Seismic full waveform inversion (FWI) represents a state-of-the-art technique for estimating the parameter model. Conventional FWI faces the challenge of cycle skipping, because it depends on waveform matching for its objective function. This challenge impedes its convergence to a satisfactory model. Recently, FWI based on unsupervised learning has gradually developed and achieved commendable results in inversion. Currently, most methods transform waveform matching into probability distributions within a latent space by neural networks to overcome the problem of cycle skipping. Because this method only retains the characteristic information of seismic data while neglecting the full wavefield information, it adversely affects both the inversion resolution and stability. To address this problem, we propose a three-step inversion strategy that integrates the adversarial networks, envelope information, and traditional FWI. This approach is designed to better utilize full wavefield information, which can rebuild low and high wavenumber components of velocity model. The demonstrations using SEG salt and Hess models, which including the salt structure, show that our proposed method can successfully reconstitute the main structure and background velocity of the salt model due to the introduction of full wavefield information.

Deep learning (DL) has emerged as a focal point in addressing various challenges within the field of exploration seismology, prominently featuring applications in seismic data interpolation. Existing neural networks utilized in exploration seismology predominantly employ real-valued nonlinear transforms on time—space seismic data. Nevertheless, the seismic signal contains significant information in its phase, whereas the real-valued transforms meet with challenges to take into account the entire phase information of nonstationary seismic data. To surmount this challenge, we propose a novel framework termed frequency-space-dependent unsupervised DL interpolation (FUDLInter). The primary objective of FUDLInter is to interpolate high-dimensional seismic data within the frequency-space domain, thereby optimizing the exploitation of intricate information derived from the fast Fourier transform representation of seismic signals. In this framework, we meticulously explore and harness the capability of a complex-valued deep convolutional neural network employing the U-Net architecture, designated as CVU-Net. This network is designed to autonomously recover each frequency component of both 3-D and 5-D seismic data. We leverage the Bernoulli sampling technique and the nonmissing elements in the subsampled data to construct a data misfit model. The efficacy of the proposed method is evaluated using both high-dimensional synthetic data and field data examples. The interpolation results from the proposed FUDLInter method outperform those achieved by alternative methods, i.e., the projection onto convex sets with an adaptive threshold schedule (APOCS), damped rank-reduction (DRR), and DenseNet methods.

To tackle the pressing issue of climate change stemming from carbon emissions, carbon capture and storage (CCS) projects have emerged worldwide, which aim to store carbon dioxide (CO2) produced during industrial production in subsurface geological structures. To ensure the efficacy of these projects, 4D seismic surveys are conducted to monitor the stored CO2and identify potential leakage at an early stage. In recent years, deep learning has been widely employed for seismic data interpretation, which has shown promising results in terms of objectivity and efficiency when compared to manual interpretation. In this study, we address the CO2monitoring challenge using a 3D encoder-decoder network with convolutional vision transformer (CvT) called CvTNet, through the supervised learning scheme. By formulating the CO2monitoring task as an image segmentation problem, we use CvTNet to generate a 3D CO2probability image from a 4D seismic image. CvTNet leverages the CvT module, which provides superior dynamic attention and global context compared to convolutional neural networks. We evaluate the effectiveness of CvTNet on the Sleipner CCS project, using a 4D seismic image (comprising a 3D baseline image from 1994 and a 3D time-lapse image from 2010) and a CO2probability image from 2010 as the CvTNet training input and label, respectively. We apply the trained model to seismic images from other monitoring years to analyze CO2plume growth during the Sleipner CCS project. Tests indicate that CvTNet achieves higher CO2segmentation accuracy than U-net and can be generalized across other 4D seismic images.

Elastic parameters play pivotal roles in geophysics, with seismic amplitude variation with offset (AVO) inversion being a common method for obtaining the parameters. In contrast to isotropic media, vertical transversely isotropic (VTI) media, which introduce anisotropic parameters to describe geological characteristics, align more closely with field strata. Conducting AVO inversion based on VTI media enhances the accuracy of inverted parameters. Conventional AVO inversion methods typically rely on low-frequency parameters or training samples, which are often generated from well-log data. However, well-log data are usually insufficient, and obtaining accurate anisotropic parameters from well-log data is challenging. These hinder the generation of low-frequency anisotropic parameters or the creation of training samples with anisotropic parameters as labels, thus impacting the accuracy of inverted parameters for VTI media. Addressing these challenges, we construct a double discriminator conditional generative adversarial network (DDCGAN) models under the constraints of the convolution model theory. Building upon the foundation, we propose a seismic AVO inversion method tailored for VTI media. The DDCGANs combine the conditional generative adversarial networks (CGANs), which have superior feature extraction ability, with the well-established convolution model theory, making it suitable for addressing AVO inversion challenges in VTI media. Iterative optimization of the constructed DDCGANs is achieved by building combined loss functions, including errors of elastic parameters and seismic data. Trial calculations using model and field data demonstrate that the proposed method can improve the accuracy of inverted parameters compared to conventional AVO inversion methods, showcasing its feasibility, advancement, and practicality.

Seismic amplitude variation with offset (AVO) inversion provides elastic parameters for reservoir identification. When processing field seismic data, conventional elastic medium AVO inversion methods typically inadequately account for the absorption of seismic waves by subsurface media, and inverted elastic parameters have accuracy upper bounds. The absorption and attenuation characteristics of subsurface media are described by quality factors introduced by viscoelastic media. The accuracy of inverted parameters will increase by studying AVO inversion methods based on viscoelastic media. Typically, low-frequency elastic parameters or conventional training samples affect how accurate conventional AVO inverted elastic parameters are. Since quality factors are typically absent from well-log data, it is challenging to produce suitable low-frequency elastic parameters and training samples. To address this issue, we propose an AVO inversion method for the viscoelastic method based on invertible neural networks (INNs) with bijective structures. We first construct a tandem INN for fitting the bidirectional mapping between elastic parameters and seismic data. Then, training parameters, which are easier to obtain than conventional training samples, are randomly generated based on the characteristics of the target work area data. Next, the forward process of the tandem INN is trained to fit the forward process from elastic parameters to seismic data. Finally, elastic parameter inversion is achieved through the reverse process of the trained tandem INN. The proposed method does not require initial elastic parameters and training samples. Model and field data tests prove that the proposed method is feasible, practical, and progressive.

Salt bodies represent a significant challenge when performing full-waveform inversion (FWI) due to convergence issues when retrieving high-contrast geological structures. Recent advances in FWI promote the adoption of data regularization to address this problem. However, the model complexity where the bodies are enclosed tends to be the leading cause of unsatisfactory results. In recent years, the implementation of deep learning to tackle this issue has been proposed; however, these solutions generally rely on a direct mapping between the input (gathers) and output data (2D salt bodies) that are usually builtusing large datasets to become effective. In this study, we propose a simple and robust methodology for 3D initial salt body building assisted by deep learning. Two pre-trained models identify reflections associated with salt bodies on 3D shot gathersfrom the SEG/EAGE 3D salt model. Then, a 3D initial salt body is outlinedand built with RTM using only the deep learning-identified reflections. Finally, the 3D salt body is embedded into a background velocity model to conclude the initial model building for FWI. The accuracy of the initial model is tested by performing FWI, where observedand modeled data are compared, showing satisfactory results.

Seismic resolution enhancement is a key step for subsurface structure characterization. Although many have proposed the use of deep learning (DL) for resolution enhancement, these are typically hindered by the limitations in the application of synthetically trained networks onto real datasets. Domain adaptation (DA) offers an approach to reduce this disparity between training and inference data, aiming through the application of data transformations to bring the distributions of both data closer to each other. We propose a simple DA procedure, termed MLReal-Lite (the light version of the earlier introduced MLReal), that mainly relies on linear operations, namely convolution and correlation; these transformations introduce aspects of the field data into the synthetic data prior to training, and vice-versa with regard to the inference stage. Taking 1-D and 2-D resolution enhancement tasks as examples, we show how the inclusion of MLReal-Lite improves the performance of neural networks. Not only do the results demonstrate notable improvements in seismic resolution, they also exhibit a higher signal-to-noise ratio (SNR) and better continuity of events, in comparison to the tests without MLReal-Lite. Finally, while illustrated on a resolution enhancement task, our proposed methodology is applicable for any seismic data of dimensions N-D, offering a DA applicable from well ties through to 3-D seismic volumes, and beyond.

Incoherent noise suppression is an indispensable step in seismic data processing. Recently, deep learning (DL) methods have gained commendable success in seismic data denoising, one of which is the supervised DL denoising method using clean data as the training label, whereas the cost of obtaining clean data is high. We investigate a robust self-supervised DL denoising method without using clean data. Bernoulli-sampled training pairs of the raw noisy data produced by the dropout layer are served to train the NN, and a Monte Carlo (MC) self-integrated technique results in further improving the denoising quality of the trained NN during the testing. Compared with the f-x deconvolution (FXDECON), deep image prior (DIP), and sparse autoencoder (SAE) methods via synthetic and real data examples, the proposed method outperforms these methods for enhancing the signal-to-noise ratio (SNR) and reducing the signal loss.

Due to the limitation of the field acquisition environment and economic cost, observed seismic data often contain lots of missing traces. Traditional low-rank matrix completion can recover missing traces by constructing linear models, but it is often insufficient for high-accuracy reconstruction. To better recover seismic data, we propose a novel 3-D seismic data reconstruction approach by constructing a nonlinear model in the frequency domain. Based on the low-rank characteristics of seismic data, we employ the low-dimensional neural network (NN) to construct a nonlinear matrix completion model, which can be optimized by the improved resilient backpropagation algorithm. After optimization, the low-dimensional variables and hidden features learned by the network can be used to update the complete frequency slice. Since the two adjacent frequency slices share highly correlative information during reconstructing data in the frequency domain, we adopt transfer learning to improve the learning efficiency of the network while sequentially reconstructing frequency slices. Compared with the traditional matrix completion, the proposed method demonstrates superior performances in the reconstruction of synthetic and field 3-D seismic data volume.

Seismic inversion is an indispensable part of the earth exploration to precisely obtain the properties of subsurface media based on seismic data. However, the lack or inaccuracy of low-frequency (LF) information in seismic data constrains the correctness of the inversion. Traditional techniques encounter challenges in compensating the LF component of seismic data. Accessing the ability of deep learning to nonlinearly map inputs to expected outputs, we develop a neural network that can map poststack data to broader band data and then to impedance. We first propose an effective preprocessing scheme incorporating both well-logging and seismic data. Then, we extrapolate the LF information in the seismic data and invert the P-wave impedance with supervised and semisupervised frameworks, respectively. In the synthetic data example, the coefficient of determination ($R^{\mathrm{ 2}}$) reaches 0.99 for LF extrapolation and 0.98 for impedance inversion. In the field data example,$R^{\mathrm{ 2}}$is 0.826 between the inverted impedance and the real impedance of the validation well. Our experiments also reveal that the LF extrapolation improves the results of the impedance inversion.

High-order staggered-grid finite-difference (SFD) schemes are preferred in elastic wave simulation for geophysical problems because they decrease the accumulation of error from grid dispersion. However, most SFD approaches reach high-order spatial but limited temporal accuracy. To tackle the issue, we develop a novel temporal and spatial high-accuracy elastic SFD scheme by selectively modifying the spatial operators of the original SFD stencil. This modification has three main advantages. First, it facilitates the design of a new SFD stencil with temporal and spatial accuracies to arbitrary even-order by a Taylor-series expansion method. Second, it helps boost the accuracy further by implementing a linear optimization method. Third, the new selectively modified SFD (SMSFD) stencil needs fewer float-point operations (FPOs) than the existing temporal high-order SFD stencil. We compare our new SMSFD scheme with spatial high-order and temporal–spatial high-order SFD schemes and show that our new elastic SMSFD scheme possesses better accuracy and stability and requires fewer FPOs than these methods.

Acquisition technology of multisource data has outstanding advantages in enhancing collection efficiency and reducing cost. However, traditional seismic data processes cannot be applied to multisource blended data. Therefore, deblending technology of multisource data is the key to the research. In this letter, we propose a deblending method of multisource seismic data based on a periodically varying cosine code (PVCC). First, we design a PVCC to blend the seismic data. Next, the blending model is transformed into the minimum problem of the objective function. Then, the blended data are decomposed in the curvelet domain. Finally, the main source data are separated based on sparse inversion. Furthermore, we use the edge processing to eliminate the boundary effect in the processed seismic data. The examples of synthetic data and field data are adopted to demonstrate that the proposed method has great potential in the deblending of multisource data. In addition, the edge processing can effectively suppress the boundary effect.

Seismic facies analysis is to study the sedimentary environment of stratigraphic sequence and provides an important basis for reservoir prediction. Most of the existing analysis methods have low efficiency and heavily rely on manual experience, and therefore, it is difficult to interpret increasingly complex seismic data. Deep learning techniques can help to solve these problems and achieve automatic seismic facies classification. We regard seismic facies classification as a target segmentation problem and propose new method and training strategies. Our workflow primarily involves four sections. First, we process the manually annotated labels and seismic data with mirroring and cropping operations to ensure that network can accept input with arbitrary size and the model training is not limited to GPU memory. Second, data augmentation is applied to automatically generate massive training samples from the processed data. Third, we build two independent networks based on encoder-decoder architecture: one identifies all seismic facies simultaneously, and the other identifies single seismic facies in each model. However, both the results of the two networks have some drawbacks. Fourth, to overcome these drawbacks, we propose an ensemble learning method to get optimized model and test it on 3-D seismic data. The testing results manifest that the proposed method can improve the predictive ability of model, accurately describe the seismic facies, and can be applicable to entire seismic data volume.

Incoherent noise is one of the most common noise widely distributed in seismic data. To improve the interpretation accuracy of the underground structure, incoherent noise needs to be adequately suppressed before the final imaging. We propose a novel method for suppressing seismic incoherent noise based on the robust low-rank approximation. After the Hankelization, seismic data will show strong low-rank features. Our goal is to obtain the stable and accurate low-rank approximation of the Hankel matrix and then reconstruct the denoised data. We construct a mixed model of the nuclear norm and the$l_{1}$norm to express the low-rank approximation of the Hankel matrix constructed in the frequency domain. Essentially, the adopted model is an optimization for the subspace similar to the online subspace tracking method, thus avoiding the time-consuming singular value decomposition (SVD). We introduce the orthonormal subspace learning to convert the nuclear norm to the$l_{1}$norm to optimize the orthonormal subspace and the corresponding coefficient. Finally, two optimization strategies—the alternating direction method and the block coordinate descent method—are applied to obtain the optimized orthonormal subspace and the corresponding coefficient for representing the low-rank approximation of the Hankel matrix. We perform incoherent noise attenuation tests on synthetic and real seismic data. Compared with other denoising methods, the proposed method produces small signal errors while effectively suppressing the seismic incoherent noise and has a high computational efficiency.

Noise attenuation plays an important role in seismic data processing. We propose a novel denoising method for seismic data based on unsupervised sparse feature learning. Our goal is to obtain the identifiable feature of the noisy seismic data and then to represent the effective signals. By preprocessing the raw data and training the autoencoder neural network with sparse constraint, the sparse feature of the seismic data can be learned and stored in the neural network. We use the adaptive moment estimation as a backpropagation algorithm to minimize the cost function with a sparse penalty term and combine the dropout technique in the training process to improve the feature extraction and generalization capability of the neural network. Then, the test data set can be reconstructed by the most important sparse features. The final denoising result can be obtained by rearranging the output test data set. Compared with three commonly used state-of-the-art denoising methods, the proposed method performs well in applications to denoising for synthetic and real seismic data.