The properties of feldspar and quartze are studied in this article from a fractal point of view using gray-scale micro-images of granite samples collected at the Fangshan (房山) granite body in Hebei (河北) Province, China, which can be regarded as an ideal granite in the sense of Vistelius. We found that there exist power-law relationships between the eigenvalues of the gray-scale matrices and their ranks for the feldspar and quartz. The fractal model used here is a λ-R model similar to the N-λ model proposed by Qiuming Cheng in 2005. Meanwhile, we found that average variances for the gray-scale matrices of feldspar are larger than those of quartz on the same sections, and this may be useful for auto-identification of feldspar and quartz as well as other minerals.
The separation of anomalies from geochemical background is an important part of data analysis because lack of such identifications might have profound influence on or even distort the final analysis results. In this article, 1 672 geochemical analytical data of 11 elements, including Cu, Mo, Ag, Sn, and others, from a region within Tibet, South China, are used as one example. Together with the traditional anomaly recognition method of using the iterative mean ±2σ, local multifractality theory has been utilized to delineate the ranges of geochemical anomalies of the elements. To different degrees, on the basis of original data mapping, C-A fractal analysis and singularity exponents, Sn differs from the other 10 elements. Moreover, geochemical mapping results based on values of the multifractal asymmetry index for all elements delineate the highly anomalous area. Similar to other 10 elements, the anomalous areas of Sn delineated by the asymmetry index distribute along the main structure orientations. According to the asymmetry indexes, the 11 elements could be classified into 3 groups: (1)Ag and Au, (2) As-Sb-Cu-Pb-Zn-Mo, and (3) Sn-Bi-W. This paragenetic association of elements can be used to interpret possible origins of mineralization, which is in agreement with petrological analysis and field survey results.
