On the Frequency-Length Distribution of the San Andreas Fault System

The frequency-length distribution of the San Andreas fault system was analyzed and compared with theoretical distributions. Both density and cumulative distributions were calculated, and errors were estimated. Neither exponential functions nor power laws are consistent with the calculated distributions over the range of studied lengths. The best fit on both density and cumulative distributions was achieved with a gamma function which mixes a power law and an exponential function. At small lengths, the gamma function behaves as a power law with an exponent of −1.3±0.3. At large lengths (above 10km), the distribution is a mixed exponential-power law function with a characteristic length scale of about 23±6 km. The gamma distribution is proposed to result from a length-dependent segmentation of a fractal fault pattern. This study shows the importance of comparing both cumulative and density distributions. It also shows that the studied range of lengths (1–100 km) is not appropriate for measuring power law exponents.

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