EXPERIMENTAL DISCOVERY OF SCALING LAWS RELATING FRACTAL DIMENSIONS AND THE LENGTH DISTRIBUTION EXPONENT OF FAULT SYSTEMS

A series of experiments scaled for gravity on the formation of faults in a laboratory model of the earth's lithosphere have shown that the obtained fault patterns are self-similar and can be characterized by various fractal dimensions. By analyzing a large set of experimental results, we discover a remarkable scaling law relating the generalized fractal dimensions D(q), the fault barycenter fractal dimension 'b' and the exponent 'a' of the fault length distribution. : D0 almost-equal-to b is independent of 'a' whereas D(q) greater-than-or-equal-to 1 = b + 2-a, for 2 less-than-or-equal-to a less-than-or-equal-to 3 as found in our experiments.