Incorporation of incomplete fault-slip data into stress tensor inversion

A fault-slip datum used in the stress tensor inversion techniques is composed of fault orientation, slip orientation and the sense of slip. Sometimes the latter two items are not available. This paper proposes a method to deal with such incomplete fault-slip data. Firstly, the constraints on stress state from full and incomplete data are theoretically specified. The admissible stresses are expressed by the probability distributions in the parameter space. The objective function of inversion is given by superposing the probability distributions for all data including full and incomplete ones. Finally, the peaks of the objective function are detected to enumerate possible solutions. The validity of the present method is tested by simulated data. The incorporation of incomplete data can enhance the detectability of stress states and expands the applicability of stress tensor inversion.