## 4 Results
The f-k spectrum corresponding to the inline direction interpolation results shown in Figure 9 is shown in Figure 11. Figure 11a shows the label data in the inline direction, and Figure 11b shows the interpolation results and corresponding residuals for each model in the inline direction. When comparing the interpolation results of each model in Figure 11b, the 3D U-Net showed relatively large residuals and poor performance, while the 3D cWGAN showed relatively small residuals and accurate prediction results compared to other models. Through analysis of the f-k spectrum, we confirmed that the 3D cWGAN outperformed other methods. Figure 10: F-k spectrum about Figure 7c. (**a**) Input data and label data with regularly 75% missing traces in crossline direction; (**b**) interpolation results and corresponding residuals (difference between interpolation result and label) about (**a**). To quantify the performance of the trained models, we use three metrics: MSE (mean squared error), PSNR (peak signal-to-noise ratio) and SSIM (structural similarity index). MSE is widely utilized as a full-reference metric for evaluating image quality, with lower values indicating better performance. MSE is calculated by following Equation (4). \[\text{MSE}=\frac{1}{N}\sum_{i=0}^{n}\Bigl{[}G(x_{i})-y_{i}\Bigr{]}^{2}, \tag{4}\]  
where \(G(x_{i})\) represents the predicted result; \(y_{i}\) represents the actual value; \(N\) represents the amount of data. PSNR is a metric commonly used to measure the quality of image representation by calculating the ratio between the maximum possible signal power and the power of the distorting noise. PSNR is calculated by following Equation (5). \[\text{PSNR}=10 log_{10}\Bigl{(}peakval^{2}\Bigr{)}/MSE, \tag{5}\]  
Figure 7:0 F-k spectrum about Figure 7:1 (**a**) Label data in inline direction; (**b**) interpolation results and corresponding residuals (difference between interpolation result and label) about (**a**). where _peakval_ (peak value) is the maximal in the image data. A larger PSNR indicates better quality of the image. SSIM is a perceptual image quality assessment metric used to measure the quality of an image. This metric compares the contrast, brightness, structure, and other aspects of an image to measure the structural similarity between the original and altered images. SSIM is calculated by following Equation (6). Figure 7:2  
where \(x\) and \(y\) represent the two images to be compared; \(\mu_{x}\), \(\mu_{y}\), \(\sigma_{x}^{2}\), \(\sigma_{y}^{2}\), and \(\sigma_{xy}\) are the mean, variance, and covariance of images \(x\) and \(y\), respectively; \(C_{1}\) and \(C_{2}\) are small constant values. The \(\text{SSIM}(x,y)\) value ranges between 0 to 1, with values closer to 1 indicating greater similarity between \(x\) and \(y\). We obtain the average values of these metrics by applying the trained model to the test dataset (Figure 12). The standard deviation of each is shown as error bars on the graph, and the \(x\)-axis represents the amount of missing data as a percentage. Figure 12a-c represents the graph of the comparison of MSE, PSNR, and SSIM, respectively, and those values for all the test cases are presented in Figure 7:3  
When 50% of the traces are regularly missing, as shown in Figure 12, the results indicate that both the 3D U-Net and 3D cWGAN exhibit similar accuracy, with the 3D U-Net having a higher MSE (indicating worse performance) and PSNR (indicating better performance), but equal SSIM compared to the 3D cWGAN. The 2D cWGAN model performs worse than other models in this case. These findings suggest that both the 3D U-Net and 3D cWGAN models can be effective in cases where 50% of traces are regularly missing. However, in all other cases except regularly missing 50%, the 3D cWGAN consistently outperformed the other two models. The 3D U-Net performs worse as the missing rate increases and is even worse than the 2D cWGAN.