Progressive denoising of seismic data via robust noise estimation in dual domains

Geophysics ◽  
2020 ◽  
Vol 85 (1) ◽  
pp. V99-V118
Author(s):  
Yi Lin ◽  
Jinhai Zhang
Keyword(s):  
Seismic Data ◽  
High Frequency ◽  
Random Noise ◽  
Denoising Method ◽  
Data Set ◽  
Edge Preserving ◽  
Space Domain ◽  
Time Space ◽  
Frequency Components ◽  
Resolution Imaging

Random noise attenuation plays an important role in seismic data processing. Most traditional methods suppress random noise either in the time-space domain or in the transformed domain, which may encounter difficulty in retaining the detailed structures. We have introduced the progressive denoising method to suppress random noise in seismic data. This method estimates random noise at each sample independently by imposing proper constraints on local windowed data in the time-space domain and then in the transformed domain, and the denoised results of the whole data set are gradually improved by many iterations. First, we apply an unnormalized bilateral kernel in time-space domain to reject large-amplitude signals; then, we apply a range kernel in the frequency-wavenumber domain to reject medium-amplitude signals; finally, we can obtain a total estimate of random noise by repeating these steps approximately 30 times. Numerical examples indicate that the progressive denoising method can achieve a better denoising result, compared with the two typical single-domain methods: the [Formula: see text]-[Formula: see text] deconvolution method and the curvelet domain thresholding method. As an edge-preserving method, the progressive denoising method can greatly reduce the random noise without harming the useful signals, especially to those high-frequency components, which would be crucial for high-resolution imaging and interpretations in the following stages.

Footprint removal from seismic data with residual dictionary learning

Geophysics ◽  
2020 ◽  
Vol 85 (4) ◽  
pp. V355-V365
Author(s):  
Julián L. Gómez ◽  
Danilo R. Velis
Keyword(s):  
Dictionary Learning ◽  
Seismic Data ◽  
Input Data ◽  
Random Noise ◽  
Coherent Noise ◽  
Edge Preservation ◽  
Data Set ◽  
Edge Preserving ◽  
Learned Dictionary ◽  
Data Volume

Dictionary learning (DL) is a machine learning technique that can be used to find a sparse representation of a given data set by means of a relatively small set of atoms, which are learned from the input data. DL allows for the removal of random noise from seismic data very effectively. However, when seismic data are contaminated with footprint noise, the atoms of the learned dictionary are often a mixture of data and coherent noise patterns. In this scenario, DL requires carrying out a morphological attribute classification of the atoms to separate the noisy atoms from the dictionary. Instead, we have developed a novel DL strategy for the removal of footprint patterns in 3D seismic data that is based on an augmented dictionary built upon appropriately filtering the learned atoms. The resulting augmented dictionary, which contains the filtered atoms and their residuals, has a high discriminative power in separating signal and footprint atoms, thus precluding the use of any statistical classification strategy to segregate the atoms of the learned dictionary. We filter the atoms using a domain transform filtering approach, a very efficient edge-preserving smoothing algorithm. As in the so-called coherence-constrained DL method, the proposed DL strategy does not require the user to know or adjust the noise level or the sparsity of the solution for each data set. Furthermore, it only requires one pass of DL and is shown to produce successful transfer learning. This increases the speed of the denoising processing because the augmented dictionary does not need to be calculated for each time slice of the input data volume. Results on synthetic and 3D public-domain poststack field data demonstrate effective footprint removal with accurate edge preservation.

Non-stationary predictive filtering for seismic random noise suppression - A tutorial

Geophysics ◽  
2021 ◽  
pp. 1-79 ◽  
Author(s):  
Hang Wang ◽  
Wei Chen ◽  
Weilin Huang ◽  
Shaohuan Zu ◽  
Xingye Liu ◽  
...  
Keyword(s):  
Seismic Data ◽  
Space Dimension ◽  
Noise Suppression ◽  
Random Noise ◽  
Spatial Dimension ◽  
Seismic Data Processing ◽  
Filtering Method ◽  
Time Space ◽  
Stationary Version ◽  
Predictive Filtering

Predictive filtering in the frequency domain is one of the most widely used denoising algorithms in the seismic data processing workflow. Predictive filtering is based on the assumption of linear/planar events in the time-space domain. In traditional predictive filtering method, the predictive filter is fixed across the spatial dimension, which cannot deal with the spatial variation of seismic data well. To handle the curving events, the predictive filter is either applied in local windows or extended to a non-stationary version. The regularized non-stationary autoregression (RNAR) method can be treated as a non-stationary extension of the traditional predictive filtering, where the predictive filter coefficients are variable in different space locations. The highly under-determined inverse problem is solved by shaping regularization with a smoothness constraint in space. We further extend the RNAR method to a more general case, where we can apply more constraints to the filter coefficients according to the features of seismic data. First, apart from the smoothness in space, we also apply a smoothing constraint in frequency, considering the coherency of the coefficients in the frequency dimension. Secondly, we apply a frequency dependent smoothing radius along the space dimension to better take advantage of the non-stationarity of seismic data in the frequency axis, and to better deal with noise. The proposed method is validated via several synthetic and field data examples.

Multichannel absorption compensation with a data-driven structural regularization

Geophysics ◽  
2019 ◽  
Vol 85 (1) ◽  
pp. V71-V80 ◽  
Author(s):  
Xiong Ma ◽  
Guofa Li ◽  
Hao Li ◽  
Wuyang Yang
Keyword(s):  
Cost Function ◽  
Structural Characteristic ◽  
Seismic Data ◽  
High Frequency ◽  
Signal To Noise Ratio ◽  
Random Noise ◽  
Frequency Noise ◽  
Characteristic Operator ◽  
High Frequency Noise ◽  
The Cost

Seismic absorption compensation is an important processing approach to mitigate the attenuation effects caused by the intrinsic inelasticity of subsurface media and to enhance seismic resolution. However, conventional absorption compensation approaches ignore the spatial connection along seismic traces, which makes the compensation result vulnerable to high-frequency noise amplification, thus reducing the signal-to-noise ratio (S/N) of the result. To alleviate this issue, we have developed a structurally constrained multichannel absorption compensation (SC-MAC) algorithm. In the cost function of this algorithm, we exploit an [Formula: see text] norm to constrain the reflectivity series and an [Formula: see text] norm to regularize the reflection structural characteristic of the compensation data. The reflection structural characteristic operator, extracted from the observed stacked seismic data, is the core of the structural regularization term. We then solve the cost function of SC-MAC by the alternating direction method of multipliers. Benefiting from the introduction of reflection structure constraint, SC-MAC improves the stability of the compensation result and inhibits the amplification of high-frequency noise. Synthetic and field data examples demonstrate that our proposed method is more robust to random noise and can not only improve the resolution of seismic data, but also maintain the S/N of the compensation seismic data.

Coherence based on spectral variance analysis

Geophysics ◽  
2018 ◽  
Vol 83 (3) ◽  
pp. O55-O66 ◽  
Author(s):  
Yanting Duan ◽  
Chaodong Wu ◽  
Xiaodong Zheng ◽  
Yucheng Huang ◽  
Jian Ma
Keyword(s):  
Fourier Transform ◽  
Seismic Data ◽  
High Frequency ◽  
Seismic Interpretation ◽  
Variance Analysis ◽  
Frequency Spectra ◽  
Amplitude Spectra ◽  
Frequency Components ◽  
Spectral Variance ◽  
Coherence Estimation

The eigenstructure-based coherence attribute is a type of efficient and mature tool for mapping geologic edges such as faults and/or channels in the 3D seismic interpretation. However, the eigenstructure-based coherence algorithm is sensitive to low signal-to-noise ratio seismic data, and the coherence results are affected by the dipping structures. Due to the large energy gap between the low- and high-frequency components, the low-frequency components play the principal role in coherence estimation. In contrast, the spectral variance balances the difference between the low- and high-frequency components at a fixed depth. The coherence estimation based on amplitude spectra avoids the effect of the time delays resulting from the dipping structures. Combining the spectral variance with the amplitude spectra avoids the effect of dipping structures and enhances the antinoise performance of the high-frequency components. First, we apply the short-time Fourier transform to obtain the time-frequency spectra of seismic data. Next, we compute the variance values of amplitude spectra. Then, we apply the fast Fourier transform to obtain the amplitude spectra of spectral variance. Finally, we calculate the eigenstructure coherence by using the amplitude spectra of spectral variance as the input. We apply the method to the theoretical models and practical seismic data. In the Marmousi velocity model, the coherence estimation using the amplitude spectra of the spectral variance as input shows more subtle discontinuities, especially in deeper layers. The results from field-data examples demonstrate that the proposed method is helpful for mapping faults and for improving the narrow channel edges’ resolution of interest. Therefore, the coherence algorithm based on the spectral variance analysis may be conducive to the seismic interpretation.

Denoising Method for Calibration Data of Landing Guidance Radar Based on EMD and Wavelet

2014 ◽  
Vol 962-965 ◽  
pp. 2856-2862
Author(s):  
De Yi Sang ◽  
Jian Jun Zhao ◽  
Li Bin Yang
Keyword(s):  
High Frequency ◽  
Low Frequency ◽  
Wavelet Denoising ◽  
Calibration Data ◽  
Wavelet Thresholding ◽  
Denoising Method ◽  
Calibration Process ◽  
Frequency Components

The noise resulted in the calibration process of the landing guidance radar can cause serious accidents. Analyse the principle of the EMD and wavelet denoising method. Points out the deficiencies of pure EMD or pure wavelet denoising method. Propose a denoising method based on EMD and wavelet. Improved the discriminanting method for high or low frequency components and the discriminanting method for wavelet thresholding. First EMD the signal, then denoise the high frequency components by wavelet, finally, combined the low frequency components and the denoised high frequency components to get the denoised data.

3-D coherency filtering

Geophysics ◽  
1997 ◽  
Vol 62 (4) ◽  
pp. 1310-1314 ◽  
Author(s):  
Qing Li ◽  
Kris Vasudevan ◽  
Frederick A. Cook
Keyword(s):  
Seismic Data ◽  
Seismic Event ◽  
Signal To Noise Ratio ◽  
Random Noise ◽  
Three Dimensions ◽  
Coherent Noise ◽  
Coherent Signal ◽  
Frequency Space ◽  
Time Space ◽  
Incoherent Noise

Coherency filtering is a tool used commonly in 2-D seismic processing to isolate desired events from noisy data. It assumes that phase‐coherent signal can be separated from background incoherent noise on the basis of coherency estimates, and coherent noise from coherent signal on the basis of different dips. It is achieved by searching for the maximum coherence direction for each data point of a seismic event and enhancing the event along this direction through stacking; it suppresses the incoherent events along other directions. Foundations for a 2-D coherency filtering algorithm were laid out by several researchers (Neidell and Taner, 1971; McMechan, 1983; Leven and Roy‐Chowdhury, 1984; Kong et al., 1985; Milkereit and Spencer, 1989). Milkereit and Spencer (1989) have applied 2-D coherency filtering successfully to 2-D deep crustal seismic data for the improvement of visualization and interpretation. Work on random noise attenuation using frequency‐space or time‐space prediction filters both in two or three dimensions to increase the signal‐to‐noise ratio of the data can be found in geophysical literature (Canales, 1984; Hornbostel, 1991; Abma and Claerbout, 1995).

Random noise attenuation using f-x regularized nonstationary autoregression

Geophysics ◽  
2012 ◽  
Vol 77 (2) ◽  
pp. V61-V69 ◽  
Author(s):  
Guochang Liu ◽  
Xiaohong Chen ◽  
Jing Du ◽  
Kailong Wu
Keyword(s):  
Seismic Data ◽  
Random Noise ◽  
Geological Structure ◽  
Least Square ◽  
Noise Attenuation ◽  
Spatial Direction ◽  
Random Noise Attenuation ◽  
Time Space ◽  
Prediction Technique ◽  
Domain Prediction

We have developed a novel method for random noise attenuation in seismic data by applying regularized nonstationary autoregression (RNA) in the frequency-space ([Formula: see text]) domain. The method adaptively predicts the signal with spatial changes in dip or amplitude using [Formula: see text] RNA. The key idea is to overcome the assumption of linearity and stationarity of the signal in conventional [Formula: see text] domain prediction technique. The conventional [Formula: see text] domain prediction technique uses short temporal and spatial analysis windows to cope with the nonstationary of the seismic data. The new method does not require windowing strategies in spatial direction. We implement the algorithm by an iterated scheme using the conjugate-gradient method. We constrain the coefficients of nonstationary autoregression (NA) to be smooth along space and frequency in the [Formula: see text] domain. The shaping regularization in least-square inversion controls the smoothness of the coefficients of [Formula: see text] RNA. There are two key parameters in the proposed method: filter length and radius of shaping operator. Tests on synthetic and field data examples showed that, compared with [Formula: see text] domain and time-space domain prediction methods, [Formula: see text] RNA can be more effective in suppressing random noise and preserving the signals, especially for complex geological structure.

Synthesis and Simplification of Fractal Profile

2011 ◽  
Vol 279 ◽  
pp. 262-265
Author(s):  
Chao Zhou ◽  
Cheng Hui Gao ◽  
Jie Chen ◽  
Lian Feng Lai
Keyword(s):  
Finite Element ◽  
Fourier Transform ◽  
Frequency Domain ◽  
Discrete Fourier Transform ◽  
High Frequency ◽  
Space Domain ◽  
Finite Element Software ◽  
Redundant Data ◽  
Frequency Components

In order to import a synthesized fractal profile into finite element software, the profile synthesized by discrete Fourier transform was studied. The synthesized profile was filtered in frequency domain in order to filter its high frequency components and to make it smooth, and then the chord deviation algorithm was used to reduce its redundant data in space domain. It was found that: after filtering, the profile is smooth but with lots of redundant data; the chord deviation algorithm can simplify the profile which is redundant in space domain; the time needed in the process of importing a profile into finite element software can be reduced greatly after profile simplification.

Interpretive advantages of 90°-phase wavelets: Part 1 — Modeling

Geophysics ◽  
2005 ◽  
Vol 70 (3) ◽  
pp. C7-C15 ◽  
Author(s):  
Hongliu Zeng ◽  
Milo M. Backus
Keyword(s):  
Seismic Data ◽  
High Frequency ◽  
Thick Layer ◽  
Amplitude Data ◽  
Frequency Components ◽  
Wireline Logs ◽  
Phase Data ◽  
Dual Polarity ◽  
Seismic Models ◽  
Zero Phase

We discuss, in a two-part article, the benefits of 90°-phase wavelets in stratigraphic and lithologic interpretation of seismically thin beds. In Part 1, seismic models of Ricker wavelets with selected phases are constructed to assess interpretability of composite waveforms in increasingly complex geologic settings. Although superior for single surface and thick-layer interpretation, zero-phase seismic data are not optimal for interpreting beds thinner than a wavelength because their antisymmetric thin-bed responses tie to the reflectivity series rather than to impedance logs. Nonsymmetrical wavelets (e.g., minimum-phase wavelets) are generally not recommended for interpretation because their asymmetric composite waveforms have large side lobes. Integrated zero-phase traces are also less desirable because they lose high-frequency components in the integration process. However, the application of 90°-phase data consistently improves seismic interpretability. The unique symmetry of 90°-phase thin-bed response eliminates the dual polarity of thin-bed responses, resulting in better imagery of thin-bed geometry, impedance profiles, lithology, and stratigraphy. Less amplitude distortion and less stratigraphy-independent, thin-bed interference lead to more accurate acoustic impedance estimation from amplitude data and a better tie of seismic traces to lithology-indicative wireline logs. Field data applications are presented in part 2 of this article.

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