FRACTAL ANALYSIS OF 3-DIMENSIONAL SPATIAL DISTRIBUTIONS OF EARTHQUAKES WITH A PERCOLATION INTERPRETATION

Although many studies have shown that faults and fractures are self-si milar over a large range of scales, none have tested the fault structu re for self-similarity in three dimensions. In this study, earthquake hypocentral locations in central and southern California were used to illuminate three-dimensional (3-D) fault structures, for which we meas ured the fractal capacity dimension, D-0(3-D). Hypocentral distributio ns from the Joshua Tree, Big Bear, and Upland aftershock sequences, as well as background seismicity at Parkfield were found to be fractal, where D-0(3-D) increased with increasing event density, asymptotically approaching a stable value. The Joshua Tree data set stabilized at D- 0(3-D) = 1.92 +/- 0.02, the Parkfield data set asymptotically approach ed D-0(3-D) 1.82, and the Big Bear data set approached D-0(3-D) = 2.01 . As a test of the effects of location errors upon the measured value of D-0(3-D), the Upland aftershock data were located with both the sou thern California Hadley and Kanamori (1977) (H-K) velocity model, and the more accurate Hauksson and Jones (1991) (H-J) velocity model. Even ts located with the H-K model asymptotically approached D-0(3-D) = 2.0 7, and events located with the H-J model approached D-0(3-D) 1.79, sug gesting that improved hypocentral locations may decrease the measured fractal dimension. One interpretation of our results of D-0(3-D) less than or equal to 2.0 for all of the hypocentral data is that earthquak es only occur on the ''percolation backbone'' of a fault network, i.e. , the active part of the network that accommodates finite strain defor mation (Sahimi et al., 1993). We show that a percolation model that al lows for healing of previously broken bonds is consistent with this in terpretation.