Seismic full-waveform inversion based on a physics-driven generative adversarial network

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.

Seismic full-waveform inversion is a core technology for obtaining high-resolution subsurface model parameters. However, its highly nonlinear characteristics and strong dependence on the initial model often lead to the inversion process getting trapped in local minima. In recent years, generative diffusion models have provided a way to regularize full-waveform inversion by learning implicit prior distributions. However, existing methods mostly use unconditional diffusion processes, ignoring the inherent physical coupling relationship between velocity and density and other physical properties. This paper proposes a full-waveform inversion method based on conditional diffusion model regularization. By improving the backbone network structure of the diffusion model, two-dimensional density information is introduced as a conditional input into the U-Net network. Experimental results show that the full-waveform inversion method based on the conditional diffusion model significantly improves the resolution and structural fidelity of the inversion results, and exhibits stronger stability and robustness when dealing with complex situations. This method effectively utilizes density information to constrain the inversion and has good practical application value. Keywords: Deep learning; Diffusion model; Full waveform inversion.

Seismic inversion is a core problem in geophysical exploration, where traditional methods suffer from high computational costs and are susceptible to initial model dependence. In recent years, deep generative model-based seismic inversion methods have achieved remarkable progress, but existing generative models struggle to balance sampling efficiency and inversion accuracy. This paper proposes an end-to-end fast seismic inversion method based on Conditional Rectified Flow[1], which designs a dedicated seismic encoder to extract multi-scale seismic features and adopts a layer-by-layer injection control strategy to achieve fine-grained conditional control. Experimental results demonstrate that the proposed method achieves excellent inversion accuracy on the OpenFWI[2] benchmark dataset. Compared with Diffusion[3,4] methods, it achieves sampling acceleration; compared with InversionNet[5,6,7] methods, it achieves higher accuracy in generation. Our zero-shot generalization experiments on Marmousi[8,9] real data further verify the practical value of the method. Experimental results show that the proposed method achieves excellent inversion accuracy on the OpenFWI benchmark dataset; compared with Diffusion methods, it achieves sampling acceleration while maintaining higher accuracy than InversionNet methods; experiments based on the Marmousi standard model further verify that this method can generate high-quality initial velocity models in a zero-shot manner, effectively alleviating the initial model dependency problem in traditional Full Waveform Inversion (FWI), and possesses industrial practical value.