNCTIONS AND FRACTAL STATISTICS OF TRACE ELEMENT DISTRIBUTIONS

Abstract

The results of numerical treatment of proton-induced X-ray emission (PIXE) data for trace element (Fe, Sr, Zn) contents in agate from the environment surrounding the city of Pavlodar (Kazakhstan) are presented in this paper. In order to mathematically characterize the zoning pattern, fractal geometry, correlation, and Fourier analyses were used for investigation of trace element distributions. Autocorrelation calculations show that oscillations in Fe, Sr, and Zn along the profile have periodic components. It is shown that trace element distributions can be described in terms of fractal geometry. The measured Hurst exponents by methods of the width and the power spectrum are mostly in the range 0.14–0.28, indicating fractal scaling and antipersistent behavior of trace elements along the profile.