Organizations: School of Data Science and Society University of North Carolina at Chapel Hill Chapel Hill, NC, USA · The Pennsylvania State University State College, PA, USA · Google DeepMind
Full Waveform Inversion (FWI) is a highly nonlinear and ill-posed problem that aims to recover subsurface velocity maps from surface-recorded seismic waveforms data. Existing data-driven FWI typically uses small models, as available datasets have limited volume, geological diversity, and spatial extent, leading to substantial concerns about overfitting. Although they perform well on synthetic datasets, current methods fail to generalize to more realistic geological structures. In this work, we show that a model trained entirely on simulated and relatively simple data can generalize remarkably well to challenging and unseen geological benchmarks. We provide a working recipe that tames a billion-parameter model for FWI through coordinated scaling across three axes: model capacity, data diversity, and training strategy. Our model achieves state-of-the-art performance on OpenFWI and significantly narrows the generalization gap in data-driven FWI. Across six challenging geophysical benchmarks, including Marmousi, 2D SEG/EAGE Salt and Overthrust, 2004 BP, Sigsbee, and SEAM Phase I, it infers complex structures absent from the training set and delivers significant performance improvements (SSIM from 0.5844 to 0.7669). Overall, our results demonstrate that with an appropriate scaling strategy, large models trained on simple synthetic data can achieve substantial generalization to more complex and realistic geological structures.
Figures & tables
Figure 1: Reconstruction results on challenging realistic benchmarks. BigFWI tends to collapse toward over-smoothed, mean-shaped solutions that miss key interfaces and salt bodies. In contrast, our model produces sharper boundaries and geologically meaningful structures.
Figure 2: Overview of progressive model enhancements and final reconstruction quality. (a) Step-wise performance improvement as each component is introduced—from baseline to data augmentation, non-causal modeling, ViT VQGAN (without bottleneck), reinforcement learning alignment, and latent gradient refinement. (b) Illustration of the final reconstruction results, showing sharp structures and fine geological details across diverse scenarios.
Model
MAE ↓
#Param
BigFWI-M ( Jin et al., 2024 )
0.0437
28M
BigFWI-L ( Jin et al., 2024 )
0.0432
87M
Causal
Baseline
0.0770
1.09B
+ Data x2
0.0463
1.09B
+ Data x10
0.0368
1.09B
Non-Causal
Data x2
0.0330
1.09B
Table 1: Quantitative comparison with baseline methods, on OpenFWI testset. Models are organized incrementally, with each row cumulatively including components introduced in prior rows.
Figure 3: Qualitative comparison of reconstructed velocity maps.
Figure 4: Qualitative comparison of reconstructed velocity maps. Our method produces sharper and finer structures.
Metrics
Model
Overall
2004 BP
Marmosi
SEAM Phase I
Overthrust
Salt
Sigsbee
MAE ↓
BigFWI-M
199.20
247.15
226.63
185.02
221.57
150.13
431.60
BigFWI-L
210.99
238.31
233.22
190.84
243.25
159.07
398.08
Ours
139.81
133.45
145.62
199.44
118.25
155.22
148.40
RMSE ↓
BigFWI-M
312.15
390.30
346.13
289.37
297.96
281.57
715.32
BigFWI-L
327.79
377.88
349.42
294.67
320.46
301.74
656.29
Ours
241.78
247.61
251.12
281.57
199.76
268.67
353.37
Table 2: Quantitative performance across six benchmark families. Our method achieves substantially lower MAE/RMSE and higher SSIM, with especially strong gains on SSIM.
Appendix figures & tables3 assets
Supplementary material from the paper’s appendix.
Appendix
Model Configuration
MAE ↓
Causal + Data x2
0.0463
Causal + Data x2 + RL
0.0344
Non-Causal + Data x2
0.0330
Non-Causal + Data x2 + RL
0.0295
Non-Causal + Data x2 + ViT-VQGAN
0.0167
Non-Causal + Data x2 + ViT-VQGAN + RL
0.0159
Appendix
Table 3: Qualitative comparison of reinforcement learning across different model configurations.
Objectives: Full-waveform inversion (FWI) is a high-resolution geophysical imaging technique that reconstructs subsurface velocity models by iteratively minimizing the misfit between predicted and observed seismic data. However, under complex geological conditions, conventional FWI suffers from strong dependence on the initial model and tends to produce unstable results when the data are sparse or contaminated by noise. Methods: To address these limitations, this paper proposes a physics-driven generative adversarial network-based full-waveform inversion method. The proposed approach integrates the data-driven capability of deep neural networks with the physical constraints imposed by the seismic wave equation, and employs adversarial training through a discriminator to enhance the stability and robustness of the inversion results. Results: Experimental results on two representative benchmark geological models demonstrate that the proposed method can effectively recover complex velocity structures and achieves superior performance in terms of structural similarity (SSIM) and signal-to-noise ratio (SNR). Conclusions: This method provides a promising solution for alleviating the initial-model dependence in full-waveform inversion and shows strong potential for practical applications.
Xinyi Zhang, Caiyun Liu, Jie Xiong +1
School of Electronic Information and Electrical Engineering, Yangtze University Jingzhou, Hubei 434023, P.R.China
Full waveform inversion (FWI) is the gold standard for subsurface imaging, with applications from carbon sequestration to energy and mineral exploration to earthquake hazard assessment. Machine learning approaches to FWI need field-scale, geologically diverse, and physically realistic training data, but existing resources such as Marmousi, SEAM, and OpenFWI fall short on spatial extent, temporal extent, geological diversity, and physical realism. We address these limitations with SubsurfaceGen, a GPU-accelerated generator for 3D velocity models and seismic data. Along with SubsurfaceGen, we release a paired dataset of 4,276 2D velocity slices, 5 s wavefields, and 8 s shot gathers drawn from 42 realistic, field-scale 3D velocity models, each spanning 10 km x 10 km laterally and 6.19 km deep at 10 m resolution. The dataset spans six geological settings -- four built with SubsurfaceGen and two drawn from prior sources -- relevant for carbon sequestration and hydrocarbon exploration. We use this dataset to evaluate neural operators on wavefield prediction and encoder-decoders on end-to-end velocity inversion, holding out one geological setting for out-of-distribution testing. These experiments surface failure modes at field-scale and demonstrate how SubsurfaceGen and the associated dataset can impact ML-based FWI.
Full-waveform inversion (FWI) is a high-resolution seismic imaging method that estimates subsurface velocity by matching simulated and recorded waveforms. However, FWI is highly nonlinear, prone to cycle skipping, and sensitive to noise, particularly when low frequencies are missing or the initial model is poor, leading to failures under imperfect acquisition. Diffusion-regularized FWI introduces generative priors to encourage geologically realistic models, but these priors typically require costly offline pretraining and can deteriorate under distribution shift. Moreover, they assume Gaussian initialization and a fixed noise schedule, in which it is unclear how to map a deterministic FWI iterate and its starting model to a well-defined diffusion time or noise level. To address these limitations, we introduce Self-Flow-Matching assisted Full-Waveform Inversion (SFM-FWI), a physics-driven framework that eliminates the need for large-scale offline pretraining while avoiding the noise-level alignment ambiguity. SFM-FWI leverages flow matching to learn a transport field without assuming Gaussian initialization or a predefined noise schedule, so the initial model can be used directly as the starting point of the dynamics. Our approach trains a single flow network online using the governing physics and observed data. At each outer iteration, we build an interpolated model and update the flow by backpropagating the FWI data misfit, providing self-supervision without external training pairs. Experiments on challenging synthetic benchmarks show that SFM-FWI delivers more accurate reconstructions, greater noise robustness, and more stable convergence than standard FWI and pretraining-free regularization methods.