Physics-guided Full Waveform Inversion using Encoder-Solver Convolutional Neural Networks

TL;DR

This work tackles the high cost of frequency-domain FWI by embedding a Shifted Laplace multigrid-augmented Encoder-Solver CNN preconditioner into both forward and adjoint Helmholtz solves, enabling efficient Jacobian- and Hessian-based updates. A data-efficient, light-weight retraining strategy aligns the preconditioner with the gradually evolving velocity field during frequency continuation, significantly reducing iteration counts and solve times in 2D SEG/EAGE salt and Marmousi experiments. The method leverages simultaneous sources, Gauss-Newton updates, and carefully designed data generation to maintain accuracy while curbing computational expense. Overall, the proposed physics-guided, retrainable DL preconditioner accelerates FWI without sacrificing fidelity, making physics-based inversion more practical for high-frequency seismic imaging.

Abstract

Full Waveform Inversion (FWI) is an inverse problem for estimating the wave velocity distribution in a given domain, based on observed data on the boundaries. The inversion is computationally demanding because we are required to solve multiple forward problems, either in time or frequency domains, to simulate data that are then iteratively fitted to the observed data. We consider FWI in the frequency domain, where the Helmholtz equation is used as a forward model, and its repeated solution is the main computational bottleneck of the inversion process. To ease this cost, we integrate a learning process of an encoder-solver preconditioner that is based on convolutional neural networks (CNNs). The encoder-solver is trained to effectively precondition the discretized Helmholtz operator given velocity medium parameters. Then, by re-training the CNN between the iterations of the optimization process, the encoder-solver is adapted to the iteratively evolving velocity medium as part of the inversion. Without retraining, the performance of the solver deteriorates as the medium changes. Using our light retraining procedures, we obtain the forward simulations effectively throughout the process. We demonstrate our approach to solving FWI problems using 2D geophysical models with high-frequency data.

Figures (9)

• Figure 1: The Encoder-Solver architecture. The Encoder receives the slowness (squared) and progressively coarsens the feature map using a convolutional layer followed by 2 consecutive ResNet layers. On the way up we up-sample the coarse vector using a convolutional layer, concatenate the feature vector of the corresponding size, and apply a ResNet layer. The Solver network maps a residual vector ${\bf r}$ to an error ${\bf e}$. The Solver integrates the learned feature vector of the Encoder at each level.
• Figure 2: The 2D SEG/EAGE salt velocity model and initial guess
• Figure 3: SEG/EAGE FWI result and the corresponding total misfit history
• Figure 4: SEG/EAGE salt model FWI average comparison. In the left column, we compare the average iteration count with and without training our model. The right column shows a comparison of the average solve time. Both comparisons were conducted for the different tolerance values.
• Figure 5: SEG/EAGE salt model FWI total iteration count and solve-time comparison.