Cross-Attention U-Net for Elastic Wavefield Decomposition in Anisotropic Media

Elastic wavefield separation in anisotropic media is essential for seismic imaging but remains challenging due to complex interactions among multiple wave modes. Traditional methods often rely on solving the Christoffel equation, which is computationally expensive, particularly in heterogeneous models. This study proposes a deep learning-based approach using a cross-attention U-Net architecture to achieve efficient vector decomposition of elastic wavefields. The model employs a dual-branch encoder with cross-attention mechanisms to preserve and exploit inter-component relationships among wavefield components. The network was trained on patches extracted from the BP (British Petroleum) 2007 anisotropic benchmark model, with ground truth labels being generated via low-rank approximation methods. Quantitative evaluations show that the cross-attention U-Net outperforms a baseline U-Net, improving the peak signal-to-noise ratio(PSNR) by 1.25 dB (44.10 dB vs. 42.85 dB) and structural similarity index (SSIM) by 0.014 (0.904 vs. 0.890). The model demonstrates effective generalization to larger domains and different geological settings, validated on both the extended BP model and the Hess vertically transversely isotropic (VTI) model. Overall, this approach provides a computationally efficient alternative to traditional separation methods while maintaining physical consistency in the separated wavefields.