Full waveform inversion with CNN-based velocity representation extension

TL;DR

This work addresses gradient-noise challenges in Full Waveform Inversion (FWI) by introducing velocity representation extension FWI (VRE-FWI), which augments the grid-based velocity with a CNN that refines the velocity prior to forward modeling within a self-supervised loss framework. Two backpropagation schemes are proposed: one where velocity updates pass through the CNN and another where the velocity update bypasses it, enabling FWIDIP-like behavior or conventional FWI when CNN weights are zero. Across SEAM, Marmousi, and field data, VRE-FWI delivers higher inversion accuracy than FWI and FWIDIP with only about a 1% increase in computational cost, and the CNN generally acts to filter gradient noise and steer updates toward denser high-wavenumber features while preserving resolution. The findings demonstrate the practicality of CNN-assisted velocity refinement for robust, high-resolution subsurface imaging and offer a pathway to combine short‑iterative convergence with noise-robust gradient updates in real-world seismic workflows.

Abstract

Full waveform inversion (FWI) updates the velocity model by minimizing the discrepancy between observed and simulated data. However, discretization errors in numerical modeling and incomplete seismic data acquisition can introduce noise, which propagates through the adjoint operator and affects the accuracy of the velocity gradient, thereby impacting the FWI inversion accuracy. To mitigate the influence of noise on the gradient, we employ a convolutional neural network (CNN) to refine the velocity model before performing the forward simulation, aiming to reduce noise and provide a more accurate velocity update direction. We use the same data misfit loss to update both the velocity and network parameters, thereby forming a self-supervised learning procedure. We propose two implementation schemes, which differ in whether the velocity update passes through the CNN. In both methodologies, the velocity representation is extended (VRE) by using a neural network in addition to the grid-based velocities. Thus, we refer to this general approach as VRE-FWI. Synthetic and real data tests demonstrate that the proposed VRE-FWI achieves higher velocity inversion accuracy compared to traditional FWI, at a marginal additional computational cost of approximately 1%.

Figures (15)

• Figure 1: The frameworks of the proposed VRE-FWI: The backpropagation used to update the velocity (a) passes through the CNN, and (b) does not pass through the CNN.
• Figure 2: The proposed CNN architecture for VRE-FWI.
• Figure 3: Comparison of results for the SEAM model: (a) True SEAM model, (b) Initial velocity model, and the inverted models obtained after 100 iterations using (c) FWI, (d) FWIDIP, (e) VRE-FWI-1, and (f) VRE-FWI-2.
• Figure 4: Velocity profiles extracted from Fig. \ref{['fig3']} at horizontal distances of (a) 6 km and (b) 10 km, respectively.
• Figure 5: Convergence curves of different FWI methods for the SEAM model.