A cellular automaton for the development of crustal shear zones

A 2-D computer automaton is developed which simulates the growth and coalescence of a network of faults, leading to the formation of a large, through-going shear zone. The simulation begins with a field of initial fault seeds which have a power-law size distribution of the form N alpha L(-m), where N is the number of fault seeds of length L and m a constant. Following fracture mechanics, the growth rate v of each fault is assumed to be a power law of its length L (v alpha L(n/2)) where n is a constant. Based on simple shear experiments with moist clay and gouge layers, faults are assumed to propagate obliquely to the simple shear direction (15 degrees from the simple shear and 30 degrees to the maximum compression sigma(1)). The rules governing fault interaction are developed by observations of the simple shear experiments and a statistical study of strike-slip faults. The extent of the interaction zone W of a fault is assumed to be proportional to the fault length L, i.e., W-RL where R is a constant. Parameters n and R are determined by comparing the automaton simulations with regional fault patterns, which gives n to be about 2 and R to be about 0.1. The resultant fault pattern is also sensitive to the initial fault seed distribution for which the acceptable range of the power-law parameter is 1 < m < 2.3. Analysis of the results indicates that the through-going shear zone which develops is fractal with a dimension of 1.02, consistent with that found by mapping natural shear zones. The length distribution of fault segments is found to be approximately log-normal and to be consistent with the displacement scaling relation observed by Wesnousky (1989) for natural faults.