Nonstatinary deconvolutive Radon transform

Geophysics ◽  
2021 ◽  
pp. 1-35
Author(s):  
Hojjat Haghshenas Lari ◽  
Ali Gholami
Keyword(s):  
Radon Transform ◽  
Seismic Data ◽  
Estimation Method ◽  
Original Data ◽  
Seismic Events ◽  
Seismic Data Processing ◽  
Convolution Operation ◽  
Inverse Transform ◽  
Time Space ◽  
Overlap Method

Different versions of the Radon transform (RT) are widely used in seismic data processing tofocus the recorded seismic events. Multiple separation, data interpolation, and noise attenuationare some of RT applications in seismic processing work-flows. Unfortunately, the conventional RTmethods cannot focus the events perfectly in the RT domain. This problem arises due to theblurring effects of the source wavelet and the nonstationary nature of the seismic data. Sometimes,the distortion results in a big difference between the original data and its inverse transform. Wepropose a nonstationary deconvolutive RT to handle these two issues. Our proposed algorithm takesadvantage of a nonstationary convolution technique. that builds on the concept of block convolutionand the overlap method, where the convolution operation is defined separately for overlapping blocks.Therefore, it allows the Radon basis function to take arbitrary shapes in time and space directions. Inaddition, we introduce a nonstationary wavelet estimation method to determine time-space-varyingwavelets. The wavelets and the Radon panel are estimated simultaneously and in an alternative way.Numerical examples demonstrate that our nonstationary deconvolutive RT method can significantlyimprove the sparsity of Radon panels. Hence, the inverse RT does not suffer from the distortioncaused by the unfocused seismic events.

Use of the slant stack for geologic or geophysical map lineament analysis

Geophysics ◽  
1997 ◽  
Vol 62 (6) ◽  
pp. 1774-1778 ◽  
Author(s):  
Robert S. Pawlowski
Keyword(s):  
Plane Wave ◽  
Radon Transform ◽  
Seismic Data ◽  
Seismic Events ◽  
Seismic Data Processing ◽  
Coherent Noise ◽  
Plane Wave Decomposition ◽  
Lineament Analysis ◽  
The Individual ◽  
Wave Decomposition

The slant‐stack technique (also known as Radon transform, τ-p transform, and plane‐wave decomposition) used in seismic data processing for discriminating between and separating seismic events of differing dips (or moveout) is applied here to the problem of geologic or geophysical map lineament analysis. The latter problem is analogous to the seismic coherent noise problem in the sense that lineaments associated with one geologic event or episode are often underprinted by the lineaments of preceding geologic disturbances and overprinted by the lineaments of subsequent disturbances. Consequently, it can be difficult to distinguish between the individual lineament sets.

Deconvolutive Radon transform

Geophysics ◽  
2017 ◽  
Vol 82 (2) ◽  
pp. V117-V125 ◽  
Author(s):  
Ali Gholami
Keyword(s):  
Data Processing ◽  
Temporal Resolution ◽  
Radon Transform ◽  
Seismic Data ◽  
Model Building ◽  
Random Noise ◽  
Velocity Model ◽  
Seismic Events ◽  
Seismic Data Processing ◽  
Band Limited

The Radon transform (RT) plays an important role in seismic data processing for its ability to focus seismic events in the transform domain. The band-limited nature of seismic events due to the blurring effects of the source wavelet, however, causes a decrease in the temporal resolution of the transform. We have developed the deconvolutive RT (DecRT) as a generalization of conventional RT and to increase the temporal resolution. Unlike the conventional counterpart, the new basis functions can take an arbitrary shape in the time direction. This method is thus proposed to adaptively infer the temporal wave shape from the input data while finding a sparse representation of it. The new transform significantly improves the sparsity and thus the temporal resolution of the resulting seismic data. The applicability of the hyperbolic DecRT in seismic data processing is demonstrated for random noise attenuation, primary and multiple separation, high-quality stacking, and automatic velocity model building. The results obtained on synthetic and field data sets confirm the effectiveness of the method in improving the time and slowness/curvature resolutions compared with conventional transforms, which leads to improved seismic processing results in the deconvolutive Radon domains.

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.

Stratal slicing, Part II: Real 3-D seismic data

Geophysics ◽  
1998 ◽  
Vol 63 (2) ◽  
pp. 514-522 ◽  
Author(s):  
Hongliu Zeng ◽  
Stephen C. Henry ◽  
John P. Riola
Keyword(s):  
Seismic Data ◽  
Large Degree ◽  
Original Data ◽  
Seismic Facies ◽  
Seismic Events ◽  
Depositional Facies ◽  
Time Model ◽  
Data Set ◽  
Geologic Time ◽  
Frequency Independent

Three‐dimensional seismic data from the Gulf of Mexico Tertiary section show a close dependence of seismic events on data frequency. While some events remain frequency independent, many events exhibit different occurrences with changing frequency and, therefore, are not parallel to geologic time surfaces. In the data set we have studied, observed maximum time transgression of seismic events is at least 120 ms traveltime on lower frequency sections. Severe interference in lower frequency data may produce false seismic facies characteristics and obscure the true stratigraphic relationships. This phenomenon has important implications for seismic interpretation, particularly for sequence stratigraphic studies. This time transgression problem is mitigated to a large degree by the stratal slicing technique discussed in Part I of this paper. Stratal slicing on a workstation is done by first tracking frequency‐independent, geologic‐time‐equivalent reference seismic events, then building a stratal time model and an amplitude stratal slice volume on the basis of linear interpolation functions between references. The new volumes have an x-, y-coordinate system the same as the original data, but a z-axis of relative geologic time. Stratal slicing is a useful new tool for basin analysis and reservoir delineation by making depositional facies mapping an easier task, especially in wedged depositional sequences. Examples show that the common depositional facies like fluvial channels, deltaic systems, and submarine turbidite deposits are often imaged from real 3-D data with relatively high lateral resolution.

scholarly journals Differential‐equation‐based seismic data filtering

Geophysics ◽  
1993 ◽  
Vol 58 (12) ◽  
pp. 1809-1819 ◽  
Author(s):  
Jianchao Li ◽  
Ken Larner
Keyword(s):  
Differential Equation ◽  
Seismic Data ◽  
Lower Cost ◽  
Seismic Signal ◽  
Seismic Data Processing ◽  
Data Filtering ◽  
Time And Space ◽  
Convolution Operation ◽  
Computational Advantage ◽  
Space Point

Suppressing noise and enhancing useful seismic signal by filtering is one of the important tasks of seismic data processing. Conventional filtering methods are implemented through either the convolution operation or various mathematical transforms. We describe a methodology for studying and implementing filters, which, unlike conventional filtering methods, is based on solving differential equations in the time and space domain. We call this differential‐equation‐based filtering (DEBF). DEBF does not require that seismic data be stationary, so filtering parameters can vary with every time and space point. Examples with two‐dimensional (2-D) synthetic and field seismic data demonstrate that the DEBF method accomplishes the desired time‐ and space‐varying temporal and move‐out filtering at lower cost than conventional frequency‐wavenumber‐domain filtering. The computational advantage in 3-D would be much greater.

EMD-seislet transform

Geophysics ◽  
2018 ◽  
Vol 83 (1) ◽  
pp. A27-A32 ◽  
Author(s):  
Yangkang Chen ◽  
Sergey Fomel
Keyword(s):  
Data Processing ◽  
Empirical Mode Decomposition ◽  
Seismic Data ◽  
Seismic Events ◽  
Variable Frequency ◽  
Seismic Data Processing ◽  
Local Slope ◽  
Mode Decomposition ◽  
Frequency Components

The seislet transform uses a prediction operator that is connected to the local slope or frequency of seismic events. We have combined the 1D nonstationary seislet transform with empirical-mode decomposition (EMD) in the [Formula: see text]-[Formula: see text] domain. We used EMD to decompose data into smoothly variable frequency components for the following 1D seislet transform. The resultant representation showed remarkable sparsity. We developed a detailed algorithm and used a field example to demonstrate the application of the new seislet transform for sparsity-promoting seismic data processing.

Nonstationary blind deconvolution of seismic records

Geophysics ◽  
2019 ◽  
Vol 84 (1) ◽  
pp. V1-V9 ◽  
Author(s):  
Hojjat Haghshenas Lari ◽  
Ali Gholami
Keyword(s):  
Seismic Data ◽  
High Performance ◽  
Blind Deconvolution ◽  
Signal To Noise Ratio ◽  
Statistical Characteristics ◽  
Time Space ◽  
Alternating Direction ◽  
Seismic Records ◽  
Nonstationary Data ◽  
Overlap Method

Seismic deconvolution used for improving the bandwidth of data is inherently nonstationary, mixed phase, and blind. Due to some restricting assumptions imposed by conventional deconvolution methods, they are either stationary or semiblind. A fully nonstationary blind deconvolution method is proposed that is able to simultaneously take into account different sources of nonstationarity and to improve the bandwidth of highly nonstationary seismic data in a fully blind manner. Based on the concept of block convolution and the overlap method, the convolutional model of seismic data is generalized to consider nonstationary cases and to model nonstationary data. This generalized convolutional model is then used for nonstationary blind deconvolution, in which the statistical characteristics of the wavelets are allowed to arbitrarily change in the vertical and horizontal directions. Given a nonstationary seismic record, several time-space-varying wavelets are simultaneously determined with the reflectivity model in an alternating direction algorithm using a variational approach. Numerical tests are presented showing the high performance of our nonstationary blind deconvolution for improving the temporal resolution of data in comparison with their stationary counterparts. The results indicate that in comparison with patched deconvolution, our nonstationary method is more robust and stable for different window sizes and it produces better results with a higher signal-to-noise ratio.

On a plane-wave based crosscorrelation-type seismic interferometry

Geophysics ◽  
2013 ◽  
Vol 78 (4) ◽  
pp. Q35-Q44 ◽  
Author(s):  
Yi Tao ◽  
Mrinal K. Sen
Keyword(s):  
Plane Wave ◽  
Seismic Data ◽  
Full Range ◽  
Computation Time ◽  
Original Data ◽  
Ocean Bottom ◽  
Ocean Bottom Seismometer ◽  
Dispersive Waves ◽  
Time Space ◽  
Data Volume

We explored a new approach to retrieve virtual seismic responses from crosscorrelating acquired seismic data in the plane-wave domain. Using this method, slant stacking is first performed over shot or receiver locations of observed seismic data to produce plane-wave transformed gathers. Crosscorrelation is then performed by selecting traces with the same ray parameters from different shot or receiver locations of the plane-wave gathers. Unlike traditional crosscorrelation-type time-space domain interferometry, where full range of ray parameters is used for each survey location, this method directly selects common ray parameters to cancel overlapping raypaths. This approach can be used to retrieve reflections in the presence of dispersive waves and to select certain ranges of ray parameters with directional wave paths for retrieval. It can avoid spurious arrivals in supervirtual interferometry when unwanted arrivals such as reflections break the requirement of conventional interferometry. In addition, computation time can be saved with this approach because plane-wave transform usually results in a reduction of the original data volume. We demonstrate this method with synthetic and ocean bottom seismometer data examples.

scholarly journals A Machine Learning-Based Seismic Data Compression and Interpretation Using a Novel Shifted-Matrix Decomposition Algorithm

2021 ◽  
Vol 11 (11) ◽  
pp. 4874
Author(s):  
Milan Brankovic ◽  
Eduardo Gildin ◽  
Richard L. Gibson ◽  
Mark E. Everett
Keyword(s):  
Real Time ◽  
Seismic Data ◽  
Matrix Decomposition ◽  
Original Data ◽  
Velocity Estimation ◽  
Singular Vectors ◽  
Well Stimulation ◽  
Marine Seismic ◽  
Value Decomposition ◽  
Seismic Data Compression

Seismic data provides integral information in geophysical exploration, for locating hydrocarbon rich areas as well as for fracture monitoring during well stimulation. Because of its high frequency acquisition rate and dense spatial sampling, distributed acoustic sensing (DAS) has seen increasing application in microseimic monitoring. Given large volumes of data to be analyzed in real-time and impractical memory and storage requirements, fast compression and accurate interpretation methods are necessary for real-time monitoring campaigns using DAS. In response to the developments in data acquisition, we have created shifted-matrix decomposition (SMD) to compress seismic data by storing it into pairs of singular vectors coupled with shift vectors. This is achieved by shifting the columns of a matrix of seismic data before applying singular value decomposition (SVD) to it to extract a pair of singular vectors. The purpose of SMD is data denoising as well as compression, as reconstructing seismic data from its compressed form creates a denoised version of the original data. By analyzing the data in its compressed form, we can also run signal detection and velocity estimation analysis. Therefore, the developed algorithm can simultaneously compress and denoise seismic data while also analyzing compressed data to estimate signal presence and wave velocities. To show its efficiency, we compare SMD to local SVD and structure-oriented SVD, which are similar SVD-based methods used only for denoising seismic data. While the development of SMD is motivated by the increasing use of DAS, SMD can be applied to any seismic data obtained from a large number of receivers. For example, here we present initial applications of SMD to readily available marine seismic data.

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