Physical Meaning of Stress Difference for Fault-Slip Analysis

Recent stress tensor inversion methods for fault-slip analysis are used to distinguish between multiple stress states to elucidate spatiotemporal change of the earth’s crustal tectonics. An estimator named the stress difference has been a practicable tool to measure the difference between stress solutions of inversion analysis. This measure corresponds to the expected difference in shear stress direction on a randomly oriented fault plane, which is, however, an approximation including several degrees of deviation. This study investigated the formula of stress difference and found the exact physical meaning, specifically the expected difference in shear stress vector which carries information on magnitude as well as direction. The present discovery is based on the analytical proportionality between the second invariant of stress tensor and the root mean square magnitude of shear stress for all orientation of fault planes. The meaningless difference in non-dimensional shear stress magnitude was found to be incorporated into the value of stress difference. This fact is not convenient for fault-slip analysis dealing only with orientations.