A Cellular Automaton for the Development of Crustal Shear Zones

Lin-Ji An, & Charles G. Sammis

Published March 20, 1996, SCEC Contribution #332

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∝L−m, were 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∝Ln/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° from the simple shear and 30° to the maximum compression σ1). 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.

An, L., & Sammis, C. G. (1996). A Cellular Automaton for the Development of Crustal Shear Zones. Tectonophysics, 253(3-4), 247-270. doi: 10.1016/0040-1951(95)00062-3.