Residual Physics-Informed Neural Networks for Seismic Tomography with Multi-Source Prior Constraints

Seismic traveltime tomography is essential for constructing subsurface velocity models that underpin high-resolution imaging and inversion. Traditional ray- and eikonal-based methods are sensitive to the starting model and lack a unified, physically consistent framework to integrate seismic data with high-confidence prior information. PINN-based approaches offer flexible, grid-free inversion but often suffer from training instability and limited use of prior constraints. We propose a Multi-Source Prior-Guided Residual Physics-Informed Neural Network (MSP-ResPINNs) to address these limitations through two key technical advancements. First, MSP-ResPINNs integrates a Residual Network (ResNet) architecture with Sinusoidal Representation (SIREN) activation to replace standard MLPs, ensuring the robust capture of high-frequency velocity gradients. Second, the framework implements a unified loss function that rigorously enforces multi-source constraints, including well-logs and geological horizons. Numerical experiments demonstrate that MSP-ResPINNs accurately reconstructs sharp velocity contrasts and complex geological features compared with conventional PINN-based approaches. Among the tested variants, the multiplicative factorization consistently provides the most stable and physically consistent results, outperforming the additive factorization.