# Algorithm for Extraction of Reflection Waves in Single-Well Imaging Based on MC-ConvTasNet
## 5 Conclusions  
We apply MC-ConvTasNet to wave separation to achieve effective extraction of reflected waves. Due to the differences in propagation distance and velocity between the direct and reflected waves, their arrival time differences between channels in the CSG are different. The Conv2d module in MC-ConvTasNet is used to obtain spatial cues between channels to help separate the direct wave and the reflected wave. Because reflectors are rarely known in field logging, synthetic data are used as a dataset in this study. A large number of theoretical waveforms of the CSG are obtained by analytical algorithms. After training, MC-ConvTasNet exhibits an excellent ability to extract reflected waves. Using three models, we compare the wave separation performance of parameter estimation, MC-ConvTasNet, a median filter and an F-K filter. In the hard-to-hard single-interface model and soft-to-hard single-interface model, the average R\({}_{\text{std}}\) of parameter estimation and the median filter is less than 12.4 dB, less than 31 dB for the F-K filter and more than 33 dB for MC-ConvTasNet. The reflected waves extracted by MC-ConvTasNet are closest to the theoretical reflected waves in both phase and shape, with the largest average R\({}_{\text{std}}\). In the double-interface model, the average R\({}_{\text{std}}\) of the other three methods is less than 0, while the average R\({}_{\text{std}}\) of MC-ConvTasNet is more than 32 dB. Despite the absence of double-interface samples in the dataset, MC-ConvTasNet exhibits excellent performance in dealing with double-interface cases, and MC-ConvTasNet trained on waveforms in the CSG domain is proven to be suitable for interfaces parallel to the wellbore axis. In the hard-to-hard single-interface model, we compare the wave separation capability of MC-ConvTasNet on waveforms without noise and waveforms with Gaussian white noise. Compared with noise-free data, the increase in the root mean square error is less than 0.06 when the signal-to-noise ratio is 20 dB. MC-ConvTasNet is applicable to data containing noise and maintains good performance. In the field logging data, MC-ConvTasNet is compared with parameter estimation, a median filter and an F-K filter. Surprisingly, MC-ConvTasNet extracts clearer and more complete reflected waves. The reflector obtained from the imaging of reflected waves extracted by MC-ConvTasNet is the clearest one, with the fewest artifacts, and MC-ConvTasNet achieves both an R\({}_{\text{dsr}}\) and an R\({}_{\text{snr}}\) exceeding 55 dB, demonstrating a superior direct wave suppression capability. Despite the dataset not including field logging data, MC-ConvTasNet is effective for field logging data analysis. When MC-ConvTasNet is used to process the waveforms of the CSG, end-to-end wave separation can be achieved. By inputting the full wave of the CSG containing the currently processed channel, MC-ConvTasNet outputs the time-domain waveforms of direct and reflected waves. It is expected to extract reflected waves in real time when the acoustic logging tool is continuously lifted. Conceptualization, data curation, investigation, methodology, software, validation, visualization, writing--original draft, writing--review and editing, W.L. ; conceptualization, funding acquisition, resources, writing--review and editing, J.X. ; funding acquisition, project administration, supervision, writing--review and editing, H.H. All authors have read and agreed to the published version of the manuscript. This work was supported by the National Natural Science Foundation of China (grant no. 12472087, grant no. 42204117, grant no. 12272107). Not applicable. The original contributions presented in this study are included in the article. Further inquiries can be directed to the corresponding author. We would like to express our sincere gratitude to [PERSON] for providing the field logging data, which were essential for the completion of this study.