Multidimensional de-aliased Cadzow reconstruction of seismic records

Geophysics ◽  
2013 ◽  
Vol 78 (1) ◽  
pp. A1-A5 ◽  
Author(s):  
Mostafa Naghizadeh ◽  
Mauricio Sacchi
Keyword(s):  
Seismic Data ◽  
Interpolation Method ◽  
Hankel Matrix ◽  
Real Data ◽  
Low Frequencies ◽  
Frequency Space ◽  
Reduced Rank ◽  
Seismic Records ◽  
Text Prediction ◽  
Eigen Decomposition

We tested a strategy for beyond-alias interpolation of seismic data using Cadzow reconstruction. The strategy enables Cadzow reconstruction to be used for interpolation of regularly sampled seismic records. First, in the frequency-space ([Formula: see text]) domain, we generated a Hankel matrix from the spatial samples of the low frequencies. To perform interpolation at a given frequency, the spatial samples were interlaced with zero samples and another Hankel matrix was generated from the zero-interlaced data. Next, the rank-reduced eigen-decomposition of the Hankel matrix at low frequencies was used for beyond-alias preconditioning of the Hankel matrix at a given frequency. Finally, antidiagonal averaging of the conditioned Hankel matrix produced the final interpolated data. In addition, the multidimensional extension of the proposed algorithm was explained. The proposed method provides a unifying thread between reduced-rank Cadzow reconstruction and beyond alias [Formula: see text] prediction error interpolation. Synthetic and real data examples were provided to examine the performance of the proposed interpolation method.

Seismic data interpolation using a fast generalized Fourier transform

Geophysics ◽  
2011 ◽  
Vol 76 (1) ◽  
pp. V1-V10 ◽  
Author(s):  
Mostafa Naghizadeh ◽  
Kristopher A. Innanen
Keyword(s):  
Fourier Transform ◽  
Seismic Data ◽  
Interpolation Method ◽  
Temporal Frequency ◽  
Real Data ◽  
Generalized Fourier Transform ◽  
Sampled Data ◽  
Low Frequencies ◽  
Mask Function ◽  
The Ideal

We have found a fast and efficient method for the interpolation of nonstationary seismic data. The method uses the fast generalized Fourier transform (FGFT) to identify the space-wavenumber evolution of nonstationary spatial signals at each temporal frequency. The nonredundant nature of FGFT renders a big computational advantage to this interpolation method. A least-squares fitting scheme is used next to retrieve the optimal FGFT coefficients representative of the ideal interpolated data. For randomly sampled data on a regular grid, we seek a sparse representation of FGFT coefficients to retrieve the missing samples. In addition, to interpolate the regularly sampled seismic data at a given frequency, we use a mask function derived from the FGFT coefficients of the low frequencies. Synthetic and real data examples can be used to examine the performance of the method.

Ground-roll attenuation using curvelet downscaling

Geophysics ◽  
2018 ◽  
Vol 83 (3) ◽  
pp. V185-V195 ◽  
Author(s):  
Mostafa Naghizadeh ◽  
Mauricio Sacchi
Keyword(s):  
Seismic Data ◽  
Curvelet Transform ◽  
Low Frequencies ◽  
High Frequencies ◽  
Seismic Records ◽  
Mask Function ◽  
Ground Roll ◽  
Least Squares Optimization ◽  
Seismic Reflections ◽  
Content Information

We have developed a ground-roll attenuation strategy for seismic records that adopts the curvelet transform. The curvelet transform decomposes the seismic events based on their dip and frequency content information. The curvelet panels that contain only either reflection or ground-roll energy can be used to alter the curvelet panels with mixed reflection and ground-roll energies. We build a curvelet-domain mask function from the ground-roll-free curvelet coefficients (high frequencies) and downscale it to the ground-roll-contaminated curvelet coefficients (low frequencies). The mask function is used inside a least-squares optimization scheme to preserve the seismic reflections and attenuate the ground roll. Synthetic and real seismic data examples show the application of the proposed ground-roll attenuation method.

Noise types and their attenuation in towed marine seismic: A tutorial

Geophysics ◽  
2020 ◽  
pp. 1-104
Author(s):  
Volodya Hlebnikov ◽  
Thomas Elboth ◽  
Vetle Vinje ◽  
Leiv-J. Gelius
Keyword(s):  
Seismic Data ◽  
Real Data ◽  
Noise Component ◽  
Industry Standard ◽  
Noise Type ◽  
Wide Range ◽  
Different Types ◽  
Seismic Records ◽  
Marine Seismic ◽  
Processing Techniques

The presence of noise in towed marine seismic data is a long-standing problem. The various types of noise present in marine seismic records are never truly random. Instead, seismic noise is more complex and often challenging to attenuate in seismic data processing. Therefore, we examine a wide range of real data examples contaminated by different types of noise including swell noise, seismic interference noise, strumming noise, passing vessel noise, vertical particle velocity noise, streamer hit and fishing gear noise, snapping shrimp noise, spike-like noise, cross-feed noise and streamer mounted devices noise. The noise examples investigated focus only on data acquired with analogue group-forming. Each noise type is classified based on its origin, coherency and frequency content. We then demonstrate how the noise component can be effectively attenuated through industry standard seismic processing techniques. In this tutorial, we avoid presenting the finest details of either the physics of the different types of noise themselves or the noise attenuation algorithms applied. Rather, we focus on presenting the noise problems themselves and show how well the community is able to address such noise. Our aim is that based on the provided insights, the geophysical community will be able to gain an appreciation of some of the most common types of noise encountered in marine towed seismic, in the hope to inspire more researchers to focus their attention on noise problems with greater potential industry impact.

A fast and simple method of spectral enhancement

Geophysics ◽  
2014 ◽  
Vol 79 (3) ◽  
pp. V75-V80 ◽  
Author(s):  
Muhammad Sajid ◽  
Deva Ghosh
Keyword(s):  
Seismic Data ◽  
Real Data ◽  
Difference Operators ◽  
Frequency Noise ◽  
Simple Method ◽  
Low Frequencies ◽  
High Frequencies ◽  
Algorithm Comparison ◽  
Spectral Enhancement ◽  
Bed Thickness

The ability to resolve seismic thin beds is a function of the bed thickness and the frequency content of the seismic data. To achieve high resolution, the seismic data must have broad frequency bandwidth. We developed an algorithm that improved the bandwidth of the seismic data without greatly boosting high-frequency noise. The algorithm employed a set of three cascaded difference operators to boost high frequencies and combined with a simple smoothing operator to boost low frequencies. The output of these operators was balanced and added to the original signal to produce whitened data. The four convolutional operators were quite short, so the algorithm was highly efficient. Synthetic and real data examples demonstrated the effectiveness of this algorithm. Comparison with a conventional whitening algorithm showed the algorithm to be competitive.

Seismic data interpolation and denoising in the frequency-wavenumber domain

Geophysics ◽  
2012 ◽  
Vol 77 (2) ◽  
pp. V71-V80 ◽  
Author(s):  
Mostafa Naghizadeh
Keyword(s):  
Least Squares ◽  
Seismic Data ◽  
Real Data ◽  
Sampled Data ◽  
Frequency Range ◽  
Unified Approach ◽  
Low Frequencies ◽  
Time Space ◽  
Least Squares Fit ◽  
Mask Function

I introduce a unified approach for denoising and interpolation of seismic data in the frequency-wavenumber ([Formula: see text]) domain. First, an angular search in the [Formula: see text] domain is carried out to identify a sparse number of dominant dips, not only using low frequencies but over the whole frequency range. Then, an angular mask function is designed based on the identified dominant dips. The mask function is utilized with the least-squares fitting principle for optimal denoising or interpolation of data. The least-squares fit is directly applied in the time-space domain. The proposed method can be used to interpolate regularly sampled data as well as randomly sampled data on a regular grid. Synthetic and real data examples are provided to examine the performance of the proposed method.

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.

scholarly journals Can learning from natural image denoising be used for seismic data interpolation?

Geophysics ◽  
2020 ◽  
Vol 85 (4) ◽  
pp. WA115-WA136 ◽  
Author(s):  
Hao Zhang ◽  
Xiuyan Yang ◽  
Jianwei Ma
Keyword(s):  
Deep Learning ◽  
Seismic Data ◽  
Interpolation Method ◽  
Signal To Noise Ratio ◽  
Curvelet Transform ◽  
Block Matching ◽  
Natural Image ◽  
Data Interpolation ◽  
Sampling Locations ◽  
Text Prediction

We have developed an interpolation method based on the denoising convolutional neural network (CNN) for seismic data. It provides a simple and efficient way to break through the problem of the scarcity of geophysical training labels that are often required by deep learning methods. This new method consists of two steps: (1) training a set of CNN denoisers to learn denoising from natural image noisy-clean pairs and (2) integrating the trained CNN denoisers into the project onto convex set (POCS) framework to perform seismic data interpolation. We call it the CNN-POCS method. This method alleviates the demands of seismic data that require shared similar features in the applications of end-to-end deep learning for seismic data interpolation. Additionally, the adopted method is flexible and applicable for different types of missing traces because the missing or down-sampling locations are not involved in the training step; thus, it is of a plug-and-play nature. These indicate the high generalizability of the proposed method and a reduction in the necessity of problem-specific training. The primary results of synthetic and field data show promising interpolation performances of the adopted CNN-POCS method in terms of the signal-to-noise ratio, dealiasing, and weak-feature reconstruction, in comparison with the traditional [Formula: see text]-[Formula: see text] prediction filtering, curvelet transform, and block-matching 3D filtering methods.

Beyond alias hierarchical scale curvelet interpolation of regularly and irregularly sampled seismic data

Geophysics ◽  
2010 ◽  
Vol 75 (6) ◽  
pp. WB189-WB202 ◽  
Author(s):  
Mostafa Naghizadeh ◽  
Mauricio D. Sacchi
Keyword(s):  
Seismic Data ◽  
Interpolation Method ◽  
Curvelet Transform ◽  
Real Data ◽  
Interpolation Scheme ◽  
Free Data ◽  
First Pass ◽  
Mask Function ◽  
To Come ◽  
Hierarchical Scale

We propose a robust interpolation scheme for aliased regularly sampled seismic data that uses the curvelet transform. In a first pass, the curvelet transform is used to compute the curvelet coefficients of the aliased seismic data. The aforementioned coefficients are divided into two groups of scales: alias-free and alias-contaminated scales. The alias-free curvelet coefficients are upscaled to estimate a mask function that is used to constrain the inversion of the alias-contaminated scale coefficients. The mask function is incorporated into the inversion via a minimum norm least-squares algorithm that determines the curvelet coefficients of the desired alias-free data. Once the alias-free coefficients are determined, the curvelet synthesis operator is used to reconstruct seismograms at new spatial positions. The proposed method can be used to reconstruct regularly and irregularly sampled seismic data. We believe that our exposition leads to a clear unifying thread between [Formula: see text] and [Formula: see text] beyond-alias interpolation methods and curvelet reconstruction. As in [Formula: see text] and [Formula: see text] interpolation, we stress the necessity of examining seismic data at different scales (frequency bands) to come up with viable and robust interpolation schemes. Synthetic and real data examples are used to illustrate the performance of the proposed curvelet interpolation method.

f-x adaptive seismic-trace interpolation

Geophysics ◽  
2009 ◽  
Vol 74 (1) ◽  
pp. V9-V16 ◽  
Author(s):  
Mostafa Naghizadeh ◽  
Mauricio D. Sacchi
Keyword(s):  
Interpolation Method ◽  
Real Data ◽  
Recursive Least Squares ◽  
Forgetting Factor ◽  
Filter Length ◽  
Frequency Space ◽  
Adaptive Prediction ◽  
Two Parameters ◽  
Spatially Variant ◽  
Selection Of

We use exponentially weighted recursive least squares to estimate adaptive prediction filters for frequency-space [Formula: see text] seismic interpolation. Adaptive prediction filters can model signals where the dominant wavenumbers vary in space. This concept leads to an [Formula: see text] interpolation method that does not require windowing strategies for optimal results. In other words, adaptive prediction filters can be used to interpolate waveforms that have spatially variant dips. The interpolation method’s performance depends on two parameters: filter length and forgetting factor. We pay particular attention to selection of the forgetting factor because it controls the algorithm’s adaptability to changes in local dip. Finally, we use synthetic- and real-data examples to illustrate the performance of the proposed adaptive [Formula: see text] interpolation method.

scholarly journals Amplitude-Preserved Wave Equation: An Example to Image the Gas Hydrate System

Energies ◽  
2021 ◽  
Vol 14 (12) ◽  
pp. 3700
Author(s):  
Jiachun You ◽  
Sha Song ◽  
Umberta Tinivella ◽  
Michela Giustiniani ◽  
Iván Vargas-Cordero
Keyword(s):  
Wave Equation ◽  
Gas Hydrate ◽  
Seismic Data ◽  
Signal To Noise Ratio ◽  
Matrix Decomposition ◽  
Real Data ◽  
High Signal ◽  
Imaging Result ◽  
Imaging Results ◽  
Seismic Records

Natural gas hydrate is an important energy source. Therefore, it is extremely important to provide a clear imaging profile to determine its distribution for energy exploration. In view of the problems existing in conventional migration methods, e.g., the limited imaging angles, we proposed to utilize an amplitude-preserved one-way wave equation migration based on matrix decomposition to deal with primary and multiple waves. With respect to seismic data gathered at the Chilean continental margin, a conventional processing flow to obtain seismic records with a high signal-to-noise ratio is introduced. Then, the imaging results of the conventional and amplitude-preserved one-way wave equation migration methods based on primary waves are compared, to demonstrate the necessity of implementing amplitude-preserving migration. Moreover, a simple two-layer model is imaged by using primary and multiple waves, which proves the superiority of multiple waves in imaging compared with primary waves and lays the foundation for further application. For the real data, the imaging sections of primary and multiple waves are compared. We found that multiple waves are able to provide a wider imaging illumination while primary waves fail to illuminate, especially for the imaging of bottom simulating reflections (BSRs), because multiple waves have a longer travelling path and carry more information. By imaging the actual seismic data, we can make a conclusion that the imaging result generated by multiple waves can be viewed as a supplementary for the imaging result of primary waves, and it has some guiding values for further hydrate and in general shallow gas exploration.

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