Fractal Dimension and b-Value on Creeping and Locked Patches of the San Andreas Fault near Parkfield, California

We tested the hypotheses (1) that the fractal dimension, D, of hypocenters are different in a locked and a creeping segment of the San Andreas fault and (2) that the relationship D (almost equal) 2b holds approximately, where b is the slope of the frequency-magnitude relationship. The test area was the 30- to 50-km fault segment north of Parkfield for which two earthquake catalogs exist: the borehole High Resolution Seismic Network data, and the U.S. Geological Survey data, which have a minimum magnitude of completeness of MC 0.4 and MC 1.0-1.2, respectively. The relative location errors in the two catalogs are estimated as 0.25 km and less than 1 km, respectively. The periods of high-quality data available extend from 1987 to 1998.5 and 1981 to 2000.2, respectively, furnishing 2609 and 3775 events for analysis, in the two catalogs. In the locked part, 0.5 < b < 0.7 and 0.96 < D < 1.14, whereas in the creeping segment, 1.1 < b < 1.6 and 1.45 < D < 1.72. However, the spatial distribution of the hypocenters in the creeping segment is not well approximated by a fractal distribution. We conclude (1) that the frequency-magnitude distribution as described by b, as well as the fractal dimension (D), are different in the locked and creeping segments near Parkfield; (2) that the spatial distribution in the creeping segment is not well approximated by a fractal distribution; and (3) that the relationship D (almost equal) 2b holds in the locked segment, where both parameters can be measured accurately. Thus, we propose that the heterogeneity of seismogenic volumes lead to differences in D and b and that these differences, where established by high-quality data, may furnish clues concerning properties of fault zones.