# Algorithm for Extraction of Reflection Waves in Single-Well Imaging Based on MC-ConvTasNet
## 3 Results
### Wave Separation for Field Logging Data  
Figure 12 shows the actual logging data of an oil field. Figure 12a is a variable density map of COG domain recordings containing waves excited by the x-axial dipole source on the cross-dipole tool and received by the first receiver in the same direction. We use red lines to circle the areas where the reflected waves are present (see Figure 12b-e). In Figure 12b, parameter estimation extracts most of the reflected waves and slightly reduces the amplitude of the direct waves. In Figure 12c,d, the median filter is shown to retain more reflection waves than the F-K filter, but it does not extract as many reflection waves as parameter estimation. Comparing the results of the four wave separation methods, MC-ConvTasNet suppresses most of the direct waves and preserves the vast majority of the reflected waves (see Figure 12e). We use the phase-shift-plus interpolation method [40] to image the reflected waves extracted by these four methods (see Figure 12f-i). The red dotted lines are used to circle the areas where the reflectors are present. In Figure 12h, the reflector is not imaged. This is because the F-K filter does not extract this part of the reflected wave. A fuzzy reflector appears in the imaging results of both parameter estimation and the median filter but there are many artifacts (see Figure 12f,g). The reflector in Figure 12i is the clearest with the fewest artifacts, obtained from the imaging of reflected waves extracted by MC-ConvTasNet, and it agrees well with the reflected waves in Figure 12e. It demonstrates that the reflected waves extracted by MC-ConvTasNet are clearer and more complete. Figure 11: Full waveforms containing noise and extracted reflected waves for the hard-to-hard single-interface model. (**a,d**) are COG full waveforms containing Gaussian white noise with signal-to-noise ratios of 20 dB and 25 dB, respectively. (**b,e**) are the reflected waves separated by MC-ConvTasNet. Trace 4 in (**b,e**) is compared with the full wave and the theoretical reflected wave, respectively, as shown in (**c,f**). The R\({}_{\text{rmsse}}\) for 20 dB and 25 dB is 0.100 and 0.0649, respectively. Figure 12: Cont. To evaluate the capability of four wave separation methods in suppressing direct waves within field logging data, we introduce two quantitative metrics: the direct wave suppression ratio and the signal-to-noise ratio. Based on the imaging results, it can be roughly estimated that the majority of the direct waves in this well section arrive before 8 ms. We evaluate the suppression capability of wave separation methods for direct waves arriving before 8 ms using the \"direct wave suppression ratio\" as an indicator. The direct wave suppression ratio between the full wave \(\mathbf{u}=[r_{1},r_{2},\ldots,r_{T}]\) and the extracted reflection wave \(\mathbf{\hat{v}}_{1}=[\hat{q}_{1},\hat{q}_{2},\ldots,\hat{q}_{T}]\) is defined as follows:  
\[\text{R}_{\text{dsr}}=10\text{log}_{10}\left( \begin{array}{c}\sum\limits_{i= 1}^{M}\left(r_{i}\right)^{2}\\ \sum\limits_{i=1}^{M}\left(\hat{q}_{i}\right)^{2}\end{array} \right).\]  
Here, \(M\) represents the total number of sampling points of the time-domain waveform within the range 0-8 ms. The direct wave suppression ratio is derived from the echo suppression ratio [41] in speech signal processing. The signal-to-noise ratio between the full wave \(\mathbf{u}\) and the extracted reflection wave \(\mathbf{\hat{v}}_{1}\) is defined as follows [13]:  
\[\text{R}_{\text{snr}}=20\text{log}_{10}\bigg{(}\frac{\text{max}(\text{abs}( \mathbf{u}))}{\text{max}(\text{abs}(\mathbf{\hat{v}}_{1}))}\bigg{)}.\]  
Both the \(\text{R}_{\text{dsr}}\) and \(\text{R}_{\text{snr}}\) are measured in decibels (dB), where higher values indicate stronger direct wave suppression capability. In the field logging data, the \(\text{R}_{\text{dsr}}\) values corresponding to the four methods of parameter estimation, the median filter, the F-K filter and MC-ConvTasNet are 4.2 dB, 14.4 dB, 18.3 dB and 55.2 dB, respectively.