# Algorithm for Extraction of Reflection Waves in Single-Well Imaging Based on MC-ConvTasNet
###### Abstract
Since the short-time Fourier transform usually only deals with the amplitude spectrum, the phase information may be inaccurate in the reconstruction, resulting in degraded speech quality T. (2018). The time-domain method usually adopts the end-to-end deep learning model, which can directly learn the separated features from the original waveform, avoiding the intermediate step of time-frequency domain conversion, and the reconstructed speech quality is usually higher. Wave-U-Net T. (2018), which is built upon the architecture of U-Net, integrates multiscale analysis and temporal domain processing for speech separation. Compared with the time-frequency domain method, Wave-U-Net has a simple structure and outstanding effect. Thereafter, [PERSON] and [PERSON] [PERSON] and [PERSON] (2018) proposed a convolutional time-domain audio separation network (Conv-TasNet) for speech separation. In Conv-TasNet, a linear encoder maps the mixed waveform to an encoded representation. Stacked dilated 1-D convolutional blocks then act as a separation module to separate encoded representations from different acoustic sources. The encoded representation containing a single sound source is then transformed into the desired source waveform using a linear decoder. Due to its superior performance, it is used in logging T. (2018). Because the quality of speech separation is greatly improved by multiple channels T. (2018), this paper realizes the reflection wave extraction by analyzing the waveform signal of a multi-channel array. In the COG domain, both the direct wave and the reflected wave from parallel interfaces have a zero inter-channel arrival time difference, which is detrimental to separation by neural networks. However, single-well imaging is also used for reflectors approximately parallel to the wellbore axis. Due to the differences in propagation distance and velocity between the direct wave and the reflected wave, the wavefront arrival time and the arrival time difference between channels in the CSG are always different. Therefore, we choose to extract the reflected wave in the CSG domain. Conv-TasNet was originally proposed for single-channel separation tasks. Inspired by the inter-channel phase difference formula, [PERSON] et al. [24] designed a new two-dimensional convolution kernel to calculate inter-channel convolution difference (ICD), supplementing Conv-TasNet with spatial clues and optimizing its parameters in a purely data-driven manner. That neural network hereafter is called MC-ConvTasNet. It works well for suppressing direct waves in this study. To address the scarcity of labeled reflection waves in field logging data, we propose to generate a dataset based on analytic algorithms. Wave separation for dipole shear wave imaging can be regarded as a supervised learning problem, with the learning target being direct and reflected waves in the time domain. When using supervised learning to train neural networks, the training dataset must include the output target (also known as the label) for each corresponding input sample [25]. The reflectors in dipole shear wave imaging are typically located several meters to tens of meters away from the borehole, which presents a challenge for directly validating the correspondence between the imaging results and the actual geological structures. This makes it difficult to accurately infer pure reflected waves based on precise geological structure information. It is difficult to meet the training requirements of neural networks only by constructing a training dataset based on field logging data. In order to obtain an efficient reflected wave extraction system, it is necessary to simulate a large number of data. A fast forward algorithm is needed to simulate actual logging and output synthesized full waveforms. [PERSON] and [PERSON] [26] derived an analytical expression for the displacement inside the borehole excited by the direct wave. The direct wave can be quickly synthesized by using the real axis integration method [27].