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Connectivity of random fault networks following a power law fault length distribution
Author(s) -
Bour Olivier,
Davy Philippe
Publication year - 1997
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/96wr00433
Subject(s) - fault (geology) , percolation (cognitive psychology) , power law , scaling , complex network , topology (electrical circuits) , computer science , statistical physics , mathematics , physics , geometry , combinatorics , statistics , geology , seismology , neuroscience , biology
We present a theoretical and numerical study of the connectivity of fault networks following power law fault length distributions, n(l ) ∼ α l − a , as expected for natural fault networks. Different regimes of connectivity are identified depending on a . For a > 3, faults smaller than the system size rule the network connectivity and classical laws of percolation theory apply. On the opposite, for a < 1, the connectivity is ruled by the largest fault in the system. For 1 < a < 3, both small and large faults control the connectivity in a ratio which depends on a . The geometrical properties of the fault network and of its connected parts (density, scaling properties) are established at the percolation threshold. Finally, implications are discussed in the case of fault networks with constant density. In particular, we predict the existence of a critical scale at which fault networks are always connected, whatever a smaller than 3, and whatever their fault density.