Sparse time-frequency representation for seismic noise reduction using low-rank and sparse decomposition

Geophysics ◽  
2016 ◽  
Vol 81 (2) ◽  
pp. V117-V124 ◽  
Author(s):  
Mohammad Amir Nazari Siahsar ◽  
Saman Gholtashi ◽  
Amin Roshandel Kahoo ◽  
Hosein Marvi ◽  
Alireza Ahmadifard
Keyword(s):  
Seismic Data ◽  
Random Noise ◽  
Real Data ◽  
Seismic Signal ◽  
Oil Field ◽  
Low Rank ◽  
Classical Formula ◽  
Sparse Decomposition ◽  
Time Frequency ◽  
Frequency Representation

Attenuation of random noise is a major concern in seismic data processing. This kind of noise is usually characterized by random oscillation in seismic data over the entire time and frequency. We introduced and evaluated a low-rank and sparse decomposition-based method for seismic random noise attenuation. The proposed method, which is a trace by trace algorithm, starts by transforming the seismic signal into a new sparse subspace using the synchrosqueezing transform. Then, the sparse time-frequency representation (TFR) matrix is decomposed into two parts: (a) a low-rank component and (b) a sparse component using bilateral random projection. Although seismic data are not exactly low-rank in the sparse TFR domain, they can be assumed as being of semi-low-rank or approximately low-rank type. Hence, we can recover the denoised seismic signal by minimizing the mixed [Formula: see text] norms’ objective function by considering the intrinsically semilow-rank property of the seismic data and sparsity feature of random noise in the sparse TFR domain. The proposed method was tested on synthetic and real data. In the synthetic case, the data were contaminated by random noise. Denoising was carried out by means of the [Formula: see text] classical singular spectrum analysis (SSA) and [Formula: see text] deconvolution method for comparison. The [Formula: see text] deconvolution and the classical [Formula: see text] SSA method failed to properly reduce the noise and to recover the desired signal. We have also tested the proposed method on a prestack real data set from an oil field in the southwest of Iran. Through synthetic and real tests, the proposed method is determined to be an effective, amplitude preserving, and robust tool that gives superior results over classical [Formula: see text] SSA as conventional algorithm for denoising seismic data.

Random noise attenuation of 2D seismic data based on sparse low-rank estimation of the seismic signal

2020 ◽  
Vol 135 ◽  
pp. 104376 ◽  
Author(s):  
Rasoul Anvari ◽  
Mokhtar Mohammadi ◽  
Amin Roshandel Kahoo ◽  
Nabeel Ali Khan ◽  
Abdulqadir Ismail Abdullah
Keyword(s):  
Seismic Data ◽  
Random Noise ◽  
Seismic Signal ◽  
Low Rank ◽  
Noise Attenuation ◽  
Random Noise Attenuation ◽  
Rank Estimation

Suppression of strong random noise in seismic data by using time-frequency peak filtering

2013 ◽  
Vol 56 (7) ◽  
pp. 1200-1208 ◽  
Author(s):  
Yue Li ◽  
BaoJun Yang ◽  
HongBo Lin ◽  
HaiTao Ma ◽  
PengFei Nie
Keyword(s):  
Seismic Data ◽  
Random Noise ◽  
Time Frequency ◽  
Frequency Peak

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.

Random denoising and signal nonlinearity approach by time-frequency peak filtering using weighted frequency reassignment

Geophysics ◽  
2013 ◽  
Vol 78 (6) ◽  
pp. V229-V237 ◽  
Author(s):  
Hongbo Lin ◽  
Yue Li ◽  
Baojun Yang ◽  
Haitao Ma
Keyword(s):  
Weight Function ◽  
Instantaneous Frequency ◽  
Seismic Data ◽  
Signal To Noise Ratio ◽  
Random Noise ◽  
Signal To Noise ◽  
Transform Method ◽  
Time Frequency ◽  
Frequency Peak ◽  
Noise Ratio

Time-frequency peak filtering (TFPF) may efficiently suppress random noise and hence improve the signal-to-noise ratio. However, the errors are not always satisfactory when applying the TFPF to fast-varying seismic signals. We begin with an error analysis for the TFPF by using the spread factor of the phase and cumulants of noise. This analysis shows that the nonlinear signal component and non-Gaussian random noise lead to the deviation of the pseudo-Wigner-Ville distribution (PWVD) peaks from the instantaneous frequency. The deviation introduces the signal distortion and random oscillations in the result of the TFPF. We propose a weighted reassigned smoothed PWVD with less deviation than PWVD. The proposed method adopts a frequency window to smooth away the residual oscillations in the PWVD, and incorporates a weight function in the reassignment which sharpens the time-frequency distribution for reducing the deviation. Because the weight function is determined by the lateral coherence of seismic data, the smoothed PWVD is assigned to the accurate instantaneous frequency for desired signal components by weighted frequency reassignment. As a result, the TFPF based on the weighted reassigned PWVD (TFPF_WR) can be more effective in suppressing random noise and preserving signal as compared with the TFPF using the PWVD. We test the proposed method on synthetic and field seismic data, and compare it with a wavelet-transform method and [Formula: see text] prediction filter. The results show that the proposed method provides better performance over the other methods in signal preserving under low signal-to-noise ratio.

scholarly journals A method of combining coherence-constrained sparse coding and dictionary learning for denoising

Geophysics ◽  
2017 ◽  
Vol 82 (3) ◽  
pp. V137-V148 ◽  
Author(s):  
Pierre Turquais ◽  
Endrias G. Asgedom ◽  
Walter Söllner
Keyword(s):  
Dictionary Learning ◽  
Seismic Data ◽  
Random Noise ◽  
A Priori ◽  
Seismic Signal ◽  
Noise Variance ◽  
A Priori Information ◽  
Seismic Section ◽  
Learned Dictionary ◽  
Priori Information

We have addressed the seismic data denoising problem, in which the noise is random and has an unknown spatiotemporally varying variance. In seismic data processing, random noise is often attenuated using transform-based methods. The success of these methods in denoising depends on the ability of the transform to efficiently describe the signal features in the data. Fixed transforms (e.g., wavelets, curvelets) do not adapt to the data and might fail to efficiently describe complex morphologies in the seismic data. Alternatively, dictionary learning methods adapt to the local morphology of the data and provide state-of-the-art denoising results. However, conventional denoising by dictionary learning requires a priori information on the noise variance, and it encounters difficulties when applied for denoising seismic data in which the noise variance is varying in space or time. We have developed a coherence-constrained dictionary learning (CDL) method for denoising that does not require any a priori information related to the signal or noise. To denoise a given window of a seismic section using CDL, overlapping small 2D patches are extracted and a dictionary of patch-sized signals is trained to learn the elementary features embedded in the seismic signal. For each patch, using the learned dictionary, a sparse optimization problem is solved, and a sparse approximation of the patch is computed to attenuate the random noise. Unlike conventional dictionary learning, the sparsity of the approximation is constrained based on coherence such that it does not need a priori noise variance or signal sparsity information and is still optimal to filter out Gaussian random noise. The denoising performance of the CDL method is validated using synthetic and field data examples, and it is compared with the K-SVD and FX-Decon denoising. We found that CDL gives better denoising results than K-SVD and FX-Decon for removing noise when the variance varies in space or time.

Wavelet transform with generalized beta wavelets for seismic time-frequency analysis

Geophysics ◽  
2017 ◽  
Vol 82 (4) ◽  
pp. O47-O56 ◽  
Author(s):  
Zhiguo Wang ◽  
Bing Zhang ◽  
Jinghuai Gao ◽  
Qingzhen Wang ◽  
Qing Huo Liu
Keyword(s):  
Wavelet Transform ◽  
Frequency Analysis ◽  
Seismic Data ◽  
Significant Information ◽  
Trade Off ◽  
Time Frequency Analysis ◽  
Time Frequency ◽  
Reflection Seismic ◽  
Seismic Waveform ◽  
Frequency Representation

Using the continuous wavelet transform (CWT), the time-frequency analysis of reflection seismic data can provide significant information to delineate subsurface reservoirs. However, CWT is limited by the Heisenberg uncertainty principle, with a trade-off between time and frequency localizations. Meanwhile, the mother wavelet should be adapted to the real seismic waveform. Therefore, for a reflection seismic signal, we have developed a progressive wavelet family that is referred to as generalized beta wavelets (GBWs). By varying two parameters controlling the wavelet shapes, the time-frequency representation of GBWs can be given sufficient flexibility while remaining exactly analytic. To achieve an adaptive trade-off between time-frequency localizations, an optimization workflow is designed to estimate suitable parameters of GBWs in the time-frequency analysis of seismic data. For noise-free and noisy synthetic signals from a depositional cycle model, the results of spectral component using CWT with GBWs display its flexibility and robustness in the adaptive time-frequency representation. Finally, we have applied CWT with GBWs on 3D seismic data to show its potential to discriminate stacked fluvial channels in the vertical sections and to delineate more distinct fluvial channels in the horizontal slices. CWT with GBWs provides a potential technique to improve the resolution of exploration seismic interpretation.

scholarly journals Removal of Random Noise in Seismic Data by Time-varying Window-length Time-frequency Peak Filtering

2016 ◽  
Vol 64 (5) ◽  
pp. 1703-1714 ◽  
Author(s):  
Pengjun Yu ◽  
Yue Li ◽  
Hongbo Lin ◽  
Ning Wu
Keyword(s):  
Seismic Data ◽  
Random Noise ◽  
Time Varying ◽  
Window Length ◽  
Time Frequency ◽  
Frequency Peak
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