An expanded de Wijs model for multifractal analysis of mineral production data

Hydrothermal ore deposits form by enriching elements and minerals from background values to very high concentrations in small volumes of the crust. The de Wijs model provides a simple and widely used mathematical description of this process; however, it does not account for the increase in density which generally attends the formation of high specific gravity minerals in many mineral deposits. We present an expanded version of the de Wijs model to investigate the distribution of ore tonnage as well as grade. The expanded model generates a log-normal relationship between ore tonnage and grade. Continuous multifractal analysis of results from the new model using the method of moments technique predicts that ore grades are multifractal (as in the original de Wijs model) but that ore tonnage values are not multifractal. Production data from vein-hosted gold deposits in the Archaean Zimbabwe craton display the log-normal relationship between ore tonnage and grade, the multifractal nature of ore grade, and the nonmultifractal nature of ore tonnage, which are generated in the expanded de Wijs model.