Unbiased multifractal analysis: Application to fault patterns

We describe a method for systematically correcting finite size and irregular geometrical boundary effects in multifractal analysis. Our multiplicative scheme is tested on synthetic measures, as well as on real fault networks. We document the largely underestimated distorsions induced by the irregular geometry of the support of the measure. Our method allows us to test for the universality of multifractal spectra by comparing results at different magnifications with their respective adjusted corrections. Our result call for a reexamination of many fractal and multifractal analysis which have been carried out without taking these effects into account.