Seismic data preprocessing significantly benefits from advanced sparse representation and domain transformation techniques to enhance denoising, wavefield separation, and data reconstruction. This study introduces a novel approach utilizing a deep learning framework for discrete sparse representation of seismic data. Our method utilizes a Swin Transformer-based encoding-decoding framework, which combines the hierarchical structures of CNNs with the self-attention mechanism of Transformers, to model both local and global information efficiently. This integration enables the precise characterization of seismic reflection events and the reconstruction of seismic records from a constructed sparse feature space. The proposed model has been rigorously tested on both simulated and field datasets, demonstrating its robustness, and potential provides superior decomposition of seismic data.

This study addresses the challenges in seismic interferometry (SI), particularly the deghosting of virtual-shot gathers affected by nonphysical reflections in marine seismic exploration. SI’s effectiveness largely depends on the distribution of seismic sources, which in field situations often leads to complex wavefield interactions and nonphysical reflections, adversely impacting data processing. Traditional methods are limited with these nonphysical reflections, and similarity-based approaches have shown potential in overcoming this challenge. In this paper, our study introduces an innovative deghosting framework based on Regularization by Denoising (RED). This approach effectively mitigates the influence of nonphysical reflections and enhances the accuracy of deghosting. We propose a simultaneous multi-shot deghosting framework that integrates RED, focusing on optimizing data similarity and computational efficiency. This is complemented by a novel denoising engine based on an enhanced BM3D method, specifically tailored for virtual-shot gathers. The efficacy of our framework is demonstrated through synthetic and field data, showcasing significant improvements in seismic data processing and offering a new paradigm for the application of seismic interferometry. This research contributes not only to the advancement of deghosting techniques but also to broadening the scope of seismic exploration.

The least-squares reverse time migration (LSRTM), through iterative minimization of residuals between seismic observational and simulated data, can produce high-quality imaging results. However, it comes at the expense of high computational costs due to many wave-equation simulations in each iteration. To enhance the inversion efficiency of LSRTM, we embraced the source encoding strategy, merging multiple seismic shot gathers into several supergather shots, thereby reducing the scale of the seismic imaging problem. This, however, introduced severe crosstalk noise in imaging results. To mitigate the issue of crosstalk noise in source-encoded LSRTM, we proposed an improved multisource LSRTM method with a nonsubsampled Shearlet transform (NSST) scheme based on the regularization by denoising (RED) framework, which was named as RED-LSRTM. Employing the RED strategy, the NSST denoising engine can be flexibly integrated into the inversion process. Specifically, an NSST denoising operator is integrated into the gradient update step to optimize the solution of the inverse problem, effectively combining gradient optimization with inversion denoising, and enabling the suppression of crosstalk noise throughout the iteration. Numerical tests on the Layer model, the Salt model, and the Marmousi model validated that NSST-based RED-LSRTM effectively enhanced the imaging quality of simultaneous-sources inversion by alleviating more migration artifacts and suppressing more crosstalk noise when compared with standard LSRTM. Owing to its simplicity, flexibility, and effectiveness, our proposed method provides a reliable choice for mitigating crosstalk noise in an inversion of the simultaneous source or blended seismic data.

Wave equation-based inversion, such as Least-Squares Reverse Time Migration (LSRTM), is a powerful seismic imaging technique. However, the performance of LSRTM in constructing high-resolution subsurface models is closely tied to the design of the gradient. The commonly usedL2gradient, derived within theL2space framework, often leads to insufficient illumination and slow convergence in inversion. To confront these issues, we introduce a novel Sobolev gradient based on Sobolev space and propose a novel inexact scaled-Sobolev gradient projection LSRTM (ISGP-LSRTM), which can correct the conventionalL2gradient, accelerates convergence and mitigates illumination deficiencies. Specifically, we construct a scaled-Sobolev gradient operator to optimize the direction of the conventional adjoint gradient, addressing the low-resolution caused by insufficient gradient information during iterations. Futhermore, by incorporating an inexact backtracking strategy, a proximal backtracking projection operator based on scaled- Sobolev gradient is constructed to refine the traditional update process in LSRTM. Numerical tests on multiple models, including the wide-angle Valley model, the truncated Marmousi model, and the fault-rich truncated Sigsbee2B model, demonstrate the superior performance of the ISGP-LSRTM inversion. The proposed approach significantly improves imaging illumination and event continuity, achieves faster convergence in iterative curves, and effectively enhances migration imaging quality.

The velocity analysis requires a significant degree of automation due to its time consuming and labor-intensive nature. Recently, clustering algorithms, an unsupervised learning method, have been used in velocity analysis to achieve automated velocity picking. Unlike supervised learning methods, this approach does not require a large amount of high-quality labeled data and high training costs. Meanwhile, existing clustering-based velocity analysis requires high-signal-to-noise ratio inputs and is particularly sensitive to multiple reflection noise, which severely limits the effectiveness of automatic velocity analysis (AVA) methods. To provide an adaptive AVA method for seismic data that contains multiple reflections, we introduce physical prior knowledge constraints within the framework of clustering algorithms. In particular, we transformed the peak picking problem in the velocity spectrum into a classification problem between primary and multiple reflections. Meanwhile, three physical attributes, velocity, amplitude, and primary similarity, are used as physical prior information for the clustering algorithm to help solving the classification problem. The synthesized and field data examples have proven the effectiveness of the proposed method.

The natural electromagnetic field observed in magnetotelluric (MT) sounding is non-stationary, making it challenging to obtain reliable frequency spectrum information using Fourier transform. In practical measurements, long-duration observations of the electromagnetic field signal are often required to obtain accurate low-frequency impedance, resulting in significant technical difficulties and high economic costs. We provide a method for estimating MT impedance using the instantaneous spectrum obtained with variation mode decomposition (VMD). By replacing the Fourier spectrum with the instantaneous spectrum, this approach mitigates the requirement for extended signal observation time when estimating low-frequency impedance. Compared to previous studies on impedance estimation, we analyze the influence of signal period number on spectrum reliability, emphasizing the effectiveness and reliability of instantaneous spectrum in dealing with non-stationary signal. The feasibility of obtaining low-frequency MT impedance from short-duration observations is also discussed. The proposed method employs VMD to extract the instantaneous spectrum and utilizes hat matrix (A projection matrix) and signal noise separation (SNS) techniques to suppress noise interference in the spectrum, thereby enhancing the reliability of the instantaneous spectrum and the resulting impedance estimates. The method is applied to synthetic data with added noise and real data collected in the Qilian region of China, and the results are compared with those obtained by using different methods. The experiments demonstrate that VMD instantaneous spectrum reliably reflects the spectral characteristics of the signal, exhibiting minimal changes as the signal duration decreases. Therefore, this method can obtain robust low-frequency impedance even with short MT time series.

This article proposes a new surface wave suppression method based on nonsubsampled Shearlet transform (NSST). First, we use a frequency wavenumber (FK) Filter to extract surface wave noise from seismic data. We then apply a Shearlet transform to both the original data and the isolated surface wave, facilitating the creation of distinct Shearlet domain subbands characterized by diverse scales and directions. Next, we calculate the similarity coefficients between each corresponding subband of the original data and separated surface wave and use the standard deviation as the criterion for subband selection to enable adaptive selection. Then, mean thresholding and Bayesian separation algorithms are applied to suppress the surface wave components in the subbands. Finally, we integrate the selected subbands and perform an inverse NSST to reconstruct the surface wave-free seismic data. Replacing the traditional subband selection method with the adaptive method can effectively improve the efficiency of surface wave suppression, and the combination of mean value thresholding and Bayesian separation algorithm suppresses the surface wave noise in the subbands, resulting in high-quality reconstructed data.

Model-based reconstruction offers an effective framework for solving diverse inverse problems in geophysical imaging, and least-squares reverse time migration (LSRTM) can be regarded as a model-based reconstruction method. While LSRTM can produce higher resolution compared to reverse time migration (RTM), it remains prone to challenges such as noise interference, computational complexity, and problems, e.g., artifacts and incomplete illumination. This study adopts the regularization by denoising (RED) strategy to alleviate these issues and further improve imaging resolution and inversion efficiency. The RED technique is notably flexible and requires just a single denoising engine. In our case, it is a filter constructed based on the curvelet transform (CT), which decomposes the imaging into wavelet coefficients of different scales and directions and applies threshold processing to achieve noise suppression. Subsequently, the CT denoising engine is integrated into the explicit RED term, which is formed by the inner product of the imaging result and its denoising residuals. The inversion result is obtained by solving the objective function using the alternating directions method of multipliers (ADMM). The effectiveness of RED-LSRTM is initially tested with the simple flat model, followed by an assessment of its imaging performance on large-angle reflection layers with a layered model. Finally, the RED-LSRTM is assessed in complex geological structures using a salt model.

Least-squares reverse time migration (LSRTM) aims to produce a high-quality migration image of complex geological structures. However, the weaker deep seismic reflections are often masked by the overlying strata in migration images. Therefore, it is difficult for the LSRTM to image the deeper structures. This letter proposes a phase-amplitude LSRTM (PA-LSRTM) in the time-frequency domain to improve the migration image of deep seismic reflections and subsalt structures. The PA-LSRTM is formulated as an inverse problem that minimizes the time-frequency phase-amplitude difference between the predicted and observed data. The seismic data was initially transformed into the time-frequency domain to establish a PA-LSRTM misfit. An amplitude factor was then introduced in the time-frequency misfit to weaken the weights of amplitude components. In this case, it emphasized the similarity of phase components. Furthermore, the sparsity promotion method was combined with a simultaneous source technique to increase the computational efficiency and reduce the crosstalk noise. The PA-LSRTM with sparsity promotion (SPA-LSRTM) misfit can finally be solved using a Fast Iterative Shrinkage-Thresholding Algorithm (FISTA). The numerical and marine field data tests demonstrate that the SPA-LSRTM can effectively produce a high-resolution image of deep structures.

Magnetotelluric (MT) impedance estimation requires a high signal-to-noise ratio (SNR). When low-SNR data are processed, it is difficult to obtain a robust MT response. In this article, based on the spectral characteristics of noise sequences, the influence of the scale and waveform of noise sequences on impedance estimates is studied, and a multiscale denoising method for MT signals is proposed. This method applies the improved complete ensemble empirical mode decomposition with adaptive noise (ICEEMDAN) to decompose the multiscale noise into different components, and then, the influence of noise on the spectrum is evaluated through the spectrum obtained by the short-time Fourier transform (STFT) of each component. This ICEEMDAN- and STFT-based MT (ICMT) denoising method can, thus, filter out the small-scale abrupt noise that has a great impact on the MT response and retain the large-scale smooth noise that has a small impact to suppress noise and reduce the loss of the effective signal at the same time. Various noises are added to a pure MT signal to test the performance of ICMT. It is demonstrated that ICMT has a small loss of effective signals and can obtain MT response results with small recovery errors, even when the SNR of the signal is as low as −20 dB. Finally, ICMT is applied to process the heavy noisy MT data in an ore concentration area. The results suggest that ICMT can effectively suppress noise, and robust impedance estimates can be obtained.

Traditional magnetotelluric (MT) impedance estimations are based on Fourier theory and carried out in the frequency domain, which has a strict stationarity requirement for the analyzed signal. However, the stationarity assumption cannot be satisfied when the data possess a low signal-to-noise ratio (SNR) and/or a short observation period. These shortcomings can cause significant errors in the MT impedance estimations, especially in the low-to-medium frequency bands. The alternating direction method of multipliers (ADMMs) and polarization analysis of the electromagnetic signal can be attached to the time-domain MT impedance estimation to address these shortcomings. This time-domain technique calculates the impedance in the time domain without Fourier transformation, and the ADMM and polarization analysis are applied to further improve the stability and convergence of the impedance estimation. Here, we present an ADMM-based method for MT impedance estimations (ADMM-MT). Various noise are added to a noise-free MT signal to test the performance of ADMM-MT. The results show that ADMM-MT yields impedance estimates with relative recovery errors below 0.2, even when the SNR of the data is 0 dB and the observation period is 60 min. We then apply ADMM-MT to field data in Inner Mongolia, China. The results indicate that the apparent resistivity curves obtained by ADMM-MT using a short time series are smooth over the 0.001–1-Hz band, which is consistent with the remote reference (RR) processing results obtained using a long time series. In contrast, the curves obtained by traditional robust estimation method are strongly biased.

Mare Moscoviense (148°E, 27°N) is one of the few large maria on the lunar farside. In this paper, the China Chang'E-2 Microwave Sounder (CELMS) data were employed to study the microwave thermal emission features of Moscoviense basin. The findings are as follows. (1) The four basaltic units present distinctly different TBperformances at noon and midnight; (2) A new understanding about the basaltic units is made according to the classification results using the maximum likelihood method; (3) The substrate temperature of Moscoviense basin is likely much higher than what we know. The results will be of great significances to understand the mare volcanism on the lunar farside.

Simultaneous-source shooting can help reduce the acquisition time cost, but at the expense of introducing strong interference (blending noise) into the acquired seismic data. It has been demonstrated previously that the deblending problem can be considered as an inversion process. In this letter, we propose a new iterative approach to solve this inversion problem. In the proposed approach, a new coherency-promoting constraint, called structuring median filtering (SMF), is proposed and used to regularize the estimated model in each iteration. The SMF processes the signal by the interactions of the input signal and another given small section of signal, namely, the structuring element. The SMF is more robust than other coherency-promoting filtering such as the median filtering and mathematical morphological filtering. Numerical experiments demonstrate that the iterative deblending based on the SMF constraint obtains a better performance and a faster convergence than the low-rank and compressed sensing constraint-based deblending approaches.