Bayesian three-dimensional seismic travel-time tomography for active- and passive-source seismic data using physics-informed neural networks

Summary Accurate three-dimensional (3D) seismic velocity modeling through seismic travel-time tomography using both active- and passive-source data provides critical underpinning models for seismicity monitoring and hazard assessment. Because travel-time tomography is an inherently ill-posed inverse problem, uncertainty quantification (UQ) of the estimated models using Bayesian methods is also important for reliable downstream interpretations and analyses. However, Bayesian inference for 3D tomography based on conventional grid-based representations faces the “curse of dimensionality” and severe computational bottlenecks. Consequently, rigorous Bayesian UQ for margin-wide 3D travel-time tomography has remained largely unexplored, despite its importance for reliable interpretation of large-scale velocity models. In this study, we propose a meshless 3D Bayesian travel-time tomography method that combines physics-informed neural networks (PINNs) with a neural representation of the velocity structure, enabling tractable and data-efficient Bayesian inference through function-space Particle-based Variational Inference (fParVI). To efficiently integrate passive-source data into the Bayesian estimation of the velocity structure, we introduce an analytical marginalization strategy that treats uncertain parameters related to the origin time and location as nuisance parameters, with passive-source relocation carried out in post-processing. We validated the capability of our approach for 3D problems through synthetic experiments. These experiments demonstrate its robustness against biased prior source locations compared to standard methods that suffer from overfitting. Furthermore, we applied the method to a real-world dataset off the Kii Peninsula, Nankai Trough, using over 380,000 travel-time picks from marine active-source surveys and natural earthquakes. Our probabilistic 3D ensemble successfully resolves key geological features, such as the Kumano Pluton, and provides data-consistent uncertainty maps that offer new quantitative insights into the reliability of previously debated deep low-velocity zones. The posterior mean hypocenters shifted mainly in the vertical direction by 10-15 km, consistent with the deterministic relocation results of a previous study. Finally, the continuous neural representation drastically reduces storage requirements for the entire ensemble velocity model, highlighting the scalability and data efficiency of the proposed framework for Bayesian seismic travel-time tomography.