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 t heir 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 frequenc y 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 averag e distance from a fault to its nearest neighbor of larger length. Measureme nts of the relevant exponents on the San Andreas fault pattern are in agree ment 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.