The thickness and spacing systematics of 30 line samples of vein arrays at ten localities have been analysed. The analytical methods were tested on four synthetic data sets. The synthetic and natural data sets were each analysed with respect to: cumulative thickness v. distance; thickness population; spacing population; the coefficient of variation of spacing, which measures clustering; the mass function, which measures the scaling of strain heterogeneity. A fundamental distinction is apparent between stratabound arrays, vein arrays in layered rocks where the veins are confined to individual mechanical units, and non-stratabound arrays which occur in rock volumes lacking persistent crack-stopping discontinuities. The stratabound arrays show regular spacing controlled by layer thickness and non-power-law thickness distributions. The non-stratabound arrays are clustered and have power-law thickness distributions resulting from the lack of a controlling length scale. Exponents of the thickness distributions have a modal value of 0.8 and do not vary significantly with lithology. Ore mineralization is favoured in non-stratabound arrays as they are more likely than stratabound arrays to form large clusters connected to a remote fluid source.
Fractals have been applied to vein systems to assess whether they have an organized and systematic structure. Understanding vein systematics allows realistic interpolation and extrapolation from available data by accurate prediction of the numbers and sizes of veins within a target volume. Vein geometries were measured from the Guanajuato epithermal Ag-Au field (Mexico) with vein attributes ranging from the millimetre to metre scale. Ores occur as mineralized quartz-calcite veins and stockworks in Tertiary sedimentary, volcanic and acid intrusive rocks. Mineralization is controlled by north-northeast-south-southwest regional extension. 1D sampling was found to be the most objective and effective way to compare the different data sets. Vein thickness distributions indicate an underlying power-law, with the scaling exponent varying between −0.66 and −0.88 over two orders of magnitude. When combined, the data maintain the same relationship over four orders of magnitude and are characterized by a slope of −0.75. Outcrop data, however, display higher densities within the stockwork. The agreement in scaling exponents between the various data sets suggests that they belong to the same overall structure and are most likely related to the same growth process.
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