Relation between the earthquake statistics and fault patterns, and fractals and percolation

Using computer simulations and analyzing experimental data, we investigate the structure of fault patterns in heterogeneous rock, and the distribution of earthquake hypocentral locations. At large length scales, the fracture networks of rock are fractal with a fractal dimension D⋍1.9 and 2.5, in 2D and 3D, respectively. We present a computer simulation model that explains these results in terms of percolation fractals. Three-dimensional fractal analysis of regional hypocentral locations yields a fractal dimension of about 1.8. This result can be explained if earthquakes are distributed on the backbone of the fractal network of fault structure with a fractal dimension equal to that of the percolation backbone. Thus, percolation provides a unified theory for the geometry of fault patterns and the spatial distribution of earthquakes.