# A Denoising Method for Seismic Data Based on SVD and Deep Learning
## 1 Introduction  
Suppressing noise to improve the quality of seismic signals has always been an essential task in seismic data processing. The denoising method for seismic data with a low signal-to-noise ratio (SNR) is a focus of attention at present [1, 2]. The traditional methods for denoising seismic data include f-x deconvolution filtering [3, 4], t-x prediction filtering [5, 6], s-transformation filtering [7], wavelet transform filtering [8], median filtering [9, 10], empirical mode decomposition [11], and singular value decomposition. The principle of the singular value decomposition (SVD) method assumes that the effective seismic information is mainly concentrated in the feature maps corresponding to large singular values. The effect of noise attenuation can be achieved by setting K = 1 or K = 2 when reconstructing. The traditional seismic data denoising methods are very effective when the SNR is high, but they are unsuitable for low SNR seismic signals. For example, SVD is used to remove seismic data noise. When the noise energy is too large, the large singular value may not represent the effective signal. At this time, it is difficult to choose the rank. When the rank is too large, too much noise will be retained, and the seismic signal becomes damaged when the rank is too small. So choosing the appropriate rank is a crucial step for the SVD method [12, 13]. Therefore, exploring a method that can effectively attenuate the noise of seismic data with a low SNR is necessary. Currently, the research on the denoising of seismic data using the SVD method is continuing, and there are some advances in the suppression of strong amplitude, random, coherent, and abnormal optical noise. For example, [PERSON] et al. [14] proposed asingular spectrum analysis method using low-rank approximation instead of truncated SVD to suppress intense interference noise. To compress and denoise seismic data, [PERSON] et al. [15] proposed a shift matrix decomposition (SMD) method that compresses seismic data by applying SVD and storing the seismic data into singular vector pairs coupled with shift vectors. These methods can suppress the noise but only partially remove it in areas without a seismic signal. However, the improved SVD method proposed by us can remove the noise in an area without a seismic signal. [PERSON] et al. [16] proposed a multi-channel SVD denoising convolution neural network, which remarkably removes random, correlated, and optical abnormal noise. However, compared with the right singular vector, noise subspaces' records are morphologically complex, which makes it more difficult to make data sets and identify seismic signals. Meanwhile, the training time of the network is longer, and the computer performance requirements are high. However, in our proposed method, the right singular vector is simple in form, easy to collect, fast in training time, and low in computer performance. [PERSON] et al. [17] used a Wiener filter based on SVD to attenuate coherent noise. In this paper, the SVD technique is improved for Gaussian noise and irregular intense amplitude noise in seismic data so that the new method effectively suppresses the noise. Considering the vast and successful application of deep learning methods in various fields, many applications in seismic exploration include seismic data denoising, seismic fault detection, seismic signal reconstruction, and seismic signal classification. For example, [PERSON] et al. [18] improved the deep convolution neural network based on a patch and used it to denoise seismic images. This method dramatically affects seismic data with a low SNR and noise that changes randomly with time and space. [PERSON] et al. [19] used a supervised full convolution neural network for 3D seismic image recognition, thus enabling accuracy and efficiency in predicting the location of faults. [PERSON] et al. [20] developed a convolutional self-coding method that can remove random noise while reconstructing seismic signals and quickly process a large amount of seismic data. [PERSON] et al.