Separating diffraction patterns helps in providing detailed information on geological structures. However, the amplitude of weak diffraction is difficult to preserve and often destroyed during the separation process, particularly when the diffraction is tangential to the reflection. Estimating an accurate local slope can effectively to predict the reflection for separating diffraction. Conventional plane-wave decomposition (PWD) method directly calculates the slope of the stack section. This leads to aliasing between reflection and diffraction slopes, resulting in loss of diffraction information. Therefore, we propose a PWD lifting scheme that mainly focuses on the slope-mapping operator between stack and migration sections. We first calculated the slope in the migration section by the conventional PWD method, and then transferred it from the migration to the stack section using the mapping operator, which was derived by the migration principle. Because the diffraction waves converge in the migration section, their slopes were not estimated and aliased with the reflection slope. This method can accurately estimate the slope and effectively distinguish between diffraction and reflection. Synthetic and field data applications demonstrate that the proposed method is effective in separating diffraction and can preserve the diffraction amplitude, even when the diffraction is tangential to the reflection.

Prestack inversion is typically based on the Zoeppritz equation combined with gradient-based optimization of objective functions. To address the limitations of traditional gradient-based algorithms that heavily rely on initial models, researchers have introduced intelligent optimization algorithms, such as particle swarm optimization (PSO), into prestack inversion to improve inversion accuracy. However, these global optimization algorithms often exhibit low computational efficiency due to insufficient consideration of gradients and the Hessian matrix. In this study, we introduce the exact Zoeppritz gradient-based global optimization (EZGBO) method, which integrates an accurate gradient and the Hessian matrix under a Bayesian framework with a three-variable Cauchy prior into the gradient-based global optimizer (GBO) to enhance inversion accuracy and efficiency. The proposed method combines the advantages of traditional Newton-like algorithms and global intelligent optimization algorithms by incorporating the accurate gradient and the Hessian matrix of the objective function into the global optimization process. This approach achieves better inversion results with fewer particles and iterations, thus enhancing computational efficiency. To ensure the stability of the stochastic global inversion, we employ adaptive edge-preserving smoothing (Ad-EPS) to facilitate optimal positioning of the population particles. Finally, we validate the proposed method using both synthetic and field data. Specifically, we compared the proposed method with quantum PSO (Q) and traditional approaches. The results show that our method excels in accuracy, stability, efficiency, and resolution, offering a novel solution to global optimization in prestack inversion.

Seismic data processing often faces challenges in accurately suppressing multiple waves while preserving primary waves. In this study, we introduce a novel approach that integrates data correlation (DC) techniques with long short-term memory (LSTM) neural networks, referred to as DC-LSTM, to address this issue. By utilizing the positional indices of primary and multiple waves in common midpoint (CMP) gathers, DC-LSTM effectively trains the LSTM model for precise prediction and suppression of multiple waves. Experimental evaluations using synthetic and real seismic data demonstrate that DC-LSTM significantly outperforms the Radon transform, offering a robust solution for enhancing seismic data quality by achieving superior primary wave preservation and reducing pseudo-frequency artifacts.

The low-rank property of seismic data has been successfully used for attenuating seismic random noise using a rank-reduction processing; however, traditional rank-reduction methods based on truncated singular-value decomposition (TSVD) require exact rank estimation, i.e., denoised results are closely associated with rank selection. To address this problem, we propose a novel and effective rank-reduction method for 3-D random noise attenuation that introduces CUR matrix decomposition to the multichannel singular-spectrum analysis (MSSA) for performing low-rank approximation as an alternative to the traditional TSVD. CUR matrix decomposition expresses a data matrix as a product of three matrices by selecting a small number of columns and rows from the data matrix to approximate low-rank components. A subspace column selection algorithm is used to randomly select columns and rows from a Hankel matrix and construct three decomposed matrices in the frequency-space domain. A stable CUR decomposition algorithm is further exploited to eliminate the potential instability problem when obtaining the CUR. The random column selection strategy of the CUR matrix decomposition can effectively obviate the exact rank requirement and achieve superior low-rank approximation results. We present 3-D synthetic and field examples to demonstrate the effectiveness of the proposed CUR-based low-rank approximation in highlighting useful signals and attenuating random noise. Results obtained using CUR matrix decomposition are comparable to those obtained using traditional low-rank methods.

The significance of seismic diffractions for the high-resolution imaging of subsurface discontinuities has been emphasized in recent years. Separating diffractions from strong specular reflected wavefields is a crucial process owing to the weak amplitude of diffractions. The low-rank (LR) characteristics of seismic data have been successfully implemented for diffracted wavefield isolation using rank-reduction methods. Traditional LR-based diffraction separation uses the optimal LR approximation of the Hankel matrix formulated from seismic data for predicting linear reflection events. However, without the Hankel structure in traditional LR approximation, the Hankel matrix of estimated reflections does not exhibit the expected LR properties, which may affect the predicted reflection accuracy. In this study, a regularized LR (RLR) approximation method that exploits the LR properties of reflection events and the corresponding Hankel structure was developed to enhance diffractions and eliminate reflections. The RLR approximation algorithm considered the LR constraint of the Hankel matrix for estimated reflections, leading to improved LR approximation. Synthetic and field examples were used to demonstrate the effectiveness of the proposed algorithm in separating diffractions and imaging small subsurface geological structures.

Seismic data often contain noise that can disturb or mask effective information. Noise elimination is an important and challenging task in seismic signal processing. Considering the high amplitude continuity of seismic events in the shot domain, this article proposes a structure-oriented denoising method that can enhance the effective events and suppress disturbing noise, including both incoherent and coherent noise. Based on the common-reflection-surface (CRS) travel time, the local slope of seismic events in the shot domain is deduced and estimated to provide structural information for plane-wave prediction. The proposed CRS-based slope depends on fewer parameters (two in 2-D) than the conventional full CRS travel time (three in 2-D), making it computationally efficient. Using the local slope, the third dimension is created using the plane-wave differential equation to predict the current trace from its neighbor traces and trimmed mean filtering (TMF) is applied in this dimension. The added dimension can be regarded as flattening the seismic events within a neighboring window and collapsing after the application of TMF. Synthetic and field datasets are employed to demonstrate the effectiveness of the proposed structure-oriented TMF. Compared with the wavelet and plane-wave destruction (PWD) methods, the proposed method can preserve more useful information with greater continuity in amplitude.

Random noise attenuation is one of the most essential steps in seismic data processing, and effective denoising methods can significantly improve the accuracy of structural imaging and data inversion. To address this issue, we propose a novel low-rank approximation method that uses a CUR matrix decomposition algorithm instead of the traditional truncated singular-value decomposition (SVD). The low-rank method is applied along the structural direction of seismic data produced by plane-wave structural prediction to strengthen the low-rank property. The CUR decomposition exhibits a matrix as a product of three matrices, C, U, and R, to obtain a low-rank approximation. The decomposed matrices are formed by randomly selecting a subset of columns and rows from the data matrix. The subspace sampling algorithm is considered as a column selection principle to compute CUR decompositions. The proposed CUR-based low-rank denoising method is directly exploited to perform low-rank approximation in the Hankelization space, thus avoiding the time-consuming SVD. To improve the accuracy of slope estimation, a robust plane-wave destruction (PWD) algorithm with nonstationary shaping regularization is provided to enhance the slope estimation of noisy data. Synthetic and field examples are used to demonstrate the effectiveness performance of the proposed CUR-based low-rank denoising method both in eliminating seismic random noise and improving computational efficiency.