# Algorithm for Extraction of Reflection Waves in Single-Well Imaging Based on MC-ConvTasNet
###### Abstract  
Single-well imaging makes use of reflected waves to image geological structures outside a borehole, with a detection distance expected to reach tens of meters. However, in the received full wave signal, reflected waves have much smaller amplitudes than borehole-guided waves, which travel directly through the borehole. To obtain clear reflected waves, we use a deep neural network, the multi-channel convolutional time-domain audio separation network (MC-ConvTasNet), to extract reflected waves. In the signal channels of the common-source gather, there exists a notable arrival time difference between direct waves and reflected waves. Leveraging this characteristic, we train MC-ConvTasNet on the common-source gathers, ultimately achieving satisfactory results in wave separation. For the hard-to-hard single-interface, soft-to-hard single-interface and double-interface models, the reflected waves extracted by MC-ConvTasNet are closer to the theoretical reflected waves in both phase and shape (the average scale-invariant signal-to-distortion ratio exceeds 32 dB) than those extracted by parameter estimation, a median filter and an F-K filter. Meanwhile, MC-ConvTasNet naturally fits in the scenarios of various inclined interfaces and interfaces parallel to the borehole axis. As an application, our method is employed on field logging data and its ability to separate waves is verified. s +
Footnote †: journal: Applied Sciences  
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can separate reflected signals. [PERSON] et al. [PERSON] et al. (2018) suggest a parameter estimation method for CSG and common-receiver gather (CRG) data to separate downgoing and upgoing waves, respectively. For common-offset gather (COG) data, an F-K filter [PERSON] et al. (2018), high-resolution Radon transform T. (2018), Karhunen-Loeve transform Karhunen-Loeve (1966), shear wave transform T. (2018) and unsupervised machine learning T. (2018) are proposed for wave separation. Median filters can be applied to COG T. (2018), CSG and CRG T. (2018) data to extract the reflected waves. However, the extraction methods mentioned above have intrinsic drawbacks. The parameter estimation and the wave field separation filter combining parametric decomposition and waveform inversion can only suppress part of the direct wave. The computational efficiency of the high-resolution Radon transform is low. The amplitude of reflected waves extracted by a median filter is jagged. Methods applied to COG data are not suitable for the cases in which the interface is parallel to the borehole axis. A clear and complete reflected wave is essential for high-quality imaging results. Therefore, it is necessary to propose a convenient and reliable method for extracting reflected waves. The separation of the reflected wave and direct wave in the recorded full wavetrains in the borehole has similarities to the separation of the target waveform and the interference waveform (or background noise) in speech separation T. (2018). In the borehole problem, the signal is excited by a single acoustic source. The signal that reaches the receiver through the well is a direct wave. The signal returned through the reflection interface is called the reflected wave. In speech separation, the reflected wave that can be distinguished from the direct wave is called echo. The reflected wave that overlaps the direct waveform is called reverberation. The borehole problem is similar to the indoor mono-source scenario problem in speech separation. There are many neural networks with good performance, fast filtering speed and high accuracy in the field of speech separation which can be used as a reference for solving the problem of reflected wave extraction. Many speech separation methods are performed in the time-frequency domain of the signal T. (2018); T. (2018); T. (2018). In general, the signal is converted into a spectrogram using short-time Fourier transform, and then the neural network performs speech separation in the time-frequency domain T. (2018).