# Seismic Data Denoising Based on Wavelet Transform and the Residual Neural Network
## 1 Introduction  
Seismic signals will inevitably be affected by instruments, environments, and other factors, resulting in the need for seismic noise attenuation. Generally, seismic noise may be broken down into two distinct categories: coherent noise and random noise. Coherent noise has apparent kinematic characteristics and certain regularity. In contrast, random noise has strong randomness, and its existence is an important factor affecting the signal-to-noise ratio (SNR) of seismic data. To suppress the noise, scholars have proposed various denoising methods, such as F-x deconvolution [1, 2], empirical modal decomposition (EMD) [3, 4], Time-frequency peak filtering method [5], median filtering method [6], and so on. Denoising seismic data in virtue of the f-x approach is hindered by the fact that it presumes the signal to be linear and stationary, which is at odds with the nonstationary nature of seismic records; in contrast, EMD captures the nonstationary nature of the signal since it is data-driven, but mode mixing can cause the time-frequency distribution to be incorrect. Owing to the nonlinearity of the signal, the frequency peak filtering based on time-frequency analysis entails a loss of amplitude when denoising; the median filtering method is presented as a simple method of removing noise from a nonstationary signal, raising distortions in the signal shape related to the filter length. Subsequently, the sparse transform emerged as a method that can distinguish between noise and valid signals and has been extensively investigated in seismic random noise suppression. With the sparse transform-based denoising method, it is assumed that the seismic data are sparse in some transform domains, after transforming the seismic data to the sparse transform domain, thresholding is applied to the coefficients, and then the processed coefficients are inverse-transformed back to the original domain. Classic sparse transforms, including Fourier transform [7, 8] and wavelet transform [9, 10], are commonly used as sensitive and effective methods. Curvelet [11], Contourlet [12], and Shearlet [13] transforms were later advanced to compensate for the wavelet transform's lack of directionality and anisotropy. However, none of the aforementioned methods are data-driven and swayed by the characteristics of their own sparse transformation bases; furthermore, despite their increased speed, allmethods still require estimating the noise level and choosing the filtering threshold. To eliminate these drawbacks and better represent the sparsity of seismic data, dictionary learning [14; 15] started to play a role in seismic data denoising. Although dictionary learning eliminates the above-mentioned drawbacks to some extent, some of the overall data are missed when learning is performed using a limited number of random patches. The aforementioned techniques for suppressing noise in seismic data have their pros and cons, so how to improve the SNR of noisy data with a better approach is always a concern. In computing [16], medicine [17], and image processing [18], the machine learning method has emerged as a leading research path since the turn of the 21 st century, in tandem with the advancement of high-performance computing capabilities. Under this influence, the neural network has been introduced to seismic data processing and has obtained favorable results. Generative adversarial networks (GANs) [19], Resnet [20], and U-Net [21] are commonly used networks. A GAN employs a method in which generators and discriminators contest each other, with generators generating data to cheat discriminators, and discriminators differing between generated and labeled data allowing generators to produce more compliant data; however, subject to pattern collapse, GAN networks may struggle to deliver the expected data. Resnet, DnCNN, and U-net all belong to convolutional neural networks (CNNs). The CNN-based noise suppression method for seismic data involves recovering the effective signal by extracting features from the dataset.