Size and spatial distributions of fault populations: Empirically synthesized evolution laws for the fractal geometries

We performed fractal analysis for 10 fault populations that are developed in continuous outcrops of Neogene sedimentary rocks. A transect line was set with reference to the principal stress axes, and the position and displacement of all faults that intersect the transect line were measured precisely. We found that both the fractal dimension of the size (net slip) frequency and that of the spatial distribution of fault displacements are determined by only two parameters: an input energy density and a dissipative energy density. These two kinds of fractal dimension evolve (decrease) as the ratio of the input energy to the dissipative energy increases, and are tied by a universal equation.