Learning seismic wave propagation: from local geometry to global physics

Seismic forward modeling is computationally expensive because a wave equation must be solved repeatedly for each source and, possibly, several velocity models. Learned surrogates could reduce this cost, but they must preserve both the local influence of heterogeneous geologic structures and the long-range coherence of propagating wavefields. We address this problem using such machine learning models as Fourier Neural Operators (FNOs), MeshGraphNets (MGNs), and Transolver. FNO provides global spectral mixing on a structured grid; MGN explicitly uses local mesh connectivity; and Transolver communicates through learned global physical states. Here, we introduce SeisGeoSolver, which composes local message passing, global physics attention, and local refinement in a shared latent state. In 2D simulations for the GeoFWI acoustic model, edge-aware models are substantially more stable in autoregressive rollout than FNO and global-only physics attention. SeisGeoSolver matches the rollout accuracy of a deeper MGN while using fewer parameters and less training time. These results confirm that explicit local geometry is essential in this setting, while global physical interaction can replace part of the local processing budget.