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.

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.

Full waveform inversion (FWI) stands as the forefront geophysical inversion approach, however, its impediment in practical applications persists due to the absence of prior information and limitations in data acquisition. Addressing this challenge, we introduce implicit FWI (IFWI) which represents subsurface models as continuous and implicit functions, thereby reducing dependency on the initial model with frequency principle in deep learning optimization. Furthermore, through the design of a specialized deep learning model that emphasizes rigorous low-frequency learning, we present a robust IFWI algorithm exhibiting high-resolution reconstruction capabilities, even when low-frequency information is absent in observations, as demonstrated in numerical experiments. Moreover, experimental findings underscore the heightened robustness, reduced data requirements, and strong generalization ability of the proposed robust IFWI algorithm. This highlights its applicability to a variety of subsurface models with diverse acquisition settings, indicating promising potential for practical seismic inversion.

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.