# Self-Supervised Shear Wave Noise Adaptive Subtraction in Ocean Bottom Node Data
## 1 Introduction
Deep learning, as a subset of machine learning, has been growing rapidly in recent years in areas such as image processing, speech recognition, and natural language processing [21; 22]. Deep learning learns and makes predictions from complex datasets by training deep neural networks (DNNs), which are artificial neural network (ANN) structures with multiple hidden layers. DNNs are able to learn abstract feature representations by combining multiple nonlinear mapping functions, especially complex nonlinear relationships [23; 24]. In recent years, deep learning methods have been developing rapidly in the field of geophysics, with applications in almost all stages of seismic processing and interpretation [25], including denoising [10], velocity model building [26], first break picking [27], interpolation [28], inversion [29; 30] and fault identification [31]. Removal of random noise using deep neural networks is usually trained based on large training sets where the inputs are contaminated data and the corresponding outputs are the clean data, which is referred to as supervised learning. The superior performance of DNNs relies on the extent to which the training set consisting of noisy-clean data pairs agrees with the distribution of the field data [32]. To address this problem, many researchers have proposed unsupervised and self-supervised denoising approaches that only require the contaminated data [33]. For example, [PERSON] et al. [34] selected favorable network architectures based on the impedance difference of noise and seismic data as a prior model for seismic data denoising and designed a stopping criterion to automatically acquire potentially clean seismic data. [PERSON] et al. [35] proposed a self-supervised method that combines the capacity of a deep denoiser and the generalization abilities of hand-crafted regularization for seismic data random noise attenuation. At the same time, all supervised, unsupervised/self-supervised methods have also made a lot of progress in coherent noise removal [10; 36]. [PERSON] et al. [37] developed a generative adversarial network (GAN) training by data pairs with and without ground roll to attenuate the ground roll in seismic data. [PERSON] et al. [38] proposed a self-supervised deep neural network method based on a hybrid loss function including localized wavefield characteristics to remove multiple waves. [PERSON] et al. [39] applied an adaptive subtraction method based on U-Net to represent the complex nonlinear relationship between real and modeled multiples. [PERSON] et al. [40] developed a convolutional neural network (CNN)-based matching algorithm to attenuate surface-related multiples. For field OBN data, the clean Z-component data are unavailable, therefore the application of supervised learning is limited. [PERSON] et al. [20] combined synthetic data with field data to construct a training set to reduce the discrepancy with field data. It trained the network as a shear wave noise extractor and then was applied to the field Z-component data. In this work, we explore a self-supervised learning approach for shear wave noise adaptive subtraction in OBN data inspired by the methods of multiple wave removal [39; 40]. To the best of our knowledge, this study first applies a self-supervised learning approach to shear wave noise suppression. Specifically, we conduct adaptive subtraction using a deep learning method. The horizontal component of OBN data are the noise model that is fed into the constructed DNN, and the output of the neural network is the actual leaked shear wave in the Z-component recordings. The method does not require clean data and is a self-supervised learning approach. We perform numerical experiments on synthetic datasets, and quantitative and qualitative analyses verify the feasibility and effectiveness of the method. In addition, the experimental results of applying the proposed method to field data show that the method effectively removes the noise without damaging the valid signals. The subsequent sections of this paper are organized as follows.