Reliability of selected procedures of stress inversion and data separation for inhomogeneous populations of calcite twins and striated faults: insights from numerical experiments

Abstract

In the course of numerical experiments selected algorithms for stress tensor inversion and separation of heterogeneous populations of calcite twins and striated faults were tested. Artificial data sets were created in a manner simulating natural processes. They were composed of data, dynamically compatible with one or two stress tensors and chaotic “noise” imitating natural imperfections. For calcite twins the classical inversion procedure is considered valid, with restrictions regarding a high proportion of chaotic data, when shape ratio of the stress tensor Φ is poorly constrained. The algorithm of Etchecopar (1984 fide Tourneret and Laurent in Tectonophysics 180:287–302, 1990) devised originally for calcite twins has been modified and applied to fault/slip data, facilitating a rejection of incompatible outliers. Two main classes of data separation procedures were tested: separation contemporary with inversion and separation prior to inversion, utilising hierarchical clustering. The separation contemporary with inversion performs moderately but often fails with complex calcite twin sets. The performance of hierarchical clustering is high, but only with a σ 1 orientation as a similarity criterion—the new strategy introduced in this contribution. For fault/slip data the hierarchical clustering with the right-dihedra construction as the similarity criterion (Nemcok et al. 1999) is satisfactory. Additionally, a new approach is proposed for fault/slip data, utilising principles of the classical algorithm for heterogeneous populations of calcite twins. Validated algorithms for striated faults were successfully applied to a natural data set from the Holy Cross Mts (central Poland).