Wavefield reconstruction inversion via physics-informed neural networks

TL;DR

This paper introduces a physics-informed neural network approach to wavefield reconstruction inversion, reducing computational costs and cycle skipping in full-waveform inversion by leveraging neural networks constrained by physical laws.

Contribution

The paper develops a novel PINN-based WRI method that efficiently reconstructs wavefields and predicts velocities with limited iterations and frequencies, enhancing FWI workflows.

Findings

Successfully reconstructs wavefields using PINNs with limited data.

Accurately predicts velocity models from reconstructed wavefields.

Demonstrates effectiveness on Sigsbee2A and Marmousi models.

Abstract

Wavefield reconstruction inversion (WRI) formulates a PDE-constrained optimization problem to reduce cycle skipping in full-waveform inversion (FWI). WRI often requires expensive matrix inversions to reconstruct frequency-domain wavefields. Physics-informed neural network (PINN) uses the underlying physical laws as loss functions to train the neural network (NN), and it has shown its effectiveness in solving the Helmholtz equation and generating Green's functions, specifically for the scattered wavefield. By including a data-constrained term in the loss function, the trained NN can reconstruct a wavefield that simultaneously fits the recorded data and satisfies the Helmholtz equation for a given initial velocity model. Using the predicted wavefields, we rely on a small-size NN to predict the velocity using the reconstructed wavefield. In this velocity prediction NN, spatial coordinates are used as input data to the network and the scattered Helmholtz equation is used to define the loss function. After we train this network, we are able to predict the velocity in the domain of interest. We develop this PINN-based WRI method and demonstrate its potential using a part of the Sigsbee2A model and a modified Marmousi model. The results show that the PINN-based WRI is able to invert for a reasonable velocity with very limited iterations and frequencies, which can be used in a subsequent FWI application.