Deep Learning-Based 3D Seismic Velocity Inversion Under Dual-Domain Sparse Representation

Three-dimensional seismic full-waveform inversion (FWI) provides high-fidelity subsurface velocity models but is restricted by high computational cost, strong nonlinearity, cycle-skipping, and heavy dependence on initial models. Although data-driven deep learning mitigates these issues, it still produces over-smoothed results with limited physical interpretability and low efficiency. To address these challenges, we propose a dual-domain sparse deep learning framework for 3D seismic velocity inversion using the discrete cosine transform (DCT). DCT compresses seismic data and velocity models into a sparse domain to remove redundancy while preserving key structural features. A geometry-adaptive network named SEDCN (Squeeze-and-Excitation Deformable Convolutional Network) is adopted to better capture irregular salt-dome geometries and sharp velocity boundaries. We train and validate the network on 676 samples from the 3D SEG/EAGE salt model, with two schemes for comparison: the proposed DCT-SEDCN and the baseline SEDCN without DCT. Numerical results show that DCT-SEDCN reduces training time by more than 90% and achieves higher PSNR and SSIM than conventional spatiotemporal-domain methods. It effectively suppresses over-smoothing, recovers salt body boundaries and stratigraphic details clearly, and generates geologically more reliable velocity models. This study confirms that DCT-based sparse representation combined with geometry-adaptive deep learning significantly improves the efficiency, accuracy, and robustness of 3D seismic velocity inversion. The framework offers a scalable solution for large-scale 3D FWI and can be extended to elastic/viscoelastic multi-parameter inversion and field data applications.