Kilometer-scale crustal stress inverted through diverse natural fractures - synthetic tests and real borehole applications

Natural fractures in the Earth's crust provide important information on the stress field. However, stress inversion based on fracture characteristics remains challenging due to inherent data uncertainty and the limitations of deterministic interpretations. Existing approaches identify the feasibility of inverting crustal stress based on fracture hydraulic conductivity data and critical shear stress assumption. In that context, the fracture data is binarily treated, which is inconsistent with the continuous and stochastic nature of fracture characteristics of shear stress and fluid flow. This can lead to inversion instability and bias. To capture fracture criticality and the associated uncertainty, we develop a probabilistic stress inversion framework in which fracture criticality is quantified via a non-binary slip probability rather than a binary state. Stress inversion is formulated as an optimization problem that links fracture criticality probability and hydraulic conductivity, yielding estimates of stress orientation and relative magnitude. To systematically evaluate the impact of data uncertainty, synthetic datasets are generated using discrete fracture network models with varying fracture population, conductivity characteristics, and orientation diversity. The synthetic tests demonstrate that inversion performance is primarily governed by fracture orientation diversity, and the probabilistic formulation remains robust under some degree of misclassification and incomplete sampling. The method is further applied to four kilometer-scale scientific boreholes: Cajon Pass, Long Valley, Nevada Test Site, and KTB, where the inverted stress states are consistent with independent observations. These findings demonstrate that fracture diversity fundamentally controls the robustness and accuracy of kilometer-scale crustal stress inversion under geological uncertainty.