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In the study of subsurface seismic imaging, solving the acoustic waveequation is a pivotal component in existing models. The advancement of deeplearning enables solving partial differential equations, including waveequations, by applying neural networks to identify the mapping between theinputs and the solution. This approach can be faster than traditional numericalmethods when numerous instances are to be solved. Previous works thatconcentrate on solving the wave equation by neural networks consider either asingle velocity model or multiple simple velocity models, which is restrictedin practice. Instead, inspired by the idea of operator learning, this workleverages the Fourier neural operator (FNO) to effectively learn the frequencydomain seismic wavefields under the context of variable velocity models. Wealso propose a new framework paralleled Fourier neural operator (PFNO) forefficiently training the FNO-based solver given multiple source locations andfrequencies. Numerical experiments demonstrate the high accuracy of both FNOand PFNO with complicated velocity models in the OpenFWI datasets. Furthermore,the cross-dataset generalization test verifies that PFNO adapts toout-of-distribution velocity models. Moreover, PFNO has robust performance inthe presence of random noise in the labels. Finally, PFNO admits highercomputational efficiency on large-scale testing datasets than the traditionalfinite-difference method. The aforementioned advantages endow the FNO-basedsolver with the potential to build powerful models for research on seismicwaves.

Solving Seismic Wave Equations on Variable Velocity Models with Fourier Neural Operator