We propose a novel machine learning-based seismic volume reconstruction method that gradually extrapolates a seed volume by referring to line data external to the seed volume. The proposed method employs the generative adversarial network (GAN) framework with gated convolution, facilitating the training process by providing feedback for the extrapolated volumes. Our approach can be applied to address the practical limitations associated with the shortage of 3-D data often encountered in seismic surveys, where 2-D data typically cover regional areas, but 3–D data are confined to small areas. To alleviate the scarcity and limited availability of seismic survey data, we introduce effective data augmentation methods that ensure the robustness and generality of our neural network even when trained with only a seed volume. Unlike a simple supervised scheme, our approach (i.e., adversarial scheme) employs an auxiliary network during the extrapolation process, which functions similarly to the discriminator in the GAN framework, improving the network’s performance for restoring strata and high-frequency features. Through numerical examples, spectral analyses, and performance evaluations for extrapolated volumes, we demonstrate that our method integrates 2-D and 3-D seismic data more effectively than the supervised scheme to produce extensive volumes. Furthermore, our method demonstrates relatively robust performance in cases where input lines show high or low consistency to each other although some artifacts are observed in the low-consistency case.

We propose a machine learning-based method that estimates a three-dimensional (3D) seismic volume from irregularly placed two-dimensional (2D) seismic lines, addressing the challenges regarding the local disturbances contained within 2D 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 3D 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 3D volumes usingL1and 3D structural similarity index measure metrics, demonstrated with numerical examples. The validation confirms that 1) the proposed method successfully reconstructs subsurface geological structures from 2D lines and 2) random filtering enhances performance for inconsistent lines. In addition, we test the applicability of the proposed method with actual 2D lines acquired from the Jeju Basin, which have various line intervals ranging from 0.5 km 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.

Full-waveform inversion (FWI) aims at building a high-resolution velocity model by fitting numerically computed seismic data to observed one. Considering both the kinematic and dynamic properties of all waves in seismic data makes FWI highly non-linear. To mitigate its non-linearity, one can preferentially build low-wavenumber background velocity first, and then retrieve high-wavenumber reflectivity. However, in the early stage of FWI, the low-wavenumber velocity update is hardly derived from the reflected waves and mainly relies on the diving waves. To secure a wider coverage of low-wavenumber velocity updates from the reflected waves in addition to the diving waves, we propose two-step FWI based on diffraction-angle filtering (DAF) for 3-D seismic reflection data. In our method, DAF, which imitates the amplitude variations of the PP partial derivative wavefields with respect to the model parameters in elastic FWI to control small, intermediate, or large diffraction-angle energy, is adopted for the scale separation of a given velocity model into a background velocity and reflectivity model. The prior reflectivity provides information on reflection wavepaths. Then, the low-wavenumber update generated along the full wavepaths can build a background velocity model with improved wavenumber coverage. In addition, DAF can be implemented without a large increase in computational effort, which enables practical applications of our method to large-scale 3-D seismic field data. Applications of DAF-based two-step FWI to 3-D synthetic and field seismic data demonstrate that DAF-based two-step FWI can build a reliable background velocity model, which leads to stable convergence toward the global minimum.

In 4-D seismic surveys performed for carbon capture and sequestration projects, it is essential to acquire consistent time-lapse data to track the behavior of carbon dioxide. However, in practice, seismic events affected by nonrepeatable effects (i.e., nonrepeatable noise) hinder the objective of these surveys. Cross-equalization (XEQ) is a task that aims to reduce differences between time-lapse data by alleviating the adverse effect of nonrepeatable noise. XEQ using a convolutional neural network was proposed and applied to poststack data. By utilizing masks derived from the eikonal equation, we design an XEQ method for prestack data, which could contribute to retrieving ancillary information impaired during stacking and migration. The inherent nature of prestack data poses challenges when changing the data domain. To address these challenges, we introduce three supplementary methods: Fourier loss, coordinate conditioning, and logarithmic rescaling. Numerical examples show that the proposed XEQ effectively suppresses nonrepeatable noise while preserving 4-D signals even for prestack data, with minimal impact on amplitude information representing the degree of change. In addition, the supplementary methods enhance the matching quality and training stability. Sensitivity analyses on several factors (i.e., seawater velocity, source characteristics, ambient noise, and inaccurate masks) demonstrate the robustness of the proposed XEQ in suppressing nonrepeatable noise.

Seismic data are often coarsely or inconsistently sampled along the acquisition geometry due to the inherent limitations in survey equipment or insufficient survey budgets. Recently, machine learning techniques have been utilized to acquire compactly sampled seismic data. Among them, the self-supervised learning-based techniques that do not require labels are actively being used, and the interpolation technique based on the blind trace network (BTN) and spectrum suppression using suppression masks through line detection has shown high accuracy. However, the interpolation technique using BTN and the suppression masks through line detection suffers from instability caused by the reconstruction loss and inaccuracy of the suppression masks. To mitigate those problems, we propose suppression masks using generalized frequency-wavenumber (f-k) trace interpolation (GFKI), patch-based learning, masked UNet, and equalized learning rate. The suppression masks using GFKI are generated by correlating the zero-padded data with the data obtained by regularly removing traces from the zero-padded data in thef-kdomain. Additionally, we divide data into patches to enhance the accuracy of the suppression masks. Masked UNet is used to constrain the output to contain the input signals at the designated positions using the binary mask in the space–time domain. Furthermore, we normalize each layer in the network so that the learning speeds for each layer can be commensurate with each other. The synthetic and field data experiments show that the proposed interpolation technique effectively suppresses aliasing of signals and enables the training process to stably converge.

Seismic data are often irregularly or insufficiently sampled along the spatial direction due to malfunctioning of receivers and limited survey budgets. Recently, machine learning techniques have begun to be used to effectively reconstruct missing traces and obtain densely sampled seismic gathers. One of the most widely used machine learning techniques for seismic trace interpolation is UNet with the mean-squared error (MSE). However, seismic trace interpolation with the UNet architecture suffers from aliasing, and the MSE used as a loss function causes an oversmoothing problem. To mitigate those problems in seismic trace interpolation, we propose a new strategy of using coarse-refine UNet (CFunet) and the Fourier loss. CFunet consists of two UNets and an upsampling process between them. The upsampling process is done by padding zeroes in the Fourier domain. We design the new loss function by combining the MSE and the Fourier loss. Unlike the MSE, the Fourier loss is not a pixelwise loss but plays a role in capturing relations between pixels. Synthetic and field data experiments show that the proposed method reduces aliased features and precisely reconstructs missing traces while accelerating the convergence of the network. By applying our strategy to realistic cases, we show that our strategy can be applied to obtain more densely sampled data from acquired data.