Characterization of geochemical distributions using multifractal models

The use of multifractals in the applied sciences has proven useful in the c haracterization and modeling of complex phenomena. Multifractal theory, has also been recently applied to the study, and characterization of geochemic al distributions, and its relation to spatial statistics clearly stated. Th e present paper proposes a two-dimensional multifractal model based on a tr inomial multiplicative cascade as a pro-ky to some geochemical distribution . The equations for the generalized dimensions, mass exponent. coarse Lipsc hitz-Holder exponent. and multifractal spectrum are derived. This model was tested with an example data set used for geochemical exploration of gold d eposits in Northwest Portugal. The element used was arsenic because a large number of sample assays were below detection limit for gold. Arsenic, howe ver, has a positive correlation with gold, and the two generations of arsen opyrite identified in the gold quartz veins were consistent with different mineralizing events, which gave rise to different gold grades. Performing t he multifractal analysis has shown problems arising in the subdivision of t he area with boxes of constant side length and in the uncertainty the edge effects produce it? the experimental estimation of the mass exponent. Howev er it was possible to closely fit a multifractal spectrum to the data with enrichment factors in the range 2.4-2.6 and constant K-1 = 1.3. Such parame ters may give some information on the magnitude of the concentration effici ency and heterogeneity of the distribution of arsenic in the mineralized st ructures. In a simple test with estimated points using ordinary lognormal k riging. the fitted multifractal model showed the magnitude of smoothing in estimated data Therefore, it is concluded that multifractal models may be u seful in the stochastic simulation of geochemical distributions.