# Semi-Supervised Training for (Pre-Stack) Seismic Data Analysis
## 1 Introduction
Table 1 summarizes recent DSSL and supervised methods closely related to our proposed method. In this work, we present a new method for training a DSSL model for unlabeled 3D pre-stack seismic data, which are seismic traces organized into gathers, also known as common depth points (CDP). CDP gathers are constructed from a systematic arrangement of controlled seismic events. In contrast to the stacked traces in post-stack seismic data, these gathers encapsulate a richer seismic dataset. This kind of information allows us to significantly enhance the performance of neural networks in seismic data analysis [46; 47]. Research on using pre-stack seismic data for reservoir characterization in DSSL is still ongoing, as well as semi-supervised learning employing shallower models [48; 49; 50; 51; 52; 53; 54]. Well-log data provide a direct and comprehensive depiction of subsurface conditions, offering detailed insights into rock and fluid properties for the depth of a borehole [55]. These properties can serve as a valuable resource for labeling pre-stack seismic data and facilitating the creation of labeled datasets, but only for seismic data near the wells. However, the availability of such datasets remains constrained due to factors like the high costs associated with well drilling and data ownership by companies, which affect subsurface modeling using deep neural networks. A valuable petroacoustic property derived from well-log data is the absolute acoustic impedance (AI), which plays a pivotal role in characterizing reservoirs for lithology, hydrocarbon potential, fluid content, and more [56]. Given the importance and challenges associated with acquiring AI, the intersection of technology and data, specifically DNN and pre-stack seismic data, holds the potential to enhance the estimation and generation of valuable data for oil exploration, which is the primary focus of our work. This study contributes to addressing the problem of training a DSSL model to estimate the absolute AI from CDP seismic data using limited labeled information derived from well-log data. This is a challenge for both computer science and geophysics. While previous related works successfully classified or estimated various geological features or petrophysical properties, predicting well-log absolute AI from pre-stack seismic data has yet to be fully explored. Extracting underlying features directly from unlabeled data is also an aspect that has not been thoroughly investigated. A substantial amount of unlabeled pre-stack seismic data are generated for the pre-training stage of the DSSL method, which enhances the training convergence speed, especially with limited labeled instances. Additionally, we have included a data augmentation step to expand the availability of labeled data by leveraging the nearest gathers to the well-log data. The nearest gathers exhibit similar patterns in their seismic traces, allowing us to generate additional labeled instances from the same well-log data. The DSSL approach employed in this study utilizes a multi-layer long short-term memory (LSTM) architecture, treating seismic data as sequential or time-series information. To circumvent random initialization, a greedy layer-wise pre-training strategy was employed, to facilitate the gradual learning of data representations in an unsupervised manner, layer by layer. Additionally, the model was fine-tuned using a limited number of labeled instances obtained from well-log data. In addition to configuring the optimizer, loss function, and neural network size, introducing dropout hyperparameters at each layer was crucial in enhancing the model's learning capability concerning the data. Furthermore, adopting a linear-epoch gradual-warm-up scheme proved instrumental in accelerating the training process when handling vast volumes of unlabeled data. To assess the effectiveness of the DSSL method, we also implemented a supervised learning approach for comparative analysis of the results and predictions.