## 3 Results  
### Gravity Data Denoising Results  
Various subsurface prism distribution models were selected as experimental subjects. In Figure 8, each row corresponds to a different subsurface geological structure. For each experiment, the columns from left to right display the following: a schematic of the subsurface prism distribution, the theoretical noise-free gravity anomaly field generated by this distribution, the observed gravity data after adding random noise, and the gravity anomaly results after denoising using the proposed algorithm. From top to bottom, the results correspond to experiments with 5%, 10%, and 15% Gaussian noise levels, respectively. The experimental results demonstrate that the proposed denoising method can effectively remove random noise from the observed data and significantly restore the true gravity anomaly features caused by subsurface structures. The denoised results show high consistency with the theoretical models and exhibit strong robustness and generalization across different geological models and noise types, validating the practicality and superiority of the proposed method for gravity data preprocessing. To further illustrate the denoising performance of the improved U-Net network, it was compared with traditional methods such as wavelet transform, moving average, and low-pass filtering. In this experimental case, three overlapping cuboids were constructed to verify the model's denoising capability in handling complex scenarios caused by overlapping bodies. The gravity anomaly was calculated on a 200 \(\times\) 200 grid with a spacing of 0.1 km. To compare the performance of different denoising methods on noisy gravity field data, experiments were conducted using a dataset with a noise level of 5%. As shown in Figure 9, the first column (a) presents the true gravity anomaly field without noise, serving as the reference for subsequent evaluation. The second column (b) shows the observed data after noise addition, where the significant interference of noise on the original gravity field signal is visible. Columns three to six (c-f) display the denoising results of the U-Net neural network, wavelet transform, moving average, and low-pass filtering, respectively. Comparative analysis reveals that the U-Net-based denoising results (c) most effectively restore the key features of the gravity field, closely matching the morphology of the true gravity anomaly field (a). The U-Net not only preserves the overall waveform but also retains detailed features. In contrast, while wavelet transform, moving average, and low-pass filtering can suppress noise to some extent, they are less effective in terms of feature completeness and accuracy. Figure 7: The relationship between training epochs and loss function. Figure 8: Comparison of denoising effects at different noise levels (\(5\%\), \(10\%\), \(15\%\)). Figure 9: Denoising results of different methods. Table 2 compares the Peak Signal-to-Noise Ratio (PSNR) performance of various denoising methods at different noise levels. For noise levels of 5%, 10%, 15%, and 30%, Table 2 lists the PSNR values for the original noisy data as well as those processed by different denoising methods, including the improved U-Net algorithm, wavelet, moving average, and low-pass methods. Higher PSNR values indicate better denoising performance. The table shows that under the same noise level, the U-Net network achieves the best denoising performance. Moreover, as the noise level increases, the advantage of the U-Net algorithm becomes more pronounced. Both horizontal and vertical comparisons of the data reveal that the proposed denoising algorithm significantly improves the PSNR values across all noise levels, demonstrating superior performance compared to other methods--especially in scenarios with a high level of noise. This indicates that the proposed denoising strategy not only effectively suppresses noise but also better preserves the original image details.