# Cross-Attention U-Net for Elastic Wavefield Decomposition in Anisotropic Media
## 3 Results
### Application to Larger Anisotropic Models  
To evaluate the scalability and robustness of the trained network, the cross-attention U-Net was first tested on a substantially larger subset of the same BP model. While the training region was limited to 200 \(\times\) 200 patches, the larger domain considered here spans 1936 \(\times\) 562 grid points and includes boundary extensions to reduce reflection artifacts. To handle this increased domain without exceeding the GPU memory limits, a sliding-patch  
Figure 5: Wavefield separation results from the U-Net for the snapshot shown in Figure 4. The top row depicts \(u_{x\_gp}\), \(u_{x\_gp}\), \(u_{z\_gp}\), and \(u_{z\_q\_g}\), and the bottom row illustrates the residual maps (scaled by a factor of three for clarity) relative to the ground truth. Higher residuals appear near complex reflections and interfaces.  
Figure 6: Wavefield separation results from the cross-attention U-Net for the same snapshot. The top row shows \(u_{x\_gp}\), \(u_{x\_gp}\), \(u_{z\_gp}\), and \(u_{z\_q\_g}\), while the bottom row presents the residual maps (also scaled by a factor of three). Compared to Figure 5, these predictions exhibit fewer artifacts and more accurate separation across all components.  
approach that is commonly used in image processing was employed [19]. This method divides the domain into partially overlapping patches, processes each patch independently, and merges the outputs through a smoothly tapered weighting function that prevents visible seams.  
Figure 7 presents the wavefield separation results for the BP model, showing the input displacement fields (\(u_{x}\) and \(u_{z}\)) in the top row, ground truth qP and qS components (\(u_{x,\text{qg}}\), \(u_{x,\text{qg}}\), \(u_{z,\text{qg}}\), \(u_{z,\text{qg}}\)) in the second row, predicted components in the third row, and difference maps in the bottom row. While the model successfully separates the wavefields across the expanded domain, the difference maps reveal some discrepancies between the predicted and ground truth components. These residuals indicate a modest decrease in performance compared to the results presented in Section 3.1, which is an expected trade-off when scaling to larger domains and implementing patch-based processing.  
To further examine the network's generalization capabilities, the same sliding-patch approach was applied to the Hess VTI (vertical transverse isotropy) model, with additional synthetic noise being injected into the wavefields. The noise was generated using a random Gaussian distribution, scaled by a relative amplitude factor up to 30% of the maximum absolute value in each snapshot. Although the network was trained exclusively on clean data, it demonstrated robust performance on this noisy dataset. As shown in the updated Figure 8, the cross-attention U-Net was able to produce coherent qP and qS components, even in the presence of noise and strong heterogeneity. Some residual artifacts were observed, particularly around high-contrast regions, but the decomposition quality remained largely consistent. These results indicate that the model can generalize to more complex data distributions beyond the training set and highlight its potential for application to real seismic datasets, where noise and heterogeneity are prevalent.  
Figure 7: Wavefield separation results on the larger BP model domain (1936 \(\times\) 562) using the sliding-patch approach. Input displacement fields (top row: \(u_{x}\) and \(u_{z}\)), ground truth qP and qS components (second row: \(u_{x,\text{qg}}\), \(u_{x,\text{qg}}\), \(u_{z,\text{qg}}\), \(u_{z,\text{qg}}\)), predicted components using the cross-attention U-Net (third row), and difference maps between the predicted and ground truth results (bottom row).