Connectivity of random fault networks following a power law fault length distribution

TLDR

Fault networks exhibit connectivity regimes that vary with the exponent a of their power‑law fault length distribution. The authors investigate how power‑law fault length distributions affect the connectivity of fault networks. Through theoretical analysis and numerical simulations, they determine the geometrical properties of fault networks and their connected components at the percolation threshold. They find that for a>3, small faults dominate and classical percolation applies, for a<1 the largest fault controls connectivity, for 1<a<3 both small and large faults jointly determine connectivity with a ratio depending on a, and they predict a critical scale at which networks are always connected regardless of a<3 and fault density.

Abstract

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 &gt; 3, faults smaller than the system size rule the network connectivity and classical laws of percolation theory apply. On the opposite, for a &lt; 1, the connectivity is ruled by the largest fault in the system. For 1 &lt; a &lt; 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.