Symmetropy of fault patterns: Quantitative measurement of anisotropy and entropic heterogeneity

The purpose of the effort in this paper is to show symmetropy of fault patterns. This quantity can be considered as a measure of entropic heterogeneity and anisotropy. We describe this measure based on the discrete Walsh transform. The specific results of its applications are obtained as follows. When a rock specimen undergoes creep in a laboratory experiment, the fault propagation can be monitored by the decrease of symmetropy. Moreover, in a fault model with self-organized criticality, fault patterns of critical states and subcritical states are distinguished by the behavior of the symmetropy: subcritical fault patterns show almost constant value of symmetropy but it takes various values during critical states. These results demonstrate that symmetropy idea can be used for the quantification of fault patterns.