An Objective Criterion for Selection of the Best Option in Hansen’s Method for Paleostress Estimation from Homogeneous Fault-Slip Data

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.