Reliability of Bootstrap-derived stress uncertainty bounds in focal mechanism inversion

Summary

Earthquake focal mechanisms provide important constraints on the crustal stress field. In stress inversion based on focal mechanism data, each mechanism contains two nodal planes, whereas the actual seismogenic fault plane is often difficult to identify. Consequently, Bootstrap resampling with random nodal plane selection is widely used to estimate uncertainties in stress inversion results. However, the reliability of these uncertainty bounds remains poorly understood. In this study, we evaluate the reliability of this approach using synthetic experiments and real fault-slip datasets. The results show that the reliability of Bootstrap-derived uncertainty bounds is jointly controlled by fault geometry and the true stress shape ratio (R). When seismogenic faults are distributed on both sides of the maximum compressive stress axis, the uncertainty bounds of principal stress orientations generally encompass the true solutions, whereas the uncertainty bounds of R may exhibit systematic biases depending on the true R value. By contrast, when faults occupy only one side of the fault space, the uncertainty bounds of both stress orientations and R may deviate from the true values. Further analysis indicates that this behavior reflects variations in the kinematic consistency between auxiliary-plane slip and the stress field under different R conditions, causing the influence of misselected nodal planes on inversion results to vary systematically. These findings highlight the importance of correctly identifying seismogenic fault planes and provide important implications for the interpretation of stress inversion uncertainties in practical applications.