# Semi-Supervised Training for (Pre-Stack) Seismic Data Analysis
## 1 Introduction  
Labeled data are essential for improving the performance and generalization of supervised deep learning algorithms in real-world problems. Different domains, such as healthcare [1, 2], natural language processing (NLP) [3, 4], and reservoir characterization [5, 6], are significantly affected, due to privacy concerns and the need for expert annotations; labeling is also time-consuming and rather costly. However, there is a large amount of unlabeled data available in these domains: medical records, images, and genetic information in healthcare [7, 8], and 3D seismic data in reservoir characterization [9, 10]. Nevertheless, unsupervised learning techniques have shown the ability to learn hidden features from vast amounts of unlabeled data, and they can be used to enhance supervised learning. Seismic data and well-log data analysis are complex because of the heterogeneous structure of the Earth's subsurface [11]. To model this kind of data requires an adequate capability to discover nonlinear relationships between the input and output of an artificial neural network (ANN). Deep neural networks (DNN) are suitable tools for these tasks. These models are widely utilized in geophysics for seismic data interpretation, such as data inversion [12, 13, 14], data quality improvement [15, 16, 17, 18, 19], geological feature classification, and petrophysical property prediction. Various studies have employed geological featureclassification; for example, [PERSON] [20], [PERSON] [21], and [PERSON] [22] used convolutional neural networks (CNNs) for seismic fault detection, salt body identification, and seismic horizon tracking, respectively. Moreover, multi-layer perceptrons (MLP) have been applied to detect gas chimneys [23] and for lithology and fluid classification [24]. On the other hand, for petrophysical property prediction, such as permeability, mineralogy, and porosity, CNNs [25; 26; 27], Boltzmann machine [28], DNNs [29], gated recurrent neural networks (RNN) [30], and bi-directional long short-term memory (BiLSTM) [27] have been utilized. Semi-supervised learning (SSL) methods can improve the performance of machine learning models by utilizing unlabeled data, particularly when supervised data are scarce. This has been shown since the early wrapper SSL methods, passing through pre-training methods and later generative methods [31]. Self-training and co-training are wrapper methods that are still used for object detection [32], image classification [33], segmentation tasks for medical images [34], and image annotation [35]. These pre-training methods, which use deep neural networks, have been applied for brain tumor classification [36] using autoencoders, epilepsy detection [37] with CNN, brain functional network classification [38], and image classification on small datasets [39], with the latter using transformer networks. Generative adversarial networks (GANs), which involve a natural unsupervised generative method but extended to semi-supervised methods, have applications in facial image recognition [40] and hate speech detection [41]. The SSL approach is termed deep semi-supervised learning (DSSL) when it involves deep neural network architectures. Recently, there has been active research in training DSSL models for reservoir characterization. For example, [PERSON] [6] detected the presence of channels or non-channels with a CNN using 3D post-stack seismic data. Seismic facies were classified from elastic features by [PERSON] [9] using a DNN and with deep autoencoders by [PERSON] [42]. In addition, seismic facies were detected from post-stack seismic data by [PERSON] [43] using a CNN. From pre-stack seismic data, [PERSON] [10] identified gas-bearing employing k-nearest neighbors (kNN) and a CNN. In Liu [42], the authors used some unlabeled elastic features for pre-training. [PERSON] [44] detected faults with CNN using synthetic and field seismic data, while [PERSON] [45] classified facies from post-stack seismic data with a GAN.