Dong-Joo Min

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 using L₁ and 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.

Horizon interpretation is one of the most labor-intensive and interpreter-dependent processes in the reservoir characterization workflow. This issue becomes critical, particularly when the quality of a seismic reflector is poor. The uncertainty caused by inaccurate seismic horizon interpretations often misleads the volumetric analyses of subsurface reservoirs. To resolve these issues, we develop a four-step machine-learning-based semiautomated horizon interpretation workflow. In the first step, we generate multiple virtual stratigraphic labels. We then generate multiple synthetic data points to mimic the features of field data by applying a cycle-consistent generative adversarial network. In the third step, we train a U-Net augmented with feature pyramid attention and a convolutional block attention module on the synthetic data set. Finally, the probabilistic distribution results are used to obtain multiple horizon selection scenarios, yielding various possible stratigraphic results. As our method yields a probability distribution rather than a single value for a given field data and seed point, we can obtain multiple possible horizon scenarios rather than a single horizon. Through uncertainty quantification, we can select an appropriate horizon among multiple scenarios. We apply our method to the Smeaheia field data set, which is characterized by numerous and large faults, and compare the results with reference interpretation to confirm its accuracy. The field data example indicates that our method can be applied to complex geologic structures.

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 three-dimensional (3D) data often encountered in seismic surveys, where two-dimensional (2D) data typically cover regional areas, but 3D 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 2D and 3D 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.

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.

Research in multi-dimensional magnetotelluric (MT) modeling and inversion, particularly within anisotropic media, is gaining substantial interest. One-dimensional (1-D) modeling is utilized as boundary conditions necessary for accurate 2-D or 3-D anisotropic modeling. Based on Maxwell's equations and interface boundary conditions, we developed a new algorithm to calculate electromagnetic fields for both 1-D isotropic and anisotropic layered models. However, this algorithm encounters stability issues at considerable depths or within exceptionally thick layers. To address these challenges, we introduced two stabilization strategies. The first strategy alters the exponential terms in the plane-wave solutions to mitigate instabilities, while the second evaluates each layer's contribution to numerical instability, replacing problematic thick layers with an infinite half-space. Through numerical tests on a four-layer anisotropic model, these strategies proved effective, ensuring stable computations of electromagnetic fields at any depth and in configurations with thick layers, thereby enhancing the model's applicability for in-depth anisotropic analyses.

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 update 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 of 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.

Seismic reflection can provide precise estimates of subsurface structures. To obtain more information on subsurfaces using the same amount of reflection data, we first compared reverse time migration (RTM) images obtained from surface seismic profile (SSP), vertical seismic profile (VSP), and single well profile (SWP) data for models that included faults with various dips. When data were sufficient, SSP, SWP, and VSP surveys were suitable for identifying horizontal structures, structures with steep slopes, and vertical structures and horizontal structures near wells, respectively. An appropriate interferometry method was selected after considering the advantages and disadvantages of each survey when using either SSP or VSP data or both, when using an inaccurate velocity model for RTM, and when noise was added to the SSP data. The estimated RTM images were observed to be improved when interferometry was applied.

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 the f-k domain. 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.

The sponge boundary condition (SBC), an absorbing boundary condition, has not been discussed considerably; additionally, it has not been commonly used owing to its low applicability. Although the SBC is similar to the equation describing intrinsic attenuation in viscoelastic media, its behavior differs from the viscoelastic case. Herein, we present a new form of the SBC, which shows similarities with intrinsic attenuation. We describe the characteristics of the conventional and new SBCs with some numerical examples. By comparing the SBCs with the perfectly matched layer (PML) boundary condition, we found that the SBCs required broader damping areas than the PML to suppress artificial reflections; however, the SBCs could compensate for this deficiency with computational efficiency. The new SBC allows using variable-sized grids for damping areas, which substantially improves the performance of the SBC to be comparable to the PML while partially preserving computational efficiency.

Seismic anisotropy is an important physical phenomenon that significantly affects wave propagation in complex sedimentary basins. When geological structures exhibit steep dips or severe folding, the symmetry axis of the transversely isotropic (TI) representation of the region can be rotated, leading to tilted transversely isotropic (TTI) media. We seek to find the optimal full-waveform inversion (FWI) strategy to estimate both the seismic velocities and the anisotropic parameters, including the tilt angle, in the presence of elastic TTI media. We first formulate the forward and inverse problems for elastic TTI media and analyse the radiation patterns of the model parameters. Based on the analyses of the radiation patterns, we propose two similar multistage FWI strategies that add inversion parameters over three stages, beginning with the isotropic parameters (horizontal P- and vertical S-wave velocity) and moving to the anisotropic parameters; the tilt angle is directly inverted in the last stage. Since diving waves, which are useful for providing long-wavelength updates, are mainly controlled by horizontal motion in anisotropic media, it is reasonable to choose the horizontal P-wave velocity rather than the vertical P-wave velocity. Then, the anisotropic parameters are inverted mainly using the reflected waves based on the isotropic background model built in the first stage. The main difference between the two multistage FWI strategies is whether the anisotropic parameter η is inverted. Comparing the two multistage FWI strategies with the simultaneous inversion strategy for a downsized version of the synthetic BP TTI model, we confirm that the multistage FWI strategies yield better inversion results than the simultaneous inversion strategy. When we compare the two multistage FWI strategies with each other for surface seismic data, ignoring η during the FWI process (focused multistage FWI) yields better inversion results for the tilt angle than those obtained with the inversion of η because η has less influence on the FWI than the other parameters and is not recovered well, which plays a role in degrading the tilt angle. Numerical examples support our conclusions that the focused multistage FWI strategy (neglecting η) is the optimal FWI strategy for TTI media and achieves computational efficiency for surface seismic data.