Stress inversion of heterogeneous fault-slip data with unknown slip sense: An objective function algorithm contouring method

Abstract

We propose a new method for stress inversion and separation of principal stress states from heterogeneous fault-slip data. The method is semi-automatic, and is based on the moment method of stress inversion (Fry 1999) in combination with the objective function algorithm (OFA) for stress separation (Shan et al 2003). In the presented routine we randomly partition the heterogeneous fault-slip dataset into subsets ranging between one and six. The number of subsets K represents the number of possible mixed stress states in the fault-slip dataset. For each partition number K, we run the OFA 1000 times. Following this we plot and contour the principal stress axes, corresponding to the minimum value of the objective function for each run, in a stereonet. By evaluating how solution clusters of principal stress axes change with increasing number of subsets K, we are able to determine the number of mixed stress states and their optimal solutions for heterogeneous fault-slip datasets. While the numbers of subsets are underestimated, solution-clusters of principal stress axes represent average stress states. However, once the correct number of subsets is reached, solution clusters align with the slip-generating principal stress axes. The solution clusters then become stable, and overestimating the number of subsets does not significantly alter their orientation. The partition number K when stability is obtained thus determines the number of mixed stress states in the heterogeneous dataset, while the corresponding highest density solution clusters give the best estimate of the slip-generating principal stress axes and corresponding stress shape ratios. The inversion routine is tested and confirmed using synthetic data and fault-slip data from the Gullkista fault in Northern Norway. Because the stress calculation is based on the moment method, the inversion routine is insensitive to the correct assessment of slip sense, and only requires the slip vector and orientation of the fault plane as input. It is therefore a robust method to evaluate the number of mixed stress states and their respective stress tensors for complex heterogeneous fault-slip data.