Separation of polyphase fault/slip data: an objective-function algorithm based on hard division

The objective-function algorithm (OFA) on the basis of hard division is presented in the paper to separate polyphase fault/slip data. The separation is made by detection of linear structures existing in the data in Fryʹs (1999) sigma space. Different from other exhaustive-search methods, the OFA is direct and robust in theory without any arbitrary assumptions. Polyphase fault/slip data are simulated under prescribed tensors in order to validate the method. The results show its efficiency in stress estimation. The accuracy of stress estimation is controlled by random errors in the orientation of fault striations and by similarity between prescribed stress vectors related to different tectonic phases. The similarity between controlling stress vectors has an obvious effect on the estimation either when random errors are sufficiently large or when some similarity coefficients between the vectors are large enough. The accuracy of stress inversion tends to decrease as the range in errors increases. The OFA makes a very good approach to recognition of similar controlling stress vectors from polyphase fault/slip data, which are often associated with spatial and temporal variation of the tectonic stress field in a region, thus critical to understanding of the formation of geological structures.