# Semi-Supervised Training for (Pre-Stack) Seismic Data Analysis
## 2 Methodology
### Seismic Data Pre-Processing  
The pre-processing phase entailed preparing the datasets for training the neural network. This involved the seismic cube as a source of features and the AI data as the target variable. A set of traces per CDP, or gather, from the seismic cube were selected, as depicted in Figure 4. A gather from the land seismic acquisition comprised 40 traces, and experimentation revealed that the neural network exhibited improved performance when trained on 18 traces per gather, following comparisons with configurations employing 6, 12, and 24 traces. Subsequently, these selected traces and the target were subjected to rescaling, resulting in values within ranges of \([-1,1]\) and \([0,1]\), respectively. In addition, seismic traces had a lower sample rate than the AI data. Consequently, an interpolation process was performed, ensuring both had the same number of samples. To provide a seismic context for each target sample, the dataset used for training was constructed by relating a window of seismic samples to each target sample, as illustrated in Figure 5. From the initial seismic point to the final one, a moving window slides across  
Figure 3: Optimal alignment achieved between the synthetic and seismic data for Well-1, along with the resultant absolute AI extracted from the synthetic data. a predefined number of samples (in this case, 53) along each gather's traces. After each windowing operation, the window slides one sample. In this way, each target sample is related to the midpoint of the window length. This approach yielded a large number of examples from each CDP. Compiling these examples spanning across multiple CDPs created the dataset. In Figure 6, each cell represents a CDP. Test examples were obtained by selecting the gather corresponding to the location of the borehole, while training examples were extracted from adjacent CDPs. Both test and training examples were consistently labeled using the well-log AI data. This approach resulted in a larger number of labeled examples compared to a single gather-based strategy using the well-log AI, which would have yielded fewer labeled examples. In turn, the labeled dataset was employed for supervised training purposes. The dataset is aptly termed \"labeled\" because, from a geoscientist's perspective, AI is a petroacoustic property exhibiting distinct stratigraphic units for various subsurface materials. For instance, the impedance values for hydrocarbon-bearing sands typically fall within the range of 17,500 to 21,500 (ft/s)*(g/cc), while water-bearing sands are found in the range of 22,000 to 24,500 (ft/s)*(g/cc). Shale encompasses values spanning from 24,500  
Figure 4: Raw seismic trace features from CDP and AI as a target from well-log. Figure 5: Windowing on 18 traces and the corresponding AI sample to build labeled examples for the dataset. Figure 6: Labeled dataset configuration for supervised learning. Expanding the labeling process to encompass the gather next to the well and the surrounding gathers. to 27,500 (ft/s)*(g/cc) [56; 58]. However, we would like to point out that this categorization is beyond the primary scope of this study, where we treated AI as individual data samples. For semi-supervised learning, the data pre-processing was similar to that of the supervised learning. However, there were slight differences in the approach. It was similar because it involved taking the same number of traces per CDP, as well as rescaling, interpolation, and windowing operations. However, while the labeled data remained consistent, the unlabeled data underwent pre-processing without including AI information, comprising features exclusively. The extent of the CDPs utilized for unlabeled examples is visually represented in Figure 7, which shows that 65% of the data were allocated for training and the remaining 35% were reserved for testing during the pre-training phase. Following that, the labeled dataset was employed for fine-tuning in the subsequent stages of the analysis.