# Seismic Blind Deconvolution Based on Self-Supervised Machine Learning
## 1 Introduction  
As a common technique for seismic data processing, deconvolution is important for applications like impedance inversion and high-resolution processing [1; 2; 3; 4]. According to the specific implementation, the present deconvolution methods can be generally divided into three categories: non-machine learning methods, supervised machine learning methods, and self-supervised machine learning methods. Classical non-machine learning deconvolution methods have gained wide applications in the past few decades. [PERSON] and [PERSON] [5] established a theoretical basis for predictive deconvolution. [PERSON] [6] proposed homomorphic deconvolution which utilized logarithmic spectrum to obtain an average wavelet and then attained the seismic wavelet and reflectivity. [PERSON] [7] proposed minimum entropy deconvolution, which was one of the first studies to explore the concept of sparsity in seismic deconvolution. Based on the prior research findings, a number of novel and influential deconvolution techniques have been proposed in recent years. [PERSON] et al. [8] proposed a blind deconvolution method based on Toeplitz-sparse matrix factorization. This method simultaneously estimated seismic wavelet and reflectivity, and can better maintain the lateral continuity of the seismic profile. [PERSON] et al. [9] developed a high-resolution seismic deconvolution method based on joint sparse representation using the stratigraphic information from well-logging reflectivity and observational seismic data. [PERSON] et al. [10] proposed a blind deconvolution method that exhibited improved fidelity and simplified parameter selection through the applicationof a compact smoothness constraint on the wavelet and a relative sparsity constraint on the reflectivity. In the classical methods widely used in the past, scholars often impose L1 or L2 norms on the reflectivity, or apply constraints such as smoothness and finite support on the wavelet. However, these constraints render the objective function challenging to solve, and the parameters of the regularization terms are also difficult to determine. As a type of artificial intelligence, machine learning algorithms enable computers to learn from experience and data without being explicitly programmed. These algorithms provide the key benefits of increased efficiency, accuracy, and scalability [11]. In recent years, machine learning methods have gradually demonstrated promising results in geophysical fields such as denoising, inversion, and fault detection [12; 13; 14; 15; 16]. In the field of deconvolution, researchers have also proposed many machine learning-based algorithms. [PERSON] et al. [17] implemented a sequential iterative approach that sequentially inverted the initial reflectivity profile, seismic wavelet, and final reflectivity profile using deep learning techniques. [PERSON] et al. [18] proposed a generalized convolution model based on deep learning and achieved high-fidelity deconvolution results in complex situations. [PERSON] et al. [19] used the information of well data to generate reflectivity sequences, and then constructed labels consistent with the relevant data to obtain well-performing networks. [PERSON] et al. [20] proposed a channel attention U-Net to establish a nonlinear mapping relationship between seismic data and reflectivity. However, most of the aforementioned methods are based on supervised machine learning, which usually relies on a large and representative training dataset comprising low-resolution seismic data and corresponding high-resolution reflectivity labels [21]. If labelled data are limited or unavailable, supervised machine learning typically cannot generalize well [22]. Therefore, the self-supervised machine learning deconvolution method, which utilizes the inherent physical prior contained within the data to guide machine learning towards yielding physically consistent results, is a valuable topic. [PERSON] et al.