Forward and inverse problems for Eikonal equation based on DeepONet

TL;DR

This paper introduces DeepONet, a neural network approach to efficiently solve forward and inverse Eikonal problems in geophysics, enabling fast predictions and velocity model reconstructions without retraining for new conditions.

Contribution

The paper develops specialized DeepONet structures for forward and inverse Eikonal problems, demonstrating improved generalization and accuracy in seismic travel time and velocity model predictions.

Findings

DeepONet accurately predicts travel time fields across various velocity models.

The approach enables velocity model reconstruction from observed travel times.

DeepONet offers a flexible, non-retraining solution for seismic inverse problems.

Abstract

Seismic forward and inverse problems are significant research areas in geophysics. However, the time burden of traditional numerical methods hinders their applications in scenarios that require fast predictions. Machine learning-based methods also have limitations as retraining is required for every change in initial conditions. In this letter, we adopt deep operator network (DeepONet) to solve forward and inverse problems based on the Eikonal equation, respectively. DeepONet approximates the operator through two sub-networks, branch net and trunk net, which offers good generalization and flexibility. Different structures of DeepONets are proposed to respectively learn the operators in forward and inverse problems. We train the networks on different categories of datasets separately, so that they can deliver accurate predictions with different initial conditions for the specific velocity model. The numerical results demonstrate that DeepONet can not only predict the travel time fields with different sources for different velocity models, but also provide velocity models based on the observed travel time data.