Three-dimensional analyses of slip distributions on normal fault arrays with consequences for fault scaling

Many fault arrays consist of echelon segments. Field data on ancient and active faults indicate that such segmented geometries have a pronounced effect on the distribution of fault slip. Outcrop measurements of slip on arrays of fault segments show that: (i) the point of maximum fault slip generally is not located at the centre of a fault segment; (ii) displacement gradients steepen towards the adjacent fault for underlapping faults; and (iii) displacement gradients become more gentle near the tips of overlapping faults. Numerical analyses suggest that mechanical interaction between neighbouring faults may cause such asymmetrical slip distributions. This interaction occurs through local perturbation of the stress field, and does not require the faults to be connected. For normal faults, the degree of fault interaction, and hence the degree of asymmetry in the slip distribution, increases with increasing fault height and fault overlap and with decreasing fault spacing. The slip magnitude along a discontinuous fault array can be nearly equal to that of a single larger continuous fault provided the segments overlap with small spacing. Fault interaction increases the ratio between fault slip and fault length, especially for closely spaced, overlapping faults. Slip-to-length ratios also depend on the three-dimensional fault shape. For normal faults, the slip-to-length ratio increases with increasing fault height. The effects of fault interaction and three-dimensional fault shape together can lead to more than one order of magnitude variation in slip-to-length ratio for the simple case of a single slip event in a homogeneous isotropic rock. One should expect greater variation for the more complex conditions found in nature. Two-dimensional fault scaling models can not represent this behaviour.