An Objective Criterion for Selection of the Best Option in Hansen’s Method for Paleostress Estimation from Homogeneous Fault-Slip Data
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Hansen’s direct linear inversion method is a rapid and robust technique for paleostress estimation from fault-slip observations. The method uses six- and nine-dimensional spaces and requires a user judgement of the best solution from four possible options, i.e., the tensors 6D, 6Df, 9D and 9Df. We propose an objective criterion for selection of the best solution. Using each of the four possible options, as the reduced stress tensor, 6D, 6Df, 9D and 9Df, the criterion computes the slip vector on each fault plane in a given population of homogeneous fault-slip data. The option that gives minimum average angle between the computed slip vectors and the true or observed slip vectors on the corresponding fault planes is the best solution. The criterion is successfully tested on 236 synthetic and 5 natural examples representing a variety of stress states in different tectonic settings. One example of the natural fault-slip observations contains a vorticity component, whereas all other test examples are devoid of vorticity. In the triaxial stress states, two correct solutions are obtained, one of which is either 6D or 6Df, and the other is 9D or 9Df. In the stress states that are characterized by axial compression or axial extension, the correct solution is either 6D or 6Df and the use of nine-dimensional space fails to invert the observations. In the natural example that contains a vorticity component, only 9D gave the correct result.
KeywordsPaleostress striated faults vorticity slip vector moment method
This study was supported by a grant from the Department of Science and Technology, Government of India to D. C. Srivastava. We are grateful to Rahul Dixit for help and rigorous testing of the method during the revision of the manuscript and to Arun Ojha for the critical reading of the revised manuscript. We are also grateful to the two reviewers for their erudite and constructive suggestions. Carlos Liesa, in particular, provided very useful suggestions that helped improve the manuscript considerably.
- Anderson, E. M. (1951). The dynamics of faulting (pp. 231–248). Edinburgh: Oliver & Boyd.Google Scholar
- Angelier, J. (1975). Sur l’analyse de measures recueillies dans des sites faillés: lùtilité dùne confrontation entre les méthodes dynamiques et cinematiques. Comptes Rendus de lÀcademie des Sciences, Paris, D281, 1805–1808.Google Scholar
- Angelier, J. (1994). Fault slip analysis and palaeostress reconstruction. In P. L. Hancock (Ed.), Continental deformation (pp. 53–101). Oxford: Pergamon Press.Google Scholar
- Angelier, J., Tarantola, A., Valette, B., & Manoussis, S. (1982b). Inversion of field data in fault tectonics to obtain the regional stress. I. Single phase fault populations: a new method of computing the stress tensor. Geophysical Journal of the Royal Astronomical Society, 69, 607–621.CrossRefGoogle Scholar
- Carey, E. (1976). Analyse numérique d’un modèle mécanique élémentaire appliqué à l’étuded’une population de failles: calcul d’un tenseurmoyen des contraintes à partir des stries de glissement, Theèe de.3èmecycle (pp. 1–1138). Orsay: Universite de Paris Sud.Google Scholar
- Carey, E., & Brunier, B. (1974). Analyse théorique et numérique dùnmod èlemécanique elementaire appliqué à létude dùn population de failles. Comptes Rendus Academy of Science, Paris, D, 279, 891–894.Google Scholar
- Delvaux, D., Levi, K., Kajara, R., & Sarota, J. (1992). Cenozoic paleostress and kinematic evolution of the Rukwa, North Malawi rift valley (East African system). Bulletin des Centres de Recherches Exploration-Production Elf-Aquitaine, 16, 383–406.Google Scholar
- Delvaux, D., & Sperner, B. (2003). Stress tensor inversion from fault kinematic indicators and focal mechanism data: The TENSOR program. In D. Nieuwland (Ed.), New insights into structural interpretation and modelling (Vol. 212, pp. 75–1100). London: Geological Society London, Special Publications.Google Scholar