Abstract
The use of multifractals in the applied sciences has proven useful in the characterization and modeling of complex phenomena. Multifractal theory has also been recently applied to the study and characterization of geochemical distributions, and its relation to spatial statistics clearly stated. The present paper proposes a two-dimensional multifractal model based on a trinomial multiplicative cascade as a proxy to some geochemical distribution. The equations for the generalized dimensions, mass exponent, coarse Lipschitz–Hölder exponent, and multifractal spectrum are derived. This model was tested with an example data set used for geochemical exploration of gold deposits in Northwest Portugal. The element used was arsenic because a large number of sample assays were below detection limit for gold. Arsenic, however, has a positive correlation with gold, and the two generations of arsenopyrite identified in the gold quartz veins are consistent with different mineralizing events, which gave rise to different gold grades. Performing the multifractal analysis has shown problems arising in the subdivision of the area with boxes of constant side length and in the uncertainty the edge effects produce in the experimental estimation of the mass exponent. However, it was possible to closely fit a multifractal spectrum to the data with enrichment factors in the range 2.4–2.6 and constant K1 = 1.3. Such parameters may give some information on the magnitude of the concentration efficiency and heterogeneity of the distribution of arsenic in the mineralized structures. In a simple test with estimated points using ordinary lognormal kriging, the fitted multifractal model showed the magnitude of smoothing in estimated data. Therefore, it is concluded that multifractal models may be useful in the stochastic simulation of geochemical distributions.
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Gonçalves, M.A. Characterization of Geochemical Distributions Using Multifractal Models. Mathematical Geology 33, 41–61 (2001). https://doi.org/10.1023/A:1007510209836
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DOI: https://doi.org/10.1023/A:1007510209836