Fractal Properties of the Distribution of Earthquake Hypocenters
  We investigate a recent suggestion that the spatial distribution of earthquake hypocenters makes a fractal set with a structure and fractal dimensionality close to those of the backbone of critical percolation clusters, by analyzing four different sets of data for the hypocenter distributions and calculating the dynamical properties of the geometrical distribution such as the spectral dimension $d_s$. We find that the value of $d_s$ is consistent with that of the backbone, thus supporting further the identification of the hypocenter distribution as having the structure of the percolation backbone. 
Hisao Nakanishi, Muhammad Sahimi, Michelle C. Robertson, Charles C.   Sammis and Mark D. Rintoul