Fractal distribution of earthquake hypocenters and its relation to fault patterns and percolation

Abstract

We argue that percolation provides a unified theory for the geometry of fault patterns and the spatial distribution of earthquakes. We analyze the structure of fracture patterns in heterogeneous rocks and find that, at large length scales, they are percolation fractals with a fractal dimension D\ensuremath{\simeq}1.9 and 2.5, in 2D and 3D, respectively. A model is proposed that can predict these results. Three-dimensional fractal analysis of spatial distribution of earthquake hypocenters yields a fractal dimension of about 1.8, the same as that of the backbone of 3D percolation clusters.