A Generalized Eikonal Solver Using Operator Learning

The Eikonal equation is a fundamental partial differential equation in geophysics to describe seismic wavefront propagation. Accurate and efficient solutions to the Eikonal equation are crucial for various geophysical applications, including seismic migration and traveltime tomography. To address the computational bottlenecks in inversion workflows, an Eikonal solver is needed that can generalize across variations in the velocity model. In this work, we propose a generalized Eikonal solver using Fourier-DeepONet, a hybrid neural operator framework that combines the strengths of DeepONet and Fourier neural operator (FNO). By leveraging DeepONet for encoding velocity models and background traveltime fields, and FNO for decoding and predicting traveltimes, Fourier-DeepONet achieves superior accuracy and flexibility compared with existing methods. Once trained, the neural operator can rapidly predict traveltimes for new, unseen velocity models and source locations without retraining, offering a substantial computational advantage. We validate the performance of the proposed method on the OpenFWI velocity families, demonstrating its superior generalization capability compared with vanilla DeepONet. Our approach offers a scalable and efficient solution for real-time seismic modeling and inversion tasks, with potential to significantly reduce computational costs in large-scale geophysical applications.