An anti-aliasing POCS interpolation method for regularly undersampled seismic data using curvelet transform

2020 ◽  
Vol 172 ◽  
pp. 103894
Author(s):  
Hua Zhang ◽  
Hengqi Zhang ◽  
Junhu Zhang ◽  
Yaju Hao ◽  
Benfeng Wang
Keyword(s):  
Seismic Data ◽  
Interpolation Method ◽  
Curvelet Transform

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.

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.

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.

scholarly journals Nonequispaced curvelet transform for seismic data reconstruction: A sparsity-promoting approach

Geophysics ◽  
2010 ◽  
Vol 75 (6) ◽  
pp. WB203-WB210 ◽  
Author(s):  
Gilles Hennenfent ◽  
Lloyd Fenelon ◽  
Felix J. Herrmann
Keyword(s):  
Seismic Data ◽  
First Generation ◽  
Second Generation ◽  
Synthetic Data ◽  
Curvelet Transform ◽  
Real Data ◽  
Sampled Data ◽  
Regularized Inversion ◽  
Irregularly Sampled Data ◽  
Fast Discrete Curvelet Transform

We extend our earlier work on the nonequispaced fast discrete curvelet transform (NFDCT) and introduce a second generation of the transform. This new generation differs from the previous one by the approach taken to compute accurate curvelet coefficients from irregularly sampled data. The first generation relies on accurate Fourier coefficients obtained by an [Formula: see text]-regularized inversion of the nonequispaced fast Fourier transform (FFT) whereas the second is based on a direct [Formula: see text]-regularized inversion of the operator that links curvelet coefficients to irregular data. Also, by construction the second generation NFDCT is lossless unlike the first generation NFDCT. This property is particularly attractive for processing irregularly sampled seismic data in the curvelet domain and bringing them back to their irregular record-ing locations with high fidelity. Secondly, we combine the second generation NFDCT with the standard fast discrete curvelet transform (FDCT) to form a new curvelet-based method, coined nonequispaced curvelet reconstruction with sparsity-promoting inversion (NCRSI) for the regularization and interpolation of irregularly sampled data. We demonstrate that for a pure regularization problem the reconstruction is very accurate. The signal-to-reconstruction error ratio in our example is above [Formula: see text]. We also conduct combined interpolation and regularization experiments. The reconstructions for synthetic data are accurate, particularly when the recording locations are optimally jittered. The reconstruction in our real data example shows amplitudes along the main wavefronts smoothly varying with limited acquisition imprint.

Adaptive subtraction using complex-valued curvelet transforms

Geophysics ◽  
2010 ◽  
Vol 75 (4) ◽  
pp. V51-V60 ◽  
Author(s):  
Ramesh (Neelsh) Neelamani ◽  
Anatoly Baumstein ◽  
Warren S. Ross
Keyword(s):  
Least Squares ◽  
Seismic Data ◽  
Seismic Reflection ◽  
Characteristic Frequency ◽  
Large Scale ◽  
Curvelet Transform ◽  
Real Data ◽  
Text Data ◽  
Data Set ◽  
Complex Valued

We propose a complex-valued curvelet transform-based (CCT-based) algorithm that adaptively subtracts from seismic data those noises for which an approximate template is available. The CCT decomposes a geophysical data set in terms of small reflection pieces, with each piece having a different characteristic frequency, location, and dip. One can precisely change the amplitude and shift the location of each seismic reflection piece in a template by controlling the amplitude and phase of the template's CCT coefficients. Based on these insights, our approach uses the phase and amplitude of the data's and template's CCT coefficients to correct misalignment and amplitude errors in the noise template, thereby matching the adapted template with the actual noise in the seismic data, reflection event-by-event. We also extend our approach to subtract noises that require several templates to be approximated. By itself, the method can only correct small misalignment errors ([Formula: see text] in [Formula: see text] data) in the template; it relies on conventional least-squares (LS) adaptation to correct large-scale misalignment errors, such as wavelet mismatches and bulk shifts. Synthetic and real-data results illustrate that the CCT-based approach improves upon the LS approach and a curvelet-based approach described by Herrmann and Verschuur.

scholarly journals Multiresolution analysis and learning for computational seismic interpretation

2018 ◽  
Vol 37 (6) ◽  
pp. 443-450 ◽  
Author(s):  
Motaz Alfarraj ◽  
Yazeed Alaudah ◽  
Zhiling Long ◽  
Ghassan AlRegib
Keyword(s):  
Multiresolution Analysis ◽  
Seismic Data ◽  
Curvelet Transform ◽  
Discrete Wavelet ◽  
Data Sets ◽  
Seismic Structure ◽  
Subsurface Structures ◽  
Gaussian Pyramid ◽  
Seismic Image ◽  
Texture Attributes

We explore the use of multiresolution analysis techniques as texture attributes for seismic image characterization, especially in representing subsurface structures in large migrated seismic data. Namely, we explore the Gaussian pyramid, the discrete wavelet transform, Gabor filters, and the curvelet transform. These techniques are examined in a seismic structure labeling case study on the Netherlands offshore F3 block. In seismic structure labeling, a seismic volume is automatically segmented and classified according to the underlying subsurface structure using texture attributes. Our results show that multiresolution attributes improve the labeling performance compared to using seismic amplitude alone. Moreover, directional multiresolution attributes, such as the curvelet transform, are more effective than the nondirectional attributes in distinguishing different subsurface structures in large seismic data sets and can greatly help the interpretation process.

A NEW FRACTAL INTERPOLATION ALGORITHM AND ITS APPLICATIONS TO SELF-AFFINE SIGNAL RECONSTRUCTION

Fractals ◽  
2011 ◽  
Vol 19 (03) ◽  
pp. 355-365 ◽  
Author(s):  
MING-YUE ZHAI ◽  
JUAN LUIS FERNÁNDEZ-MARTÍNEZ ◽  
JAMES W. RECTOR
Keyword(s):  
Seismic Data ◽  
Interpolation Method ◽  
Signal Reconstruction ◽  
Theoretical Data ◽  
Arbitrary Point ◽  
Seismic Profile ◽  
Great Accuracy ◽  
Vertical Scaling ◽  
Real Field ◽  
Fractal Interpolation

A new fractal interpolation method called PPA (Pointed Point Algorithm) based on IFS is proposed to interpolate the self-affine signals with the expected interpolation error, solving the problem that the ordinary fractal interpolation can't get the value of any arbitrary point directly, which has not been found in the existing literatures. At the same time, a new method to calculate the vertical scaling factors is proposed based on the genetic algorithm, which works together with the PPA algorithm to get the better interpolation performance. Experiments on the theoretical data and real field seismic data show that the proposed interpolation schemes can not only get the expected point's value, but also get a great accuracy in reconstruction of the seismic profile, leading to a significant improvement over other trace interpolation methods.

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