5D seismic data regularization by a damped least-norm Fourier inversion

Geophysics ◽  
2010 ◽  
Vol 75 (6) ◽  
pp. WB103-WB111 ◽  
Author(s):  
Side Jin
Keyword(s):  
Seismic Data ◽  
Fourier Coefficients ◽  
Fourier Transforms ◽  
Low Frequency ◽  
Original Data ◽  
Spatial Spectrum ◽  
Small Data ◽  
Inversion Algorithm ◽  
Fourier Inversion ◽  
Discrete Fourier Transforms

Regularizing inadequate and irregularly sampled seismic data is one of important problems in seismic data processing. An improvement to existing methods to solve this problem is proposed by applying a 5D regularization/interpolation scheme with a damped least-norm Fourier inversion. Under the assumption of planar seismic events within small data windows, the spatial spectrum of regularized data for a fixed frequency should be sparse and have minimum damped norm. The inversion scheme consists in finding a set of regularly spaced spatial Fourier coefficients by minimizing its damped norm for each frequency, subject to the condition that the resulting spatial Fourier coefficients also faithfully reconstruct the original data. The damping factors are automatically derived from the amplitude spectra of the regularized low-frequency data. With the guidance of the damping factors and automatic adjustment of wavenumber ranges according to the Nyquist sampling theory, the proposed inversion algorithm naturally yields a one-step solution for both stabilization and antialiasing of the interpolation problem. A distinctive feature of the method is that it uses high-dimensional nonuniform fast Fourier transforms to evaluate expensive discrete Fourier transforms involved in conjugate gradient iterations. This improves the computational efficiency. The results of applying this algorithm to synthetic and field data demonstrate that it performs well when applied to highly irregular data and outperforms lower dimensional interpolation schemes.

Five-dimensional interpolation: Recovering from acquisition constraints

Geophysics ◽  
2009 ◽  
Vol 74 (6) ◽  
pp. V123-V132 ◽  
Author(s):  
Daniel Trad
Keyword(s):  
Seismic Data ◽  
Original Data ◽  
Spatial Spectrum ◽  
Optimal Interpolation ◽  
Multidimensional Data ◽  
Inversion Algorithm ◽  
Five Dimensions ◽  
Fourier Reconstruction ◽  
Simultaneous Interpolation ◽  
Seismic Amplitudes

Although 3D seismic data are being acquired in larger volumes than ever before, the spatial sampling of these volumes is not always adequate for certain seismic processes. This is especially true of marine and land wide-azimuth acquisitions, leading to the development of multidimensional data interpolation techniques. Simultaneous interpolation in all five seismic data dimensions (inline, crossline, offset, azimuth, and frequency) has great utility in predicting missing data with correct amplitude and phase variations. Although there are many techniques that can be implemented in five dimensions, this study focused on sparse Fourier reconstruction. The success of Fourier interpolation methods depends largely on two factors: (1) having efficient Fourier transform operators that permit the use of large multidimensional data windows and (2) constraining the spatial spectrum along dimensions where seismic amplitudes change slowly so that the sparseness and band limitation assumptions remain valid. Fourier reconstruction can be performed when enforcing a sparseness constraint on the 4D spatial spectrum obtained from frequency slices of five-dimensional windows. Binning spatial positions into a fine 4D grid facilitates the use of the FFT, which helps on the convergence of the inversion algorithm. This improves the results and computational efficiency. The 5D interpolation can successfully interpolate sparse data, improve AVO analysis, and reduce migration artifacts. Target geometries for optimal interpolation and regularization of land data can be classified in terms of whether they preserve the original data and whether they are designed to achieve surface or subsurface consistency.

Simultaneous inversion of prestack seismic data for rock properties using simulated annealing

Geophysics ◽  
2002 ◽  
Vol 67 (6) ◽  
pp. 1877-1885 ◽  
Author(s):  
Xin‐Quan Ma
Keyword(s):  
Simulated Annealing ◽  
Seismic Data ◽  
Low Frequency ◽  
Optimization Procedure ◽  
P Wave ◽  
Rock Properties ◽  
Inversion Method ◽  
Inversion Algorithm ◽  
Simultaneous Inversion ◽  
Reflection Seismic

A new prestack inversion algorithm has been developed to simultaneously estimate acoustic and shear impedances from P‐wave reflection seismic data. The algorithm uses a global optimization procedure in the form of simulated annealing. The goal of optimization is to find a global minimum of the objective function, which includes the misfit between synthetic and observed prestack seismic data. During the iterative inversion process, the acoustic and shear impedance models are randomly perturbed, and the synthetic seismic data are calculated and compared with the observed seismic data. To increase stability, constraints have been built into the inversion algorithm, using the low‐frequency impedance and background Vs/Vp models. The inversion method has been successfully applied to synthetic and field data examples to produce acoustic and shear impedances comparable to log data of similar bandwidth. The estimated acoustic and shear impedances can be combined to derive other elastic parameters, which may be used for identifying of lithology and fluid content of reservoirs.

scholarly journals Tutorial: Spectral bandwidth extension — Invention versus harmonic extrapolation

Geophysics ◽  
2017 ◽  
Vol 82 (4) ◽  
pp. W1-W16 ◽  
Author(s):  
Chen Liang ◽  
John Castagna ◽  
Ricardo Zavala Torres
Keyword(s):  
Seismic Data ◽  
High Frequency ◽  
Low Frequency ◽  
Original Data ◽  
Spectral Bandwidth ◽  
Bandwidth Extension ◽  
Seismic Resolution ◽  
Earth Structures ◽  
Seismic Sections ◽  
Phase Acceleration

Various postprocessing methods can be applied to seismic data to extend the spectral bandwidth and potentially increase the seismic resolution. Frequency invention techniques, including phase acceleration and loop reconvolution, produce spectrally broadened seismic sections but arbitrarily create high frequencies without a physical basis. Tests in extending the bandwidth of low-frequency synthetics using these methods indicate that the invented frequencies do not tie high-frequency synthetics generated from the same reflectivity series. Furthermore, synthetic wedge models indicate that the invented high-frequency seismic traces do not improve thin-layer resolution. Frequency invention outputs may serve as useful attributes, but they should not be used for quantitative work and do not improve actual resolution. On the other hand, under appropriate circumstances, layer frequency responses can be extrapolated to frequencies outside the band of the original data using spectral periodicities determined from within the original seismic bandwidth. This can be accomplished by harmonic extrapolation. For blocky earth structures, synthetic tests show that such spectral extrapolation can readily double the bandwidth, even in the presence of noise. Wedge models illustrate the resulting resolution improvement. Synthetic tests suggest that the more complicated the earth structure, the less valid the bandwidth extension that harmonic extrapolation can achieve. Tests of the frequency invention methods and harmonic extrapolation on field seismic data demonstrate that (1) the frequency invention methods modify the original seismic band such that the original data cannot be recovered by simple band-pass filtering, whereas harmonic extrapolation can be filtered back to the original band with good fidelity and (2) harmonic extrapolation exhibits acceptable ties between real and synthetic seismic data outside the original seismic band, whereas frequency invention methods have unfavorable well ties in the cases studied.

Simultaneous reconstruction of seismic reflections and diffractions using a global hyperbolic Radon dictionary

Geophysics ◽  
2018 ◽  
Vol 83 (6) ◽  
pp. V315-V323 ◽  
Author(s):  
Amr Ibrahim ◽  
Paolo Terenghi ◽  
Mauricio D. Sacchi
Keyword(s):  
Seismic Data ◽  
Seismic Reflection ◽  
Small Data ◽  
Inversion Algorithm ◽  
Efficient Tool ◽  
Reconstruction Methods ◽  
Simultaneous Reconstruction ◽  
Sparse Inversion ◽  
Data Windows ◽  
Seismic Reflections

We have developed a new transform with basis functions that closely resemble seismic reflections and diffractions. The new transform is an extension of the classic hyperbolic Radon transform and accounts for the apex shifts of the seismic reflection hyperbolas and the asymptote shifts of the seismic diffraction hyperbolas. The adjoint and forward operators of the proposed transform are computed using Stolt operators in the frequency domain to increase the computational efficiency of the transform. This new transform is used, in conjunction with a sparse inversion algorithm, to reconstruct common-shot gathers. Our tests indicate that this new transform is an efficient tool for interpolating coarsely sampled seismic data in cases in which one cannot use small data windows to validate the linear event assumption that is often made by Fourier-based reconstruction methods.

APPLICATION OF THE EMPIRICAL MODE DECOMPOSITION METHOD TO GROUND-ROLL NOISE ATTENUATION IN SEISMIC DATA

2013 ◽  
Vol 31 (4) ◽  
pp. 619 ◽  
Author(s):  
Luiz Eduardo Soares Ferreira ◽  
Milton José Porsani ◽  
Michelângelo G. Da Silva ◽  
Giovani Lopes Vasconcelos
Keyword(s):  
Empirical Mode Decomposition ◽  
Seismic Data ◽  
Low Frequency ◽  
High Amplitude ◽  
Seismic Line ◽  
Seismic Processing ◽  
Mode Decomposition ◽  
Ground Roll ◽  
Fortran 90 ◽  
Emd Method

ABSTRACT. Seismic processing aims to provide an adequate image of the subsurface geology. During seismic processing, the filtering of signals considered noise is of utmost importance. Among these signals is the surface rolling noise, better known as ground-roll. Ground-roll occurs mainly in land seismic data, masking reflections, and this roll has the following main features: high amplitude, low frequency and low speed. The attenuation of this noise is generally performed through so-called conventional methods using 1-D or 2-D frequency filters in the fk domain. This study uses the empirical mode decomposition (EMD) method for ground-roll attenuation. The EMD method was implemented in the programming language FORTRAN 90 and applied in the time and frequency domains. The application of this method to the processing of land seismic line 204-RL-247 in Tacutu Basin resulted in stacked seismic sections that were of similar or sometimes better quality compared with those obtained using the fk and high-pass filtering methods.Keywords: seismic processing, empirical mode decomposition, seismic data filtering, ground-roll. RESUMO. O processamento sísmico tem como principal objetivo fornecer uma imagem adequada da geologia da subsuperfície. Nas etapas do processamento sísmico a filtragem de sinais considerados como ruídos é de fundamental importância. Dentre esses ruídos encontramos o ruído de rolamento superficial, mais conhecido como ground-roll . O ground-roll ocorre principalmente em dados sísmicos terrestres, mascarando as reflexões e possui como principais características: alta amplitude, baixa frequência e baixa velocidade. A atenuação desse ruído é geralmente realizada através de métodos de filtragem ditos convencionais, que utilizam filtros de frequência 1D ou filtro 2D no domínio fk. Este trabalho utiliza o método de Decomposição em Modos Empíricos (DME) para a atenuação do ground-roll. O método DME foi implementado em linguagem de programação FORTRAN 90, e foi aplicado no domínio do tempo e da frequência. Sua aplicação no processamento da linha sísmica terrestre 204-RL-247 da Bacia do Tacutu gerou como resultados, seções sísmicas empilhadas de qualidade semelhante e por vezes melhor, quando comparadas as obtidas com os métodos de filtragem fk e passa-alta.Palavras-chave: processamento sísmico, decomposição em modos empíricos, filtragem dados sísmicos, atenuação do ground-roll.

scholarly journals Low-Frequency Expansion Approach for Seismic Data Based on Compressed Sensing in Low SNR

2021 ◽  
Vol 11 (11) ◽  
pp. 5028
Author(s):  
Miaomiao Sun ◽  
Zhenchun Li ◽  
Yanli Liu ◽  
Jiao Wang ◽  
Yufei Su
Keyword(s):  
Reflection Coefficient ◽  
Compressed Sensing ◽  
Objective Function ◽  
Low Frequency ◽  
Original Data ◽  
Seismic Exploration ◽  
High Signal ◽  
Inversion Process ◽  
Frequency Information ◽  
Low Snr

Low-frequency information can reflect the basic trend of a formation, enhance the accuracy of velocity analysis and improve the imaging accuracy of deep structures in seismic exploration. However, the low-frequency information obtained by the conventional seismic acquisition method is seriously polluted by noise, which will be further lost in processing. Compressed sensing (CS) theory is used to exploit the sparsity of the reflection coefficient in the frequency domain to expand the low-frequency components reasonably, thus improving the data quality. However, the conventional CS method is greatly affected by noise, and the effective expansion of low-frequency information can only be realized in the case of a high signal-to-noise ratio (SNR). In this paper, well information is introduced into the objective function to constrain the inversion process of the estimated reflection coefficient, and then, the low-frequency component of the original data is expanded by extracting the low-frequency information of the reflection coefficient. It has been proved by model tests and actual data processing results that the objective function of estimating the reflection coefficient constrained by well logging data based on CS theory can improve the anti-noise interference ability of the inversion process and expand the low-frequency information well in the case of a low SNR.

scholarly journals Cell shape characterization and classification with discrete Fourier transforms and self-organizing maps

2017 ◽  
Vol 93 (3) ◽  
pp. 323-333 ◽  
Author(s):  
Fabian L. Kriegel ◽  
Ralf Köhler ◽  
Jannike Bayat-Sarmadi ◽  
Simon Bayerl ◽  
Anja E. Hauser ◽  
...  
Keyword(s):  
Cell Shape ◽  
Fourier Transforms ◽  
Self Organizing Maps ◽  
Discrete Fourier Transforms ◽  
Shape Characterization ◽  
Self Organizing
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