Antileakage Fourier transform for seismic data regularization in higher dimensions

Geophysics ◽  
2010 ◽  
Vol 75 (6) ◽  
pp. WB113-WB120 ◽  
Author(s):  
Sheng Xu ◽  
Yu Zhang ◽  
Gilles Lambaré
Keyword(s):  
Fourier Transform ◽  
Seismic Data ◽  
Computational Cost ◽  
Real Data ◽  
Higher Dimensions ◽  
Accurate Estimation ◽  
Data Sets ◽  
Spectral Leakage ◽  
Wavenumber Domain ◽  
Data Regularization

Wide-azimuth seismic data sets are generally acquired more sparsely than narrow-azimuth seismic data sets. This brings new challenges to seismic data regularization algorithms, which aim to reconstruct seismic data for regularly sampled acquisition geometries from seismic data recorded from irregularly sampled acquisition geometries. The Fourier-based seismic data regularization algorithm first estimates the spatial frequency content on an irregularly sampled input grid. Then, it reconstructs the seismic data on any desired grid. Three main difficulties arise in this process: the “spectral leakage” problem, the accurate estimation of Fourier components, and the effective antialiasing scheme used inside the algorithm. The antileakage Fourier transform algorithm can overcome the spectral leakage problem and handles aliased data. To generalize it to higher dimensions, we propose an area weighting scheme to accurately estimate the Fourier components. However, the computational cost dramatically increases with the sampling dimensions. A windowed Fourier transform reduces the computational cost in high-dimension applications but causes undersampling in wavenumber domain and introduces some artifacts, known as Gibbs phenomena. As a solution, we propose a wavenumber domain oversampling inversion scheme. The robustness and effectiveness of the proposed algorithm are demonstrated with some applications to both synthetic and real data examples.

Antileakage Fourier transform for seismic data regularization

Geophysics ◽  
2005 ◽  
Vol 70 (4) ◽  
pp. V87-V95 ◽  
Author(s):  
Sheng Xu ◽  
Yu Zhang ◽  
Don Pham ◽  
Gilles Lambaré
Keyword(s):  
Fourier Transform ◽  
Fourier Coefficient ◽  
Seismic Data ◽  
Fourier Coefficients ◽  
Real Data ◽  
Sampled Data ◽  
Spectral Leakage ◽  
Irregular Grid ◽  
Fourier Basis ◽  
Data Regularization

Seismic data regularization, which spatially transforms irregularly sampled acquired data to regularly sampled data, is a long-standing problem in seismic data processing. Data regularization can be implemented using Fourier theory by using a method that estimates the spatial frequency content on an irregularly sampled grid. The data can then be reconstructed on any desired grid. Difficulties arise from the nonorthogonality of the global Fourier basis functions on an irregular grid, which results in the problem of “spectral leakage”: energy from one Fourier coefficient leaks onto others. We investigate the nonorthogonality of the Fourier basis on an irregularly sampled grid and propose a technique called “antileakage Fourier transform” to overcome the spectral leakage. In the antileakage Fourier transform, we first solve for the most energetic Fourier coefficient, assuming that it causes the most severe leakage. To attenuate all aliases and the leakage of this component onto other Fourier coefficients, the data component corresponding to this most energetic Fourier coefficient is subtracted from the original input on the irregular grid. We then use this new input to solve for the next Fourier coefficient, repeating the procedure until all Fourier coefficients are estimated. This procedure is equivalent to “reorthogonalizing” the global Fourier basis on an irregularly sampled grid. We demonstrate the robustness and effectiveness of this technique with successful applications to both synthetic and real data examples.

Relative time seislet transform

Geophysics ◽  
2020 ◽  
Vol 85 (2) ◽  
pp. V223-V232 ◽  
Author(s):  
Zhicheng Geng ◽  
Xinming Wu ◽  
Sergey Fomel ◽  
Yangkang Chen
Keyword(s):  
Seismic Data ◽  
Computational Cost ◽  
Lifting Scheme ◽  
Real Data ◽  
Data Sets ◽  
Relative Time ◽  
New Approach ◽  
New Formulation ◽  
Wavelet Lifting ◽  
Seismic Images

The seislet transform uses the wavelet-lifting scheme and local slopes to analyze the seismic data. In its definition, the designing of prediction operators specifically for seismic images and data is an important issue. We have developed a new formulation of the seislet transform based on the relative time (RT) attribute. This method uses the RT volume to construct multiscale prediction operators. With the new prediction operators, the seislet transform gets accelerated because distant traces get predicted directly. We apply our method to synthetic and real data to demonstrate that the new approach reduces computational cost and obtains excellent sparse representation on test data sets.

Denoising seismic data using the nonlocal means algorithm

Geophysics ◽  
2012 ◽  
Vol 77 (1) ◽  
pp. A5-A8 ◽  
Author(s):  
David Bonar ◽  
Mauricio Sacchi
Keyword(s):  
Seismic Data ◽  
Random Noise ◽  
Seismic Energy ◽  
Real Data ◽  
Spatial Proximity ◽  
Data Sets ◽  
Noise Attenuation ◽  
Nonlocal Means ◽  
Reflection Seismic ◽  
Generally True

The nonlocal means algorithm is a noise attenuation filter that was originally developed for the purposes of image denoising. This algorithm denoises each sample or pixel within an image by utilizing other similar samples or pixels regardless of their spatial proximity, making the process nonlocal. Such a technique places no assumptions on the data except that structures within the data contain a degree of redundancy. Because this is generally true for reflection seismic data, we propose to adopt the nonlocal means algorithm to attenuate random noise in seismic data. Tests with synthetic and real data sets demonstrate that the nonlocal means algorithm does not smear seismic energy across sharp discontinuities or curved events when compared to seismic denoising methods such as f-x deconvolution.

Diffraction images and their attributes based on asymmetric summation: real data application

2020 ◽  
Author(s):  
Maxim I. Protasov ◽  
◽  
Vladimir A. Tcheverda ◽  
Valery V. Shilikov ◽  
◽  
...  
Keyword(s):  
Seismic Data ◽  
Real Data ◽  
Data Sets ◽  
Data Application ◽  
Diffraction Imaging

The paper deals with a 3D diffraction imaging with the subsequent diffraction attribute calculation. The imaging is based on an asymmetric summation of seismic data and provides three diffraction attributes: structural diffraction attribute, point diffraction attribute, an azimuth of structural diffraction. These attributes provide differentiating fractured and cavernous objects and to determine the fractures orientations. Approbation of the approach was provided on several real data sets.

HM-ICP: Fast 3-D Registration Algorithm with Hierarchical and Region Selection Approach of M-ICP

2006 ◽  
Vol 18 (6) ◽  
pp. 765-771 ◽  
Author(s):  
Haruhisa Okuda ◽  
◽  
Yasuo Kitaaki ◽  
Manabu Hashimoto ◽  
Shun’ichi Kaneko ◽  
...  
Keyword(s):  
Computational Cost ◽  
Real Data ◽  
Data Sets ◽  
Least Mean Square ◽  
Target Region ◽  
Icp Algorithm ◽  
Registration Algorithm ◽  
Region Selection ◽  
Data Points ◽  
Iterative Closest Point Algorithm

This paper presents a novel fast and highly accurate 3-D registration algorithm. The ICP (Iterative Closest Point) algorithm converges all the 3-D data points of two data sets to the best-matching points with minimum evaluation values. This algorithm is in widespread use because it has good validity for many applications, but it extracts a heavy computational cost and is very sensitive to error. This is because it uses all the data points of two data sets and least mean square optimization. We previously proposed the M-ICP algorithm, which uses M-estimation to realize robustness against outlying gross noise with the original ICP algorithm. In this paper, we propose a novel algorithm called HM-ICP (Hierarchical M-ICP), which is an extension of the M-ICP that selects regions for matching and hierarchical searching of selected regions. This method selects regions by evaluating the variance of distance values in the target region, and homogeneous topological mapping. Some fundamental experiments using real data sets of 3-D measurement demonstrate the effectiveness of the proposed method, achieving a reduction of more than ten thousand times for computational costs. We also confirmed an error of less than 0.1% for the measurement distance.

Bayesian linearized rock-physics inversion

Geophysics ◽  
2016 ◽  
Vol 81 (6) ◽  
pp. D625-D641 ◽  
Author(s):  
Dario Grana
Keyword(s):  
Granular Media ◽  
Computational Cost ◽  
Rock Physics ◽  
Real Data ◽  
Data Sets ◽  
New Approach ◽  
Amplitude Variation With Offset ◽  
Fluid Properties ◽  
Rock Physics Modeling ◽  
Physics Modeling

The estimation of rock and fluid properties from seismic attributes is an inverse problem. Rock-physics modeling provides physical relations to link elastic and petrophysical variables. Most of these models are nonlinear; therefore, the inversion generally requires complex iterative optimization algorithms to estimate the reservoir model of petrophysical properties. We have developed a new approach based on the linearization of the rock-physics forward model using first-order Taylor series approximations. The mathematical method adopted for the inversion is the Bayesian approach previously applied successfully to amplitude variation with offset linearized inversion. We developed the analytical formulation of the linearized rock-physics relations for three different models: empirical, granular media, and inclusion models, and we derived the formulation of the Bayesian rock-physics inversion under Gaussian assumptions for the prior distribution of the model. The application of the inversion to real data sets delivers accurate results. The main advantage of this method is the small computational cost due to the analytical solution given by the linearization and the Bayesian Gaussian approach.

Accurate poststack acoustic-impedance inversion by well-log calibration

Geophysics ◽  
2009 ◽  
Vol 74 (5) ◽  
pp. R59-R67 ◽  
Author(s):  
Igor B. Morozov ◽  
Jinfeng Ma
Keyword(s):  
Seismic Data ◽  
Acoustic Impedance ◽  
Joint Inversion ◽  
Low Frequency ◽  
Real Data ◽  
Data Sets ◽  
Frequency Model ◽  
Physical Constraints ◽  
Impedance Inversion ◽  
Reliable Solution

The seismic-impedance inversion problem is underconstrained inherently and does not allow the use of rigorous joint inversion. In the absence of a true inverse, a reliable solution free from subjective parameters can be obtained by defining a set of physical constraints that should be satisfied by the resulting images. A method for constructing synthetic logs is proposed that explicitly and accurately satisfies (1) the convolutional equation, (2) time-depth constraints of the seismic data, (3) a background low-frequency model from logs or seismic/geologic interpretation, and (4) spectral amplitudes and geostatistical information from spatially interpolated well logs. The resulting synthetic log sections or volumes are interpretable in standard ways. Unlike broadly used joint-inversion algorithms, the method contains no subjectively selected user parameters, utilizes the log data more completely, and assesses intermediate results. The procedure is simple and tolerant to noise, and it leads to higher-resolution images. Separating the seismic and subseismic frequency bands also simplifies data processing for acoustic-impedance (AI) inversion. For example, zero-phase deconvolution and true-amplitude processing of seismic data are not required and are included automatically in this method. The approach is applicable to 2D and 3D data sets and to multiple pre- and poststack seismic attributes. It has been tested on inversions for AI and true-amplitude reflectivity using 2D synthetic and real-data examples.

Adaptive multiple subtraction based on multiband pattern coding

Geophysics ◽  
2016 ◽  
Vol 81 (1) ◽  
pp. V69-V78 ◽  
Author(s):  
Jinlin Liu ◽  
Wenkai Lu
Keyword(s):  
Seismic Data ◽  
Real Data ◽  
Data Sets ◽  
Subtraction Problem ◽  
Frequency Bands ◽  
Main Challenge ◽  
Multiple Elimination ◽  
Pattern Coding

Adaptive multiple subtraction is the key step of surface-related multiple elimination methods. The main challenge of this technique resides in removing multiples without distorting primaries. We have developed a new pattern-based method for adaptive multiple subtraction with the consideration that primaries can be better protected if the multiples are differentiated from the primaries. Different from previously proposed methods, our method casts the adaptive multiple subtraction problem as a pattern coding and decoding process. We set out to learn distinguishable patterns from the predicted multiples before estimating the multiples contained in seismic data. Hence, in our method, we first carried out pattern coding of the predicted multiples to learn the special patterns of the multiples within different frequency bands. This coding process aims at exploiting the key patterns contained in the predicted multiples. The learned patterns are then used to decode (extract) the multiples contained in the seismic data, in which process those patterns that are similar to the learned patterns were identified and extracted. Because the learned patterns are obtained from the predicted multiples only, our method avoids the interferences of primaries in nature and shows an impressive capability for removing multiples without distorting the primaries. Our applications on synthetic and real data sets gave some promising results.

Multiple attenuation with 3D high-order high-resolution parabolic Radon transform using lower frequency constraints

Geophysics ◽  
2020 ◽  
Vol 85 (3) ◽  
pp. V317-V328
Author(s):  
Jitao Ma ◽  
Guoyang Xu ◽  
Xiaohong Chen ◽  
Xiaoliu Wang ◽  
Zhenjiang Hao
Keyword(s):  
High Resolution ◽  
Radon Transform ◽  
Seismic Data ◽  
Computational Cost ◽  
Real Data ◽  
Multiple Model ◽  
Multiple Attenuation ◽  
Common Depth Point ◽  
Frequency Constraint ◽  
Parabolic Radon Transform

The parabolic Radon transform is one of the most commonly used multiple attenuation methods in seismic data processing. The 2D Radon transform cannot consider the azimuth effect on seismic data when processing 3D common-depth point gathers; hence, the result of applying this transform is unreliable. Therefore, the 3D Radon transform should be applied. The theory of the 3D Radon transform is first introduced. To address sparse sampling in the crossline direction, a lower frequency constraint is introduced to reduce spatial aliasing and improve the resolution of the Radon transform. An orthogonal polynomial transform, which can fit the amplitude variations in different parabolic directions, is combined with the dealiased 3D high-resolution Radon transform to account for the amplitude variations with offset of seismic data. A multiple model can be estimated with superior accuracy, and improved results can be achieved. Synthetic and real data examples indicate that even though our method comes at a higher computational cost than existing techniques, the developed approach provides better attenuation of multiples for 3D seismic data with amplitude variations.

Adaptive singular spectrum analysis for seismic denoising and interpolation

Geophysics ◽  
2019 ◽  
Vol 84 (2) ◽  
pp. V133-V142 ◽  
Author(s):  
Hojjat Haghshenas Lari ◽  
Mostafa Naghizadeh ◽  
Mauricio D. Sacchi ◽  
Ali Gholami
Keyword(s):  
Spectrum Analysis ◽  
Seismic Data ◽  
Singular Spectrum Analysis ◽  
Computational Cost ◽  
Hankel Matrix ◽  
Real Data ◽  
Singular Spectrum ◽  
Value Decomposition ◽  
Spatially Varying ◽  
Spatial Patches

We have developed an adaptive singular spectrum analysis (ASSA) method for seismic data denoising and interpolation purposes. Our algorithm iteratively updates the singular-value decomposition (SVD) of current spatial patches using the most recently added spatial sample. The method reduces the computational cost of classic singular spectrum analysis (SSA) by requiring QR decompositions on smaller matrices rather than the factorization of the entire Hankel matrix of the data. A comparison between results obtained by the ASSA and SSA methods, in which the SVD applies to all of the traces at once, proves that the ASSA method is a valid way to cope with spatially varying dips. In addition, a comparison of the ASSA method with the windowed SSA method indicates gains in efficiency and accuracy. Synthetic and real data examples illustrate the effectiveness of our method.

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