Reviving Legacy Seismic Data via Machine Learning Technique—Part 2: Estimating 3-D Seismic Volumes From 2-D Seismic Lines With VQ-VAE

We propose a machine learning-based method that estimates a 3-D seismic volume from irregularly placed 2-D seismic lines, addressing the challenges regarding the local disturbances contained within 2-D lines (e.g., seismic misties and discrepant seismic characteristics across lines). To overcome these challenges, we employ the vector-quantized variational autoencoder (VQ-VAE) framework, which effectively captures global structures in data. Through appropriate data augmentation processes, the network is trained with diverse samples despite the limited availability of seismic volumes, enhancing its generality for estimating 3-D structures. Specifically, numerous training samples are generated from five seismic volumes with various augmentation methods, including perspective transform along the horizontal axes, horizontal flipping, polarity reversal, and random signal-level perturbations (e.g., smooth gain functions and convolution filters). In addition, a two-stage training process, into which randomly generated convolution filters are incorporated, further strengthens the robustness to local disturbances. We validate and evaluate the trained network on unseen 3-D volumes using $L_{1}$ and 3-D structural similarity index measure (3D-SSIM) metrics, demonstrated with numerical examples. The validation confirms that: 1) the proposed method successfully reconstructs subsurface geological structures from 2-D lines and 2) random filtering enhances performance for inconsistent (IC) lines. In addition, we test the applicability of the proposed method with actual 2-D lines acquired from the Jeju Basin, which have various line intervals ranging from 0.5 to 4 km. The testing results show that the network effectively manages intervals up to 2 km but struggles to estimate structures beyond straightforward horizontal layers at intervals of 4 km.