Fractals in petrology

A fractal (power-law) distribution is the only statistical distribution applicable to a scale-invariant process. One of the major problems in petrology is the distribution of trace elements in the Earthʹs crust. Extreme values of this distribution result in ore deposits. There is accumulating observational evidence that tonnage–grade statistics of ore deposits are often fractal (power-law). Rayleigh distillation and chromatographic models can explain power-law (fractal) distributions for the extreme values of trace element concentrations. An alternative fractal approach to problems in petrology is to use self-affine fractals. The standard approach is to take a Fourier transform of a continuous signal (an example would be the concentration of a mineral along a linear track). If the Fourier coefficients scale as a power-law of the wavelength, the distribution is a self-affine fractal. Many well logs give this result. Multifractal analyses can also be applied to problems in petrology.