Yangkang Chen

Dealiased Seismic Data Interpolation Using Seislet Transform With Low-Frequency Constraint

Interpolating regularly missing traces in seismic data is thought to be much harder than interpolating irregularly missing seismic traces, because many sparsity-based approaches cannot be used due to the strong aliasing noise in the sparse domain. We propose to use the seislet transform to perform a sparsity-based approach to interpolate highly undersampled seismic data based on the classic projection onto convex sets (POCS) framework. Many numerical tests show that the local slope is the main factor that will affect the sparsity and antialiasing ability of seislet transform. By low-pass filtering the undersampled seismic data with a very low bound frequency, we can get a precise dip estimation, which will make the seislet transform capable for interpolating the aliased seismic data. In order to prepare the optimum local slope during iterations, we update the slope field every several iterations. We also use a percentile thresholding approach to better control the reconstruction performance. Both synthetic and field examples show better performance using the proposed approach than the traditional prediction based and the F-K-based POCS approaches.

Seismic Time–Frequency Analysis via Empirical Wavelet Transform

Time-frequency analysis is able to reveal the useful information hidden in the seismic data. The high resolution of the time-frequency representation is of great importance to depict geological structures. In this letter, we propose a novel seismic time-frequency analysis approach using the newly developed empirical wavelet transform (EWT). It is the first time that EWT is applied in analyzing multichannel seismic data for the purpose of seismic exploration. EWT is a fully adaptive signal-analysis approach, which is similar to the empirical mode decomposition but has a consolidated mathematical background. EWT first estimates the frequency components presented in the seismic signal, then computes the boundaries, and extracts oscillatory components based on the boundaries computed. Synthetic, 2-D, and 3-D real seismic data are used to comprehensively demonstrate the effectiveness of the proposed seismic time-frequency analysis approach. Results show that the EWT can provide a much higher resolution than the traditional continuous wavelet transform and offers the potential in precisely highlighting geological and stratigraphic information.

Separation of simultaneous sources using a structural-oriented median filter in the flattened dimension

Simultaneous-source shooting can help tremendously shorten the acquisition period and improve the quality of seismic data for better subsalt seismic imaging, but at the expense of introducing strong interference (blending noise) to the acquired seismic data. We propose to use a structural-oriented median filter to attenuate the blending noise along the structural direction of seismic profiles. The principle of the proposed approach is to first flatten the seismic record in local spatial windows and then to apply a traditional median filter (MF) to the third flattened dimension. The key component of the proposed approach is the estimation of the local slope, which can be calculated by first scanning the NMO velocity and then transferring the velocity to the local slope. Both synthetic and field data examples show that the proposed approach can successfully separate the simultaneous-source data into individual sources. We provide an open-source toy example to better demonstratethe proposed methodology. HighlightsWe propose a novel structural-oriented median filter to attenuate the blending noise.We flatten the seismic record in local spatial windows followed by MF in flattened dimension.The local slope can be accurately estimated from velocity-slope transformation.Several simulated synthetic and field data examples show the successful performance.An open-source toy example to better demonstrate the proposed methodology.

An open-source Matlab code package for improved rank-reduction 3D seismic data denoising and reconstruction

Simultaneous seismic data denoising and reconstruction is a currently popular research subject in modern reflection seismology. Traditional rank-reduction based 3D seismic data denoising and reconstruction algorithm will cause strong residual noise in the reconstructed data and thus affect the following processing and interpretation tasks. In this paper, we propose an improved rank-reduction method by modifying the truncated singular value decomposition (TSVD) formula used in the traditional method. The proposed approach can help us obtain nearly perfect reconstruction performance even in the case of low signal-to-noise ratio (SNR). The proposed algorithm is tested via one synthetic and field data examples. Considering that seismic data interpolation and denoising source packages are seldom in the public domain, we also provide a program template for the rank-reduction based simultaneous denoising and reconstruction algorithm by providing an open-source Matlab package. HighlightsTraditional rank-reduction based algorithm will cause residual noise.An improved rank reduction method by slightly modifying the TSVD formula.Synthetic and field data examples show very encouraging results.An open-source Matlab code package for seismic processing is introduced.

Iterative Deblending With Multiple Constraints Based on Shaping Regularization

It has been previously shown that blended simultaneous-source data can be successfully separated using an iterative seislet thresholding algorithm. In this letter, I combine iterative seislet thresholding with a local orthogonalization technique via a shaping regularization framework. During the iterations, the deblended data and its blending noise section are not orthogonal to each other, indicating that the noise section contains significant coherent useful energy. Although the leakage of useful energy can be retrieved by updating the deblended data from the data misfit during many iterations, I propose to accelerate the retrieval of the leakage energy using iterative orthogonalization. It is the first time that multiple constraints are applied in an underdetermined deblending problem, and the new proposed framework can overcome the drawback of a low-dimensionality constraint in a traditional 2-D deblending problem. Simulated synthetic and field data examples show the superior performance of the proposed approach.

Simultaneous-Source Separation Using Iterative Seislet-Frame Thresholding

The distance-separated simultaneous-sourcing (DSSS) technique can make the smallest interference between different sources. In a distance-separated simultaneous-source acquisition with two sources, we propose the use of a novel iterative seislet-frame thresholding approach to separate the blended data. Because the separation is implemented in common shot gathers, there is no need for the random scheduling that is used in conventional simultaneous-source acquisition, where random scheduling is applied to ensure the incoherent property of blending noise in common midpoint, common receiver, or common offset gathers. Thus, DSSS becomes more flexible. The separation is based on the assumption that the local dips of the data from different sources are different. We can use the plane-wave destruction algorithm to simultaneously estimate the conflicting dips and then use seislet frames with two corresponding local dips to sparsify each signal component. Then, the different signal components can be easily separated. Compared with the FK-based approach, the proposed seislet-frame-based approach has the potential to obtain better separated components with less artifacts because the seislet frames are local transforms while the Fourier transform is a global transform. Both simulated synthetic and field data examples show very successful performance of the proposed approach.

Random noise attenuation by a selective hybrid approach using f − x empirical mode decomposition

Empirical mode decomposition (EMD) becomes attractive recently for random noise attenuation because of its convenient implementation and ability in dealing with non-stationary seismic data. In this paper, we summarize the existing use of EMD in seismic data denoising and introduce a general hybrid scheme which combines f???x EMD with a dipping-events retrieving operator. The novel hybrid scheme can achieve a better denoising performance compared with the conventional f???x EMD and selected dipping event retriever. We demonstrate the strong horizontal-preservation capability of f???x EMD that makes the EMD based hybrid approach attractive. When f???x EMD is applied to a seismic profile, all the horizontal events will be preserved, while leaving few dipping events and random noise in the noise section, which can be dealt with easily by applying a dipping-events retrieving operator to a specific region for preserving the useful dipping signal. This type of incomplete hybrid approach is termed a selective hybrid approach. Two synthetic and one post-stack field data examples demonstrate a better performance of the proposed approach.

Multi-step damped multichannel singular spectrum analysis for simultaneous reconstruction and denoising of 3D seismic data

Multichannel singular spectrum analysis (MSSA) is an effective approach for simultaneous seismic data reconstruction and denoising. MSSA utilizes truncated singular value decomposition (TSVD) to decompose the noisy signal into a signal subspace and a noise subspace and weighted projection onto convex sets (POCS)-like method to reconstruct the missing data in the appropriately constructed block Hankel matrix at each frequency slice. However, there still exists some residual noise in signal space due to two major factors: the deficiency of traditional TSVD and the iteratively inserted observed noisy data during the process of weighted POCS like iterations. In this paper, we first further extend the recently proposed damped MSSA (DMSSA) for random noise attenuation, which is more powerful in distinguishing between signal and noise, to simultaneous reconstruction and denoising. Then combined with DMSSA, we propose a multi-step strategy, named multi-step damped MSSA (MS-DMSSA), to efficiently reduce the inserted noise during the POCS like iterations, thus can improve the final performance of simultaneous reconstruction and denoising. Application of the MS-DMSSA approach on 3D synthetic and field seismic data demonstrates a better performance compared with the conventional MSSA approach.

Deblending using normal moveout and median filtering in common-midpoint gathers

The benefits of simultaneous source acquisition are compromised by the challenges of dealing with intense blending noise. In this paper, we propose a processing workflow for blended data. The incoherent property of blending noise in the common-midpoint gathers is utilized for applying median filtering along the spatial direction after normal moveout (NMO) correction. The key step in the proposed workflow is that we need to obtain a precise velocity estimation which is required by the subsequent NMO correction. Because of the intense blending noise, the velocity scan cannot be obtained in one step. We can recursively polish both the deblended result and the velocity estimation by deblending using the updated velocity estimation and velocity scanning using the updated deblended result. We use synthetic and field data examples to demonstrate the performance of the proposed approach. The migrated image of deblended data is cleaner than that of blended data and is similar to that of unblended data.

Structure-oriented singular value decomposition for random noise attenuation of seismic data

Singular value decomposition (SVD) can be used both globally and locally to remove random noise in order to improve the signal-to-noise ratio (SNR) of seismic data. However, it can only be applied to seismic data with simple structure such that there is only one dip component in each processing window. We introduce a novel denoising approach that utilizes a structure-oriented SVD, and this approach can enhance seismic reflections with continuous slopes. We create a third dimension for a 2D seismic profile by using the plane-wave prediction operator to predict each trace from its neighbour traces and apply SVD along this dimension. The added dimension is equivalent to flattening the seismic reflections within a neighbouring window. The third dimension is then averaged to decrease the dimension. We use two synthetic examples with different complexities and one field data example to demonstrate the performance of the proposed structure-oriented SVD. Compared with global and local SVDs, and f–x deconvolution, the structure-oriented SVD can obtain much clearer reflections and preserve more useful energy.