The geometric and statistical evolution of normal fault systems: an experimental study of the effects of mechanical layer thickness on scaling laws

Detailed analyses of two scaled experimental models of distributed extension that differ only in the thickness of the mechanical layer reveal how normal-fault systems evolve with increasing strain. Faults grow increasingly by linkage and become regularly spaced; the proportion of active structures decreases and converges with that of inactive structures. Large faults contribute increasingly to strain accommodation. The size-frequency distribution of fault lengths changes from power-law (fractal) to exponential, non-linear and dynamic length-displacement scaling arises, and the system becomes less multifractal and more homogeneous. These observations validate many predictions of numerical and geometric models of normal fault growth and system evolution. We propose a generalized three-stage model in which mechanical stratigraphy at times restricts fault growth and the degree of elastic fault interaction. The thickness of the mechanical layer influences the relative timing of stages in this model, as well as the geometry and statistics of the system. As faults encounter and breach multiple mechanical layers, systems may exhibit different scaling attributes at different structural or mechanical levels. Thus, systems may oscillate between different stages of this model, complicating fault-population statistics. We present our data as evidence of the existence of upper and lower bounds for the scale invariant behavior of fault systems, as predicted by Mandelbrot for natural fracture systems.