Considering the limitation of the Gabor transform due to the uncertainty principle, where time and frequency resolution cannot both be maximized simultaneously, we propose a post-processing strategy for the time-frequency spectrum to mitigate this limitation and improve time-frequency concentration. In the frequency band of seismic data, the time and frequency window sizes of the Gabor transform are fixed, implying that the Gabor transform’s time-frequency spectrum is formed by the 2D convolution of a high-resolution time-frequency spectrum with a Gaussian-shaped point spread function (PSF). Therefore, based on compressed sensing theory, we use sparse constraints to the time-frequency spectrum and solve the 2D deconvolution of the Gabor transform’s time-frequency spectrum using the alternating direction method of multipliers algorithm to eliminate the influence of the time-frequency window function. The PSF used for deconvolution is determined by the variances of the time and frequency windows, and by altering the size of the PSF, we can obtain frequency-sparse Gabor transform (FSGT) and time-sparse Gabor transform (TSGT). Simulation signals demonstrate the effectiveness of this post-processing strategy. For actual data, we prove that the sparse Gabor transform can enhance time-frequency concentration and improve the accuracy of seismic data analysis by integrating thin layer identification and frequency-dependent amplitude variation with offset attributes.

Convolutional neural network-domain full-waveform inversion (CNNFWI) is a powerful technique for reconstructing high-resolution subsurface parameters by iteratively updating network parameters. This approach eliminates the need for a large training dataset as required by data-driven inversion methods and avoids artificially deriving the gradient of the objective function with respect to the inversion parameters in the conventional adjoint-state inversion method. However, CNNFWI remains an ill-posed inverse problem, with the potential of the optimization process converging to local minima. To produce a favorable reconstruction, we develop a feature-boosted CNN for inversion. This work focuses on two key innovations. First, instead of adding a regularization term to the loss function, our approach employs differential operators on multichannel feature maps to enhance the boundary features of geological structures. Second, we incorporate coordinate attention to improve feature representation by considering both spatial location dependencies and channel correlations. The combination of these two modifications enhances the inversion performance, particularly in accurately depicting the shape and velocity of structures. Moreover, we investigate the upsampling (Us) operation within the network architecture responsible for transforming low-resolution feature maps into high-resolution outputs, identifying the optimal Us method suited for CNNFWI. To examine the impact of neural network architecture components on inversion, synthetic experiments are conducted with both an anomaly model and the overthrust model. We performed a comprehensive comparison with previous CNNFWI and conventional FWI methods. The numerical results conclusively demonstrate the effectiveness of our approach in achieving superior subsurface velocity models. Finally, we synthesize time-lapse seismic data with the well-known Kimberlina model to confirm the potential of our framework in providing a high-quality description of reservoir changes due to carbon injection.

Attenuation and the occurrence of missing traces are prevalent challenges in field seismic data, significantly affecting subsequent processing and imaging. While numerous studies have been conducted to address these issues, both traditional methods and deep learning approaches often treat seismic data reconstruction and attenuation compensation as distinct problems. This fragmented approach may neglect the potential correlation and shared characteristics between compensation and reconstruction. Consequently, this paper presents a novel nonlinear activation-free network (CSNAF-Net3+) specifically designed to simultaneously conduct seismic data reconstruction and attenuation compensation. The proposed network integrates U-Net3+, NAFNet, and CBAM methodologies, leveraging the automatic feature learning and end-to-end processing capabilities inherent in deep learning. This integration significantly enhances performance in both reconstruction and compensation tasks. Numerical simulation and field data tests demonstrate that CSNAF-Net3+ exhibits exceptional efficacy in addressing issues related to missing traces, attenuation, and noise. Notably, it achieves substantial improvements in reconstructing and compensating for extensive gaps within continuously missing traces. Moreover, we further introduce a more accurate and robust compensation method based on a multi-Qvalue model training framework. This strategy possesses significant potential to improve the network’s adaptability for field seismic data.

Subsurface intrinsic attenuation poses challenges for accurate velocity estimation in full waveform inversion. While conventionalQ-compensated full waveform inversion (Q-FWI) enables attenuation compensation, its gradient illumination suffers from substantial attenuation and distortion beneath high-attenuation anomalies. This leads to imbalanced parameter updates between high- and low-attenuation regions, degrading the inverted velocity accuracy beneath low-Qzones. This study develops a newQ-FWI framework through the constant-fractional Laplacian attenuation compensation operator, which incorporatesQ-compensation into the gradient formulation while maintaining kinematic consistency in heterogeneous attenuative media. Unlike traditionalQ-FWI approaches, our method establishes physically consistent compensation mechanisms that yield balanced gradients and significantly enhance velocity reconstruction accuracy in complex attenuative geological settings. Numerical experiments with 2D and 3D synthetic models validate the method’s capability to generate geologically plausible velocity structures, with theQ-compensated gradient demonstrating superior convergence properties. Field data applications further confirm the practical applicability of the proposedQ-FWI methodology for reservoir characterization.

Migration artifacts are usually presented in the migrated image or angle-domain common-image gathers (ADCIGs) recovered from the seismic migration operators. When these migration artifacts are not properly suppressed, they may significantly degrade the accuracy of subsequent structure interpretation, amplitude-versus-angle inversion, and reservoir characterization. In this article, we apply an angle-domain least-squares migration (ADLSM) method to suppress these migration artifacts presented in the migrated ADCIGs. There are two key points in this proposed method. The first point is that we explicitly compute the angle-domain Hessian matrix and invert it by the regularized linear inversion technique. Thanks to the introduction of diagonally band Hessian matrix, the migration artifacts at the far-field can be effectively suppressed. The second point is that we have incorporated the smoothness prior of the reflection-angle-dependent reflectivity image along the reflection angle direction into the linear inversion. We determine the validity of the proposed ADLSM method within the Kirchhoff migration. Through the SEG/EAGE Salt model and field data, we demonstrate that the proposed ADLSM method can effectively and efficiently suppress these migration artifacts in the migrated ADCIGs recovered from the Kirchhoff migration. In addition, even when the migration velocity is less than the true velocity model, this method remains valid.

Unsupervised methods for single 3-D seismic data reconstruction, such as deep image prior (DIP) and Bernoulli sampling (BS) frameworks, have achieved promising results. However, they suffer from expensive computational costs caused by a large number of iterations. Moreover, in the absence of labels, the final reconstructed results often require visual inspection to pick out, which inevitably introduces subjective errors. To address the above problems, we introduce local Pearson correlation coefficient (LPCC) and local mean absolute error (LMAE) to assess the correlation and difference between seismic traces. The mean values of LPCC (MLPCC) and LMAE (MLMAE) for all nonedge traces in the reconstructed result can evaluate the quality of the reconstructed result based on the internal similarity and internal difference of 3-D seismic data without labels. We further develop an MLPCC-MLMAE-based early stopping strategy. The training process will stop once the number of values behind the highest MLPCC has reached the patience value, and the MLMAE is used as one of the indispensable constraints for the highest MLPCC. We apply the proposed early stopping strategy to the DIP and BS frameworks and demonstrate that it has the ability to significantly reduce computational costs through experiments on synthetic and field data, which makes the DIP and BS frameworks a major step toward practical production. Furthermore, the quantitative evaluation metrics allow the network to automatically and intelligently monitor the training process, and the prediction at the end of iteration is used as the final reconstructed result, thus eliminating the need for human intervention.

The field acquired seismic data are often irregular, which affects the accuracy of subsequent processing algorithms. We develop a framework based on a dual-attention-based wavelet integrated convolutional neural network (DAWCNN) constrained via stochastic structural similarity (S3IM) for reconstruction of seismic data with regularly as well as irregularly missing traces. The proposed method utilizes discrete wavelet transform (DWT) and inverse wavelet transform (IWT) to preserve the valid information. It also leverages skip connections based on the group multiaxis Hadamard product attention (GHPA) mechanism and spatial attention (SA) mechanism to perform the fusion of more critical and refined multiscale features and subband feature recalibration, respectively. Additionally, a hybrid loss function is designed, which reduces the pixel differences through mean square error (MSE) loss and the differences in local structures and stochastic nonlocal structures via S3IM loss. We evaluate the proposed method on synthetic and field data. The numerical experiments demonstrate the effective and superior reconstruction capability of the proposed method, which outperforms four traditional and deep learning (DL)-based benchmark algorithms. The proposed method can also perform reconstruction and denoising simultaneously.

This research work deals with the establishment of a deconvolution approach with enhanced spatial resolution. The main focus of the developed algorithm is to remove the spatial smoothing effect of seismic data and to recover the seismic response of high-angle geological bodies, such as faults, thereby improving the accuracy of reservoir imaging. We assume that the data introduce smoothing of the spatial direction in the acquisition and processing, resulting in reduced resolution of geological body boundaries and fault response. We then employ the edge method and exhaustion method to estimate the spatial smoothing function and construct the 2-D (or 3-D) point spread function with a seismic wavelet. Additionally, low-resolution seismic data are generated by convolving unsmoothed reflection coefficients with a point spread function. Therefore, we proceed with constructing an optimized objective function and increasing the sparse constraint on the reflection coefficient. Utilizing the alternating direction of multipliers method, we can arrive at the reflection coefficient, which removes the effect of spatial smoothing. This reflection coefficient can be convolution with the high-resolution wavelet to obtain enhanced resolution data, and the subsurface impedance information can also be achieved with the low-frequency background.

In existing window time-frequency analysis methods, its resolution is commonly limited by the uncertainty principle. The time resolution and the frequency resolution restrict each other and cannot reach the maximum at the same time. For this reason, we employ the secondary processing technology of the time-frequency spectrum to enhance the time resolution of the S-transform (ST). By performing multiband filtering with a filter bank, the ST is capable of receiving the signal under different frequencies and its time-frequency coefficient. The window size is different, that is, the low-frequency time window is long, resulting in low time resolution and high-frequency resolution. The high-frequency time window is short, which makes the time resolution high and the frequency resolution low; however, the window size for the time component of each frequency is fixed. Based on the above idea, we perform “de-window” processing for each frequency component signal. We assume that the time-frequency spectrum is sparse without “windowing,” so the window effect can be removed by sparse inversion. Based on the alternating direction method of multipliers (ADMM), we use the nonnegative penalty terms and sparse terms for the joint constraints to solve the optimization problem, and obtain the sparse time-frequency spectrum to enhance the time resolution. This time sparse ST (TSST) obtained by the proposed method is suitable for improving the ability of thin-layer identification and also for the analysis of transient signals.

In this study, for the problems of poor energy aggregation and low resolution of velocity direction in the velocity spectrum obtained by stacking or semblance velocity analysis, we propose a sparse velocity analysis strategy, which is a secondary processing of the velocity spectrum based on sparse inversion method. In this approach, we assume that velocity spectrum at each time instant is formed by the convolution of a spike function with a window function, which reduces the resolution of the velocity spectrum in velocity direction due to the presence of a blurry window function. Accordingly, we use hyperbolic events with known velocities to extract a deconvolution operator in velocity direction, and then use the sparse inversion theory to perform deconvolution with velocity spectrum at each time instant to remove the effect of the blurry window function. In deconvolution, we apply nonnegative constraints and use the alternating direction method of multipliers (ADMM) for making all the high-resolution velocity spectrum values positive, and obtain a high-resolution velocity spectrum after “de-window,” that is, the sparse velocity spectrum. The algorithm is a secondary processing of velocity spectrum, which is computationally efficient, and can accomplish high-resolution analysis and modeling of velocity.

This article proposes a pre-stack deconvolution algorithm for the seismic common midpoint (CMP) gathers. Due to the low signal-to-noise ratio (SNR), poor lateral continuity of seismic CMP gathers, and residual time differences, conventional deconvolution algorithms struggle to enhance the resolution while maintaining the SNR. As a result, the data after deconvolution are overwhelmed by noise. In addition, the deconvolution methods in the Radon transform domain are limited by the tailing of focal points in the Radon domain. Therefore, this research employs the Radon transform as a sparse-promoting transform for deconvolution. By applying thresholds in the Radon domain, this algorithm suppresses noise and reduces the instability of deconvolution. Depending on the noise distribution, either the$L_{2}$norm or the$L_{1}$norm is flexibly chosen as the fitting term to enhance the algorithm’s versatility. Leveraging the strong denoising capability of the Radon transform, this algorithm improves resolution on gathers with a low SNR while enhancing lateral continuity. Model and actual data tests indicate that the algorithm effectively enhances the resolution of gathers, thus facilitating pre-stack amplitude versus offset (AVO) analysis and pre-stack inversion.

High-resolution prestack inversion combining the well-logging and seismic data is a significant geophysical task and can be achieved by two kinds of stochastic inversion approaches, the geostatistical inversion (GSI) and Bayesian linearized inversion (BLI). Nevertheless, the existing GSI is restricted by the heavy iteration calculation. Although BLI can avoid this issue, it suffers from the large core matrix inverse. A fast multi-Gaussian inversion (FMG_INV) is proposed herein to achieve the well-log and seismic combined inversion with higher efficiency than GSI and BLI. FMG_INV is derived from prestack BLI, which requires a large core matrix inverse. However, FMG_INV utilizes a simplification strategy and reduces the core matrix dimension of BLI. This improvement is presented under the assumption of statistical independence between well-logging and seismic data, which relieves the issue of large matrix inverse in BLI to a great extent. Moreover, the spatial and statistical correlation between different parameters in prestack stochastic inversion is presented by a multi-Gaussian distribution and may reduce inversion accuracy, and FMG_INV solves this problem by a novel decorrelation strategy. The 1-D, 2-D, and 3-D field tests and a synthetic data test are given herein to verify the effectiveness of FMG_INV. The 1-D and 2-D tests of traditional BLI are also conducted for comparison. The results demonstrate that FMG_INV achieves the same satisfying inversion accuracy and resolution with BLI but much lower time consumption than BLI.

The natural damping effect of the Earth typically results in significant distortion of seismic waveforms, which greatly diminishes the precise of subsequent processes such as parameter inversion, migration imaging, and reservoir description. Compensating for this attenuation is crucial to achieving precise underground parameter measurements. While inversion or imaging techniques that rely on wave path compensation have the potential to address attenuation effects better, they encounter challenges, including heightened demands for input models, rapidly escalating algorithm intricacy, and computational burdens. Consequently, developing novel attenuation compensation methods that balance computational efficiency and accuracy is important in enhancing the precision of exploring complex reservoirs. This study utilizes a groundbreaking convolutional neural network (CNN), which integrates an attention mechanism and residual learning. This network establishes an inherent link between attenuated seismic data and their nonattenuated counterparts, effectively accomplishing data-driven compensation for seismic data attenuation. The more advanced acoustic (nonattenuated) full-waveform inversion (FWI) or reverse time migration framework is directly applied to enhance the modeling or imaging of attenuated seismic data with improved accuracy and efficiency. Simulation data and actual test results confirm that the suggested Q-compensation approach successfully enhances the amplitude of deep structural reflection signals, rectifies phase distortion induced by attenuation, and widens the seismic frequency range. This mitigates issues such as the cycle-skipping problem associated with low-frequency absence in traditional FWI and the numerical instability and increased computational complexity found in attenuation compensation FWI. Furthermore, the imaging profile’s resolution is further heightened due to the effective attenuation correction and enhancement of high-frequency components.

Bayesian linearized inversion (BLI) stands out as an exceptional stochastic inversion method in the realms of geophysics and remote sensing. It excels in estimating inversion results and assessing their uncertainty with remarkable efficiency. However, one of the challenges faced by BLI lies in the inversion of its core matrix. To surmount this limitation, an innovative dimension reduction strategy is proposed based on the discrete cosine transform (DCT), thus formulating a rapid BLI approach termed DCT-BLI. Within this method, the DCT-based reduction strategy effectively compresses a large sparse matrix by extracting its essential information, transforming the inversion of this sizable matrix into the inversion of a reduced-size counterpart. A compression factor (CF), defined as the size ratio of matrices after and before reduction, quantifies the extent of matrix reduction. DCT-BLI integrates the strengths of both BLI and the DCT-based reduction strategy. Leveraging this reduction approach, DCT-BLI tackles the challenge of inverting its sizable core matrix. Through the synthetic and field data tests, DCT-BLI exhibits clear superiority over BLI in terms of efficiency, and the DCT-based reduction method achieves a remarkable two-thirds reduction in the core matrix size of BLI without compromising inversion accuracy.

Time-domain elastic full waveform inversion (FWI) uses seismic data to recover the high-resolution subsurface medium properties for structural imaging and lithologic identification. The approximate pulse generated by the explosion source in seismic exploration evolves into a limited bandwidth seismic wavelet through the propagation of the seismic wave in the underground medium, exhibiting strong energy near the dominant frequency and weak energy far away. Therefore, time-domain FWI using the band-limited seismic wavelet can only match the energy of the dominant frequencies present in a dataset to a large extent, resulting in insufficient low-wavenumber updates of model parameters because of the weak energy of low frequencies. To remove the effect of finite-frequency-band wavelet spectra from the time-domain FWI, we propose a time-domain elastic FWI without wavelet spectral limitation. In our method, a newly refined seismic wavelet with a normalized amplitude and accurate phase is used to propagate seismic waves in the time domain. Data residual measurement is performed based on the summation of single-frequency residuals between the normalized synthetic and observed frequencies. The adjoint-state method is used to approximate the gradients of the model parameters, and the decoupled wavefields obtained by the phase-sensitive detection method were involved in the gradient calculation. Overall, the proposed method helps FWI to avoid falling into local minima by enhancing the low-wavenumber reconstruction of the velocity models. The elastic FWI numerical tests and field data FWI application demonstrate that our approach can reliably recover high-precision inversion results.

The generalized seismic wavelets (GSWs) are defined by fractional derivatives of the Gaussian function, whose asymmetry allows them to represent seismic signals more accurately than the commonly used symmetrical Ricker wavelet. The latter is a particular case with a second derivative of the Gaussian function. To better obtain the GSW, which could be well-matched with seismic signals, this article proposes the$\boldsymbol {n}$th power Fourier spectrum analysis method for GSWs. First, based on the$\boldsymbol {n}$th power Fourier spectrum of GSWs, the proposed method builds the mathematical relationship between the frequency characteristics (e.g., central frequency and bandwidth) and the statistical properties (e.g., mean frequency and deviation). Second, according to the$\boldsymbol {n}$th power Fourier spectrum, we propose a weighting calculation method for the derivative order$\boldsymbol {u}$of the Gaussian function. This method could be used for estimating GSWs matched the seismic first-arrival record, which is conducive to improving the accuracy of seismic imaging, inversion, and$Q$analysis. In theory, our proposed weighting method has better robustness and noise resistance than the traditional spectrum analysis method based on the power or amplitude spectrum. The experiment of synthetic noise, including first-arrival record and vertical seismic profiling (VSP) field data, shows the effectiveness of the proposed approach.

Most previous studies focus on using complex deep neural networks to learn diverse features of massive synthetic data. In more realistic situations with a limited number of data pairs, complex networks not only have higher computational complexity, increasing training time and reducing inference speed, but also tend to over-fit a small amount of training data, thus having weak generalization capability. To address the aforementioned problem, we propose a lightweight architecture for real-time velocity inversion in realistic situations, the bilateral inversion network (BiInNet). BiInNet uses lightweight ResNet18, ShuffleNetV2, and modified MobileNetV2 as backbones, taking into account the inversion accuracy and inference speed. To reduce the redundant information in common shot gathers and focus on graphical property features which are strongly correlated with velocity, the intermediate results of velocity analysis, semblances, and interval velocity models are prepared as data pairs. Numerical experiments show that BiInNet can infer interval velocity models in real-time, with frames per second (FPS) up to 76.90 when ResNet18 is used as the backbone. Moreover, BiInNet achieves the best inversion accuracy on more realistic fold models, fault models, salt models, and noisy dataset (NFOMD) when adopting ShuffleNetV2 as the backbone, which illustrates that BiInNet can be applied to velocity inversion tasks of different geological structures and is robust to noise. Adopting transfer learning to fine-tune pretrained model, BiInNet is effectively applicable to velocity reversal models and field data, which further demonstrates the reliability of the proposed method and provides a practical velocity inversion scheme when the field data pairs are insufficient.

Most existing traditional and deep learning (DL)-based methods used for random noise attenuation or reconstruction of seismic data typically only process two-dimensional (2-D) data. Very few methods are able to perform both denoising and reconstruction tasks for three-dimensional (3-D) seismic data. We develop a framework based on a self-supervised 3-D partial convolutional neural network (3-DPCNN) for multi-task processing of single 3-D seismic data volume, including random noise attenuation, reconstruction, and simultaneous denoising and reconstruction. The proposed method utilizes 3-D spatial structure information via 3-D convolution kernels and exploits Bernoulli sampling to generate training data pairs and test data. Attributed to Bernoulli sampling, the 3-DPCNN can be trained with only one noisy and/or corrupted seismic data volume; therefore, all supervised information is derived from the original data, and no external supervised information is required. The data augmentation strategy does not always boost the performance of the 3-DPCNN. Therefore, whether it is used and which transform is randomly employed are determined by the task type and the data. In addition, a double ensemble learning strategy is employed to boost 3-DPCNN performance and avoid randomness in the predictions. We evaluate the proposed method using multiple synthetic and field data. The experiments show that the proposed method has remarkable denoising and reconstruction abilities and is competitive with and even superior to a variety of traditional and DL-based benchmark algorithms.