A stress inversion procedure for automatic recognition of polyphase fault/slip data sets

In deformed rocks fault/slip data are commonly heterogeneous due to variation of the tectonic stress field. Previous methods for separating heterogeneous fault/slip data are based upon hard division, and do not take into account the indeterminable nature of the data. The indeterminability is controlled by many factors such as inaccuracy in the measurement of fault/slip data, heterogeneity of the stress field, and similarity between controlling stress tensors. A new method for separating heterogeneous fault/slip data uses fuzzy C-lines clustering algorithms. It is applied in Fryʹs (1999) sigma space, in which nonlinear stress inversion is rendered as a solution of hyperlines normal to the girdle of the datum vectors. The method is efficient and quick to make the optimal division and the optimal stress estimates for any chosen division number. From a variety of estimated divisions, the concept of a partition coefficient is introduced (K), which is maximised to determine the best division. As the partition coefficient is only dependent upon the division number and the internal structure of the fault/slip data, the best division obtained in this way is more sound and objective than with previous methods. Two examples illustrate the validity of this method.