We used a novel iterative estimation scheme for separation of blended seismic data from simultaneous sources. The scheme is based on an augmented estimation problem that can be solved by iteratively constraining the deblended data using shaping regularization in the seislet domain. We formulated the forward modeling operator in the common-receiver domain, in which two sources were assumed to be blended using a random time-shift dithering approach. The nonlinear shaping-regularization framework offered some freedom in designing a shaping operator to constrain the model in an underdetermined inverse problem. We designed the backward operator and the shaping operator for the shaping-regularization framework. The backward operator can be optimally chosen as half of the identity operator in the two-source case, and the shaping operator can be chosen as coherency-promoting operator. The high performance deblending effect of the iterative framework was tested on three numerically blended synthetic data s...

Iterative deblending of simultaneous-source seismic data using seislet-domain shaping regularization

Seismic data interpolation is a longstanding issue. Most current methods are only suitable for randomly missing cases. To deal with regularly missing cases, an antialiasing strategy should ...

Deep-learning-based seismic data interpolation: A preliminary result

The Cadzow rank-reduction method can be effectively utilized in simultaneously denoising and reconstructing 5D seismic data that depends on four spatial dimensions. The classic version of Cadzow rank-reduction method arranges the 4D spatial data into a level-four block Hankel/Toeplitz matrix and then applies truncated singular value decomposition (TSVD) for rank-reduction. When the observed data is extremely noisy, which is often the feature of real seismic data, traditional TSVD cannot be adequate for attenuating the noise and reconstructing the signals. The reconstructed data tends to contain a significant amount of residual noise using the traditional TSVD method, which can be explained by the fact that the reconstructed data space is a mixture of both signal subspace and noise subspace. In order to better decompose the block Hankel matrix into signal and noise components, we introduced a damping operator into the traditional TSVD formula, which we call the damped rank-reduction method. The damped rank-reduction method can obtain a perfect reconstruction performance even when the observed data has extremely low signal-to-noise ratio (SNR). The feasibility of the improved 5D seismic data reconstruction method was validated via both 5D synthetic and field data examples. We presented comprehensive analysis of the data examples and obtained valuable experience and guidelines in better utilizing the proposed method in practice. Since the proposed method is convenient to implement and can achieve immediate improvement, we suggest its wide application in the industry.

Simultaneous denoising and reconstruction of 5-D seismic data via damped rank-reduction method

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.

Seismic Time–Frequency Analysis via Empirical Wavelet Transform

Multichannel singular spectrum analysis (MSSA) is an effective algorithm for random noise attenuation in seismic data, which decomposes the vector space of the Hankel matrix of the noisy signal into a signal subspace and a noise subspace by truncated singular value decomposition (TSVD). However, this signal subspace actually still contains residual noise. We have derived a new formula of low-rank reduction, which is more powerful in distinguishing between signal and noise compared with the traditional TSVD. By introducing a damping factor into traditional MSSA to dampen the singular values, we have developed a new algorithm for random noise attenuation. We have named our modified MSSA as damped MSSA. The denoising performance is controlled by the damping factor, and our approach reverts to the traditional MSSA approach when the damping factor is sufficiently large. Application of the damped MSSA algorithm on synthetic and field seismic data demonstrates superior performance compared with the conve...

Damped multichannel singular spectrum analysis for 3D random noise attenuation

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 $F\mbox{--}K$ -based POCS approaches.

Shuwei Gan

Papers

Simultaneous denoising and reconstruction of 5-D seismic data via damped rank-reduction method

Damped multichannel singular spectrum analysis for 3D random noise attenuation

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

Compressive sensing for seismic data reconstruction via fast projection onto convex sets based on seislet transform

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