Using Fourier neural operators to generate multi-resolution seismic wavefields

Ángel Ramos Hernández, Tianze Zhang, Kristopher A. Innanen

Numerical solvers have been effective in approximating the wave equation and its variations. However, the discrete nature of conventional solvers imposes a trade-off between resolution and computational cost, which can be a significant drawback when multiple forward simulations are required to solve a problem (e.g., FWI and uncertainty quantification). Data-driven deep learning techniques, such as Fourier neural operators, have gained popularity due to their ability to learn from data and solve complex partial differential equations (PDEs) at low computational cost. From this point of view, we present the results of numerical experiments that combine finite difference solutions to the acoustic wave equation with Fourier Neural Operators. Our target is to investigate how this method can move between different resolutions and assess the accuracy of their solutions across various spatial resolutions to potentially enable cheaper training and faster solutions to the wave equation.