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Clustering and size distributions of fault patterns: Theory and measurements

The fractal geometry of fault systems has been mainly characterized by two scaling‐laws describing either their spatial distribution (clustering) or their size distribution. However, the relationships between the exponents of both scaling‐laws has been poorly investigated. We show theoretically and numerically that the fractal dimension D and the exponent a of the frequency length distribution of fault networks, are related through the relation x=(a−1)/D, where x is the exponent of a new scaling law involving the average distance from a fault to its nearest neighbor of larger length. Measurements of the relevant exponents on the San Andreas fault pattern are in agreement with the theoretical analysis and allows us to test the fragmentation models proposed in the literature. We also found a correlation between the position of a fault and its length so that large faults have their nearest neighbor located at greater distances than small faults.