  In the study of subsurface seismic imaging, solving the acoustic wave
equation is a pivotal component in existing models. The advancement of deep
learning enables solving partial differential equations, including wave
equations, by applying neural networks to identify the mapping between the
inputs and the solution. This approach can be faster than traditional numerical
methods when numerous instances are to be solved. Previous works that
concentrate on solving the wave equation by neural networks consider either a
single velocity model or multiple simple velocity models, which is restricted
in practice. Instead, inspired by the idea of operator learning, this work
leverages the Fourier neural operator (FNO) to effectively learn the frequency
domain seismic wavefields under the context of variable velocity models. We
also propose a new framework paralleled Fourier neural operator (PFNO) for
efficiently training the FNO-based solver given multiple source locations and
frequencies. Numerical experiments demonstrate the high accuracy of both FNO
and PFNO with complicated velocity models in the OpenFWI datasets. Furthermore,
the cross-dataset generalization test verifies that PFNO adapts to
out-of-distribution velocity models. Moreover, PFNO has robust performance in
the presence of random noise in the labels. Finally, PFNO admits higher
computational efficiency on large-scale testing datasets than the traditional
finite-difference method. The aforementioned advantages endow the FNO-based
solver with the potential to build powerful models for research on seismic
waves.
