Seismic wave propagation and inversion with Neural Operators

TL;DR

This paper introduces Neural Operators for seismic wave simulation, enabling rapid, flexible solutions to the wave equation across various models, significantly reducing computational costs in seismic tomography and inversion.

Contribution

It presents a novel neural operator framework trained on diverse simulations, allowing fast, grid-free seismic wave solutions adaptable to different models and source locations.

Findings

Neural Operators achieve near an order of magnitude speedup over traditional methods.

The approach successfully models seismic wave propagation in 2D acoustic equations.

Demonstrates applicability to seismic tomography with efficient gradient computation.

Abstract

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.