Full waveform inversion method based on diffusion model

Full waveform inversion (FWI) recovers subsurface velocity from seismic recordings by solving a severely ill-posed, nonconvex PDE-constrained optimization. Classical regularizers stabilize the inversion but fail to reproduce realistic geological structures; recent diffusion-prior methods improve realism at the cost of a fragile trade-off between data fidelity and prior consistency. We propose Decoupled Latent Optimization (DLO), which relaxes the standard latent-optimization formulation into a quadratic-penalty objective over an auxiliary physical variable and a latent variable. The data-fidelity gradient acts in physical space, the diffusion sampler contributes only through a decoded prior sample, and the standard smoothed-velocity initialization of classical FWI is preserved. On the OpenFWI benchmark, DLO outperforms classical regularizers and existing diffusion-based methods under clean, noisy, and missing-trace acquisitions. The prior, trained on 70*70 OpenFWI models, transfers directly to the Marmousi and Overthrust benchmarks, where DLO recovers intricate fault structures and remains robust to initialization smoothing and measurement noise.

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.

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.