New York Inc. Fractal Dimension of Brittle Fracture

Summary. Using a worldwide catalog of earthquakes we analyze the distribution of distances between pairs of earthquake hypocenters to determine the spatial fractal dimension 6 of an earthquake fracture. As the time span of the catalog increases, 8 asymptotically reaches the value 2.1-2.2 for shallow earthquakes. Approximately the same asymptotic value of dimension is obtained for a catalog of earthquakes with aftershocks removed. This value is compared with other known determinations of 6 for brittle fractures. The fractal dimension declines to 1.8-1.9 for intermediate events (depth interval 71-280 km) and to about 1.5-1.6 for deeper events. Taking into account various possible errors and biases, we conclude that the fractal dimension of brittle shear fracture in rocks is 2.20-+ 0.05. Key words, earthquake catalog statistics, spatial distribution of hypocenters, fractal dimension, brittle fracture of rock