Physics-informed waveform inversion using pretrained wavefield neural operators

TL;DR

This work tackles the cost and instability of full waveform inversion (FWI) by marrying a pretrained Fourier Neural Operator (FNO) for fast, frequency-domain wavefield predictions with a physics-informed loss that enforces the wave equation. The neural operator is frozen during inversion, and a PDE residual term, weighted by $\lambda$, regularizes the data misfit to yield cleaner, more accurate velocity models than vanilla neural-operator FWI, demonstrated on OpenFWI CurveVelA and the Overthrust model, including unseen-velocity tests. Results show substantial improvements in reconstruction quality and stability under full-domain and surface-only observations, with negligible computational overhead compared to standard FWI. The approach highlights a practical path to real-time subsurface monitoring by leveraging prior information in neural operators while enforcing physical consistency through PDE constraints.

Abstract

Full waveform inversion (FWI) is crucial for reconstructing high-resolution subsurface models, but it is often hindered, considering the limited data, by its null space resulting in low-resolution models, and more importantly, by its computational cost, especially if needed for real-time applications. Recent attempts to accelerate FWI using learned wavefield neural operators have shown promise in efficiency and differentiability, but typically suffer from noisy and unstable inversion performance. To address these limitations, we introduce a novel physics-informed FWI framework to enhance the inversion in accuracy while maintaining the efficiency of neural operator-based FWI. Instead of relying only on the L2 norm objective function via automatic differentiation, resulting in noisy model reconstruction, we integrate a physics constraint term in the loss function of FWI, improving the quality of the inverted velocity models. Specifically, starting with an initial model to simulate wavefields and then evaluating the loss over how much the resulting wavefield obeys the physical laws (wave equation) and matches the recorded data, we achieve a reduction in noise and artifacts. Numerical experiments using the OpenFWI and Overthrust models demonstrate our method's superior performance, offering cleaner and more accurate subsurface velocity than vanilla approaches. Considering the efficiency of the approach compared to FWI, this advancement represents a significant step forward in the practical application of FWI for real-time subsurface monitoring.

Figures (20)

• Figure 1: A diagram of the physics-informed FWI using trained neural operators based wavefield solutions. 'FNO' denotes the learned simulation engine for the wavefield solutions, whose parameters are frozen during FWI. The red line denotes the path to evaluate the physics-constrained loss, and the blue dashed line denotes the backpropagation process with automatic differentiation to update the input velocity. The rest, which excludes the path to evaluate the physics-constrained loss, is the vanilla neural operator-based FWI using the L2 norm objective function.
• Figure 2: The architecture of the FNO for learned wavefield solutions.
• Figure 3: The training loss history for the learned wavefield solutions and the relative errors for the real and imaginary parts of the wavefield on the validation set.
• Figure 4: From left to right are the true velocity (a), corresponding real (b) and imaginary (c) parts of the background wavefield due to a single source at $(0.98 km, 0.025 km)$ with a frequency of 8.8 Hz .
• Figure 5: From left to right are the smoothed initial velocity, corresponding real and imaginary parts of the observed wavefield due to a single source at $(0.98 km, 0.025 km)$ with a frequency of 8.8 Hz .