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.

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.

scholarly journals Coherent noise suppression by learning and analyzing the morphology of the data

Geophysics ◽  
2017 ◽  
Vol 82 (6) ◽  
pp. V397-V411 ◽  
Author(s):  
Pierre Turquais ◽  
Endrias G. Asgedom ◽  
Walter Söllner
Keyword(s):  
Seismic Data ◽  
Noise Suppression ◽  
Morphological Diversity ◽  
Seismic Signal ◽  
Coherent Noise ◽  
Data Set ◽  
Redundant Dictionary ◽  
Manual Search ◽  
Mechanical Noise ◽  
Learned Dictionary

We have developed a method for suppressing coherent noise from seismic data by using the morphological differences between the noise and the signal. This method consists of three steps: First, we applied a dictionary learning method on the data to extract a redundant dictionary in which the morphological diversity of the data is stored. Such a dictionary is a set of unit vectors called atoms that represent elementary patterns that are redundant in the data. Because the dictionary is learned on data contaminated by coherent noise, it is a mix of atoms representing signal patterns and atoms representing noise patterns. In the second step, we separate the noise atoms from the signal atoms using a statistical classification. Hence, the learned dictionary is divided into two subdictionaries: one describing the morphology of the noise and the other one describing the morphology of the signal. Finally, we separate the seismic signal and the coherent noise via morphological component analysis (MCA); it uses sparsity with respect to the two subdictionaries to identify the signal and the noise contributions in the mixture. Hence, the proposed method does not use prior information about the signal and the noise morphologies, but it entirely adapts to the signal and the noise of the data. It does not require a manual search for adequate transforms that may sparsify the signal and the noise, in contrast to existing MCA-based methods. We develop an application of the proposed method for removing the mechanical noise from a marine seismic data set. For mechanical noise that is coherent in space and time, the results show that our method provides better denoising in comparison with the standard FX-Decon, FX-Cadzow, and the curvelet-based denoising methods.

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.

Edge-preserving frequency-offset denoising of seismic data

Geophysics ◽  
2018 ◽  
Vol 83 (5) ◽  
pp. V293-V303 ◽  
Author(s):  
Julián L. Gómez ◽  
Danilo R. Velis
Keyword(s):  
Spatial Dimension ◽  
Frequency Offset ◽  
Coherent Noise ◽  
Edge Preservation ◽  
Data Set ◽  
Edge Preserving ◽  
Seismic Amplitude ◽  
Amplitude Data ◽  
Fitting Error ◽  
New Algorithms

We have developed new algorithms for denoising 2D or 3D poststack seismic-amplitude data that use simple edge-preserving smoothing operators in the frequency-offset domain. The algorithms are aimed to attenuate random and coherent noise, to enhance the signal energy and lateral continuity, and to preserve structural discontinuities such as faults. The methods consist of fitting the frequency slices of the data in the spatial dimension by means of low-order polynomials. We use an overlapping window operator to select the fitting parameters for each point of the slice from the neighborhood with minimum fitting error to provide edge preservation. Various synthetic examples and a field data set are used to demonstrate the strengths and limitations of the algorithms. The denoised outputs indicate enhanced edge preservation of seismic features, which reflects clearer details of semblance attributes.

Spectral structure-oriented filtering of seismic data with self-adaptive paths

Geophysics ◽  
2019 ◽  
Vol 84 (5) ◽  
pp. V271-V280
Author(s):  
Julián L. Gómez ◽  
Danilo R. Velis
Keyword(s):  
Seismic Data ◽  
Random Noise ◽  
Noise Removal ◽  
Quality Data ◽  
Spectral Structure ◽  
Data Sets ◽  
Coherent Noise ◽  
Edge Preserving ◽  
3D Data ◽  
Self Adaptive

We have developed an algorithm to perform structure-oriented filtering (SOF) in 3D seismic data by learning the data structure in the frequency domain. The method, called spectral SOF (SSOF), allows us to enhance the signal structures in the [Formula: see text]-[Formula: see text]-[Formula: see text] domain by running a 1D edge-preserving filter along curvilinear self-adaptive trajectories that connect points of similar characteristics. These self-adaptive paths are given by the eigenvectors of the smoothed structure tensor, which are easily computed using closed-form expressions. SSOF relies on a few parameters that are easily tuned and on simple 1D convolutions for tensor calculation and smoothing. It is able to process a 3D data volume with a 2D strategy using basic 1D edge-preserving filters. In contrast to other SOF techniques, such as anisotropic diffusion, anisotropic smoothing, and plane-wave prediction, SSOF does not require any iterative process to reach the denoised result. We determine the performance of SSOF using three public domain field data sets, which are subsets of the well-known Waipuku, Penobscot, and Teapot surveys. We use the Waipuku subset to indicate the signal preservation of the method in good-quality data when mostly background random noise is present. Then, we use the Penobscot subset to illustrate random noise and footprint signature attenuation, as well as to show how faults and fractures are improved. Finally, we analyze the Teapot stacked and depth-migrated subsets to show random and coherent noise removal, leading to an improvement of the volume structural details and overall lateral continuity. The results indicate that random noise, footprints, and other artifacts can be successfully suppressed, enhancing the delineation of geologic structures and seismic horizons and preserving the original signal bandwidth.

ROBUST SVD FILTERING FOR LOW SIGNAL-TO-NOISE RATIO SEISMIC DATA

Geophysics ◽  
2021 ◽  
pp. 1-51
Author(s):  
Chao Wang ◽  
Yun Wang
Keyword(s):  
Seismic Data ◽  
Signal To Noise Ratio ◽  
Singular Values ◽  
New Method ◽  
Signal To Noise ◽  
Coherent Noise ◽  
Edge Preserving ◽  
Singular Vectors ◽  
Reduced Rank ◽  
Noise Ratio

Reduced-rank filtering is a common method for attenuating noise in seismic data. As conventional reduced-rank filtering distinguishes signals from noises only according to singular values, it performs poorly when the signal-to-noise ratio is very low, or when data contain high levels of isolate or coherent noise. Therefore, we developed a novel and robust reduced-rank filtering based on the singular value decomposition in the time-space domain. In this method, noise is recognized and attenuated according to the characteristics of both singular values and singular vectors. The left and right singular vectors corresponding to large singular values are selected firstly. Then, the right singular vectors are classified into different categories according to their curve characteristics, such as jump, pulse, and smooth. Each kind of right singular vector is related to a type of noise or seismic event, and is corrected by using a different filtering technology, such as mean filtering, edge-preserving smoothing or edge-preserving median filtering. The left singular vectors are also corrected by using the filtering methods based on frequency attributes like main-frequency and frequency bandwidth. To process seismic data containing a variety of events, local data are extracted along the local dip of event. The optimal local dip is identified according to the singular values and singular vectors of the data matrices that are extracted along different trial directions. This new filtering method has been applied to synthetic and field seismic data, and its performance is compared with that of several conventional filtering methods. The results indicate that the new method is more robust for data with a low signal-to-noise ratio, strong isolate noise, or coherent noise. The new method also overcomes the difficulties associated with selecting an optimal rank.

Noise suppression in 2D and 3D seismic data with data-driven sifting algorithms

Geophysics ◽  
2019 ◽  
Vol 85 (1) ◽  
pp. V1-V10
Author(s):  
Julián L. Gómez ◽  
Danilo R. Velis ◽  
Juan I. Sabbione
Keyword(s):  
Seismic Data ◽  
Noise Suppression ◽  
Department Of Energy ◽  
Time Slice ◽  
3D Seismic ◽  
Coherent Noise ◽  
Data Set ◽  
Amplitude Data ◽  
3D Volume ◽  
2D And 3D

We have developed an empirical-mode decomposition (EMD) algorithm for effective suppression of random and coherent noise in 2D and 3D seismic amplitude data. Unlike other EMD-based methods for seismic data processing, our approach does not involve the time direction in the computation of the signal envelopes needed for the iterative sifting process. Instead, we apply the sifting algorithm spatially in the inline-crossline plane. At each time slice, we calculate the upper and lower signal envelopes by means of a filter whose length is adapted dynamically at each sifting iteration according to the spatial distribution of the extrema. The denoising of a 3D volume is achieved by removing the most oscillating modes of each time slice from the noisy data. We determine the performance of the algorithm by using three public-domain poststack field data sets: one 2D line of the well-known Alaska 2D data set, available from the US Geological Survey; a subset of the Penobscot 3D volume acquired offshore by the Nova Scotia Department of Energy, Canada; and a subset of the Stratton 3D land data from South Texas, available from the Bureau of Economic Geology at the University of Texas at Austin. The results indicate that random and coherent noise, such as footprint signatures, can be mitigated satisfactorily, enhancing the reflectors with negligible signal leakage in most cases. Our method, called empirical-mode filtering (EMF), yields improved results compared to other 2D and 3D techniques, such as [Formula: see text] EMD filter, [Formula: see text] deconvolution, and [Formula: see text]-[Formula: see text]-[Formula: see text] adaptive prediction filtering. EMF exploits the flexibility of EMD on seismic data and is presented as an efficient and easy-to-apply alternative for denoising seismic data with mild to moderate structural complexity.

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).

Predictive removal of scattered noise

Geophysics ◽  
2006 ◽  
Vol 71 (2) ◽  
pp. V41-V49 ◽  
Author(s):  
Gérard C. Herman ◽  
Colin Perkins
Keyword(s):  
Mathematical Model ◽  
Wave Propagation ◽  
Surface Wave ◽  
Seismic Data ◽  
Coherent Noise ◽  
Data Set ◽  
Near Surface ◽  
Unique Data ◽  
Surface Wave Propagation ◽  
Petroleum Development

Land seismic data can be severely contaminated with coherent noise. We discuss a deterministic technique to predict and remove scattered coherent noise from land seismic data based on a mathematical model of near-surface wave propagation. We test the method on a unique data set recorded by Petroleum Development of Oman in the Qarn Alam area (with shots and receivers on the same grid), and we conclude that it effectively reduces scattered noise without smearing reflection energy.

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