Shaohuan Zu

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.

An effective approach to attenuate random noise based on compressive sensing and curvelet transform

Random noise attenuation is an important step in seismic data processing. In this paper, we propose a novel denoising approach based on compressive sensing and the curvelet transform. We formulate the random noise attenuation problem as an L 1 norm regularized optimization problem. We propose to use the curvelet transform as the sparse transform in the optimization problem to regularize the sparse coefficients in order to separate signal and noise and to use the gradient projection for sparse reconstruction (GPSR) algorithm to solve the formulated optimization problem with an easy implementation and a fast convergence. We tested the performance of our proposed approach on both synthetic and field seismic data. Numerical results show that the proposed approach can effectively suppress the distortion near the edge of seismic events during the noise attenuation process and has high computational efficiency compared with the traditional curvelet thresholding and iterative soft thresholding based denoising methods. Besides, compared with f-x deconvolution, the proposed denoising method is capable of eliminating the random noise more effectively while preserving more useful signals.

One-Step Slope Estimation for Dealiased Seismic Data Reconstruction via Iterative Seislet Thresholding

The seislet transform can be used to interpolate regularly undersampled seismic data if an accurate local slope map can be obtained. The dealiasing capability of such method highly depends on the accuracy of the estimated local slope, which can be achieved by using the low-frequency components of the aliased seismic data in an iterative manner. Previous approaches to solving this problem have been limited to the unstable estimation of local slope via a large number of iterations. Here, we propose a new way to obtain the slope estimation. We first estimate the NMO velocity and then use a velocity-slope transformation to get the optimal local slope. The new method allows us to avoid the iterative slope estimation and can obtain an accurate slope field in one step. The one-step slope estimation can significantly accelerate the iterative seislet domain thresholding process and can also stabilize the iterative inversion. Both synthetic and field data examples are used to demonstrate the performance by using the proposed approach compared with alternative approaches.

Multiple-Reflection Noise Attenuation Using Adaptive Randomized-Order Empirical Mode Decomposition

We propose a novel approach for removing noise from multiple reflections based on an adaptive randomized-order empirical mode decomposition (EMD) framework. We first flatten the primary reflections in common midpoint gather using the automatically picked normal moveout velocities that correspond to the primary reflections and then randomly permutate all the traces. Next, we remove the spatially distributed random spikes that correspond to the multiple reflections using the EMD-based smoothing approach that is implemented in the

Deblending of Simultaneous-source Seismic Data using Fast Iterative Shrinkage-thresholding Algorithm with Firm-thresholding

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Interpolating Big Gaps Using Inversion With Slope Constraint

domain. The trace randomization approach can make the spatially coherent multiple reflections random along the space direction and can decrease the coherency of near-offset multiple reflections. The EMD-based smoothing method is superior to median filter and prediction error filter in that it can help preserve the flattened signals better, without the need of exact flattening, and can preserve the amplitude variation much better. In addition, EMD is a fully adaptive algorithm and the parameterization for EMD-based smoothing can be very convenient.

Empirical Low-Rank Approximation for Seismic Noise Attenuation

In this paper, an improved algorithm is proposed to separate blended seismic data. We formulate the deblending problem as a regularization problem in both common receiver domain and frequency domain. It is suitable for different kinds of coding methods such as random time delay discussed in this paper. Two basic approximation frames, which are iterative shrinkage-thresholding algorithm (ISTA) and fast iterative shrinkage-thresholding algorithm (FISTA), are compared. We also derive the Lipschitz constant used in approximation frames. In order to achieve a faster convergence and higher accuracy, we propose to use firm-thresholding function as the thresholding function in ISTA and FISTA. Two synthetic blended examples demonstrate that the performances of four kinds of algorithms (ISTA with soft- and firm-thresholding, FISTA with soft- and firm-thresholding) are all effective, and furthermore FISTA with a firm-thresholding operator exhibits the most robust behavior. Finally, we show one numerically blended field data example processed by FISTA with firm-thresholding function.

Application of Principal Component Analysis in Weighted Stacking of Seismic Data

Seismic data interpolation or reconstruction plays an important role in seismic data processing. Many processing steps, such as high resolution processing, wave-equation migration, amplitude-versus-offset and amplitude-versus-azimuth analysis, require regularly sampled data. The reconstruction can be posed as an inverse problem, which is known to be ill posed and requires constraints to obtain unique and stable solutions. In this letter, we propose an iterative scheme to interpolate the big gaps with a slope constraint. In the first iteration, the smooth radius must be large to estimate the smooth dip from the decimated data, and a large scaling parameter can guarantee the stability of the inversion. In the later iterations, the smooth radius will be shortened in order to get a more accurate dip estimation from the updated result. When the dip estimation is accurate, a small scaling parameter can not only guarantee the convergence of the inversion but also obtain a result with high signal-to-noise ratio. We compare the proposed method with the well-known projection-onto-convex-sets method on synthetic and field data examples. The interpolation results illustrate the advantage of the proposed method in interpolating the big gaps.

Three-Operator Proximal Splitting Scheme for 3-D Seismic Data Reconstruction

The low-rank approximation method is one of the most effective approaches recently proposed for attenuating random noise in seismic data. However, the low-rank approximation approach assumes that the seismic data has low rank for its

SVD-Constrained MWNI With Shaping Theory

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