  Seismic wave propagation forms the basis for most aspects of seismological
research, yet solving the wave equation is a major computational burden that
inhibits the progress of research. This is exacerbated by the fact that new
simulations must be performed when the velocity structure or source location is
perturbed. Here, we explore a prototype framework for learning general
solutions using a recently developed machine learning paradigm called Neural
Operator. A trained Neural Operator can compute a solution in negligible time
for any velocity structure or source location. We develop a scheme to train
Neural Operators on an ensemble of simulations performed with random velocity
models and source locations. As Neural Operators are grid-free, it is possible
to evaluate solutions on higher resolution velocity models than trained on,
providing additional computational efficiency. We illustrate the method with
the 2D acoustic wave equation and demonstrate the method's applicability to
seismic tomography, using reverse mode automatic differentiation to compute
gradients of the wavefield with respect to the velocity structure. The
developed procedure is nearly an order of magnitude faster than using
conventional numerical methods for full waveform inversion.
