# Three-Dimensional Velocity Field Interpolation Based on Attention Mechanism
## 3 Experiments
### Real Data  
For real data, our objective is to validate the performance of the network constructed in this paper further. Due to the fact that real data typically consist of only a limited amount of data and are unevenly distributed, as shown in Figure 8, the network represents different perspectives of sampled data. The combination of 3 DUnet and JointA 3 DUnet with dilated convolutions has shown promising interpolation results on synthetic data. Therefore, we test the interpolation performance of these two networks on real data directly. Figure 8: Different slices of real data are displayed. (**a**) Slice A. (**b**) Slice B.  
Figure 6: Interpolation results of simulated data with the addition of dilated convolution. (**a**) 3 DUnet with dilated convolution. (**b**) JointA 3 DUnet with dilated convolution. Figure 7: Comparison of interpolation results for simulated data between 3 DUnet and JointA 3 DUnet. Figure 9 displays the interpolated result images in real data. It can be observed that, in the interpolation process of real data, the combination of 3 DUnet and dilated convolutions leads to discontinuous layers in high value areas, while the integration of JointA 3 DUnet and dilated convolutions can overcome this difficulty. The comparison of interpolation results is shown in Figure 10, where the JointA 3 DUnet network has a lower observation point error and overall higher performance, compared with 3 DUnet combined with dilated convolution. The interpolation results obtained from both methods have high SNR values, which is due to the inherent smoothing effect of Unet when used for interpolation tasks, resulting in high SNR values for both interpolation results. After adding inflation convolution, JointA 3 DUnet reduces the relative error at the observation points by 47.34% compared with 3 DUnet. It can be observed that, for more complex measured data, the method mentioned in this paper has precise interpolation effects, especially for more delicate geological structures such as faults, where JointA 3 DUnet can restore their shapes better. We selected a channel of data for plotting the line chart, as shown in Figure 11, It can be seen that the obtained interpolation results are very close to the real curve, and the errors are also found to be within a smaller range after the difference is taken. In order to compare and evaluate the interpolation ability of JointA 3 DUnet combined with dilated convolution for three-dimensional velocity field data with different sampling rates, we conducted interpolation experiments on the original real dataset, with sampling rates of 20% and 30%. The 20% sampling is based on resampling the data sampled at 30%, and the distribution of the two sets of data is the same. The obtained three-dimensional velocity field interpolation results are shown in Figure 12.  
Figure 10: Comparison of interpolation results for real data between 3 DUnet and JointA 3 DUnet. Figure 9: Interpolation results of real data with the addition of dilated convolution. (**a**) 3 DUnet with dilated convolution. (**b**) JointA 3 DUnet with dilated convolution. The figure demonstrates that the interpolation effects of 30% and 20% sampling are highly similar, and the 3D velocity field data are well recovered. Although the introduction of the attention mechanism improves the model's performance, it also increases the complexity and training difficulty. To address this issue, we decided to adopt a transfer learning strategy to enhance the training efficiency and performance. Figure 13 compares the network convergence curves before and after the transfer learning implementation. It can be observed that, after utilizing transfer learning, the convergence speed is accelerated, and the network performs well in reconstructing velocity field data in sparse areas. The interpolation effect diagram is shown in Figure 14. From the figure, it can be seen that, after adding the idea of transfer to the JointA 3 DUnet network, its three-dimensional interpolation ability has been improved in terms of speed and quality.