Reciprocity-aware PINN-based seismic traveltime tomography and uncertainty quantification for models with irregular topography

SUMMARY In recent years, physics-informed neural networks (PINNs) have emerged as a powerful tool for seismic traveltime modelling and tomography. However, conventional PINNs do not consider applicable physical priors or quantify the uncertainty of the inverse problem, which is critical for reliable geological interpretation with topographical complexity. Thus, we propose a comprehensive PINN-based framework designed to tackle the critical challenge of inverting for the velocity in models with irregular topography, while also quantifying the inherent uncertainty. Leveraging automatic differentiation, our mesh-free approach directly accommodates complex surfaces without the need for specialized grids. To enhance inversion accuracy and physical consistency, we uniquely incorporate additional physical priors, namely well-log velocity profile and the principle of reciprocity. Furthermore, to address the non-uniqueness of the inverse problem, we integrate Monte Carlo (MC) Dropout to efficiently quantify model uncertainty without architectural modifications. Through 2-D and 3-D experiments on synthetic and real-world geological models, we demonstrate that our method accurately inverts for velocity structures with highly irregular topography. Results show that the inclusion of physical priors significantly improves model performance, while uncertainty quantification via MC dropout successfully highlights regions of higher uncertainty in the inverted velocity field, aligning with geological complexities in the velocities. This work establishes a robust and practical methodology for accurate and reliable seismic tomography in challenging geological settings.