Three-Dimensional Seismic Traveltime Simulation Using Physics-Informed Unet Fourier Neural Operator

Seismic traveltime is crucial information of seismic waves. However, conventional numerical methods for three-dimensional traveltime simulation face significant challenges. These methods require extensive computations across the entire 3D domain, particularly for complex velocity models with dense grid points. Numerical eikonal solvers face a bigger limitation regarding efficiency for 3D scenarios when multiple simulations are needed for different sources in practical applications. To overcome these limitations, we have developed a deep learning-based approach for 3D traveltime modeling, capable of handling multiple seismic sources and diverse velocity models, named the Physics-Informed Unet Fourier Neural Operator (PIUFNO). We use velocity models and background traveltimes as inputs and perturbed traveltimes as outputs, and the eikonal equation is integrated as a loss function. PIUFNO achieves efficient and accurate traveltime modeling. The proposed approach demonstrates can not only calculate the traveltimes accurately and efficiently for velocity models used in the training domin but also be generalized to the new velocity models to obtain reasonable traveltime solutions, showcasing robust predictive capabilities.