Fractality in geology: A possible use of fractals in the studies of partial melting processes

Abstract

The use of nonlinear and chaotic dynamics and fractal approaches in the studies of the Earth has increased in the last decade. A large number of geological objects show a power-law or fractal distribution, which suggests that these objects do not require any characteristic length-scale or time in their definition. Fractals can be used in studies of magma mixing and mingling, mantle convection, lava flows, percolation properties of veins and ore mineralization, and to separate geochemical anomalies. It is shown that the width of migmatitic leucosomes in the Estonian basement rock follows power-law distributions and shows fractal properties. Despite the differences in size and number of measured leucosomes and veins, differences in host rock types and formation conditions, the studied leucosome and vein data set shows good power-law distributions with exponents, m, usually between 1.0 and 1.9. The spacing of leucosomes and veins in rock section is not a random feature, but fractal (fractal dimension D = 0.77-0.79). Using the power-law size distribution for the melt batches, the total volume of the melt phase, as well as the relative contributions of the largest batch (dominant for m < 1) and of the smallest batches (dominant for m > 1), are estimated. The relationship between the magmatic leucosome width-distribution exponent, and the melt batch size-distribution is derived.