Efficient Joint Inversion of Fault Geometry and Slip Distribution via Tree-structured Bayesian Optimization and Helmert Variance Component Estimation

Summary Geodetic observations, such as GNSS and InSAR, are increasingly used to investigate co-seismic surface deformation. Efficiently and simultaneously resolving fault geometry and slip distribution from surface displacements is essential for understanding earthquake processes, accurately estimating seismic magnitude and comprehensively assessing seismic hazard. Current mainstream approaches typically rely on Bayesian inference, such as Monte Carlo sampling. However, these methods typically suffer from long burn-in periods, low computational efficiency, strong sensitivity to initial parameter values and step sizes. Given these limitations, conventional approaches may yield suboptimal fits for the observations. To overcome these limitations, we propose and develop a novel Tree-structured Bayesian Optimization method (TBO), integrated with Helmert Variance Component Estimation (HVCE), to jointly determine fault geometry and slip distribution. To rigorously assess the feasibility and reliability of the proposed approach, we test it using both synthetic and real earthquake data. In the synthetic tests, we evaluate its robustness under a variety of conditions, including different fault types, varying types and densities of geodetic observations, diverse sub-fault sizes and asperities, and complex multi-fault scenarios. Four sets of synthetic experiments are designed, and the results conclusively demonstrate that the proposed method achieves stable and reliable performance in inverting fault geometry and slip distribution. Furthermore, comparative analysis with existing methodologies shows that our approach yields substantially improved computational efficiency, significantly reduced sensitivity to initial conditions, and smaller misfits to observations. Finally, we apply the method to the 2021 Mw 6.4 Yangbi earthquake in Yunnan, China. The retrieved fault geometry and slip distribution successfully explain the fault kinematics and the observed surface deformation field, thereby confirming the applicability and robustness of the method for real earthquake event analysis.