A fast reduced-rank interpolation method for prestack seismic volumes that depend on four spatial dimensions

Geophysics ◽  
2013 ◽  
Vol 78 (1) ◽  
pp. V21-V30 ◽  
Author(s):  
Jianjun Gao ◽  
Mauricio D. Sacchi ◽  
Xiaohong Chen
Keyword(s):  
Spatial Data ◽  
Toeplitz Matrix ◽  
Seismic Data ◽  
Random Noise ◽  
Computational Cost ◽  
Reconstruction Method ◽  
Rank Reduction ◽  
Lanczos Bidiagonalization ◽  
Reduced Rank ◽  
Block Toeplitz Matrix

Rank reduction strategies can be employed to attenuate noise and for prestack seismic data regularization. We present a fast version of Cadzow reduced-rank reconstruction method. Cadzow reconstruction is implemented by embedding 4D spatial data into a level-four block Toeplitz matrix. Rank reduction of this matrix via the Lanczos bidiagonalization algorithm is used to recover missing observations and to attenuate random noise. The computational cost of the Lanczos bidiagonalization is dominated by the cost of multiplying a level-four block Toeplitz matrix by a vector. This is efficiently implemented via the 4D fast Fourier transform. The proposed algorithm significantly decreases the computational cost of rank-reduction methods for multidimensional seismic data denoising and reconstruction. Synthetic and field prestack data examples are used to examine the effectiveness of the proposed method.

Robust reduced-rank filtering for erratic seismic noise attenuation

Geophysics ◽  
2015 ◽  
Vol 80 (1) ◽  
pp. V1-V11 ◽  
Author(s):  
Ke Chen ◽  
Mauricio D. Sacchi
Keyword(s):  
Gaussian Noise ◽  
Seismic Data ◽  
Random Noise ◽  
Singular Spectrum Analysis ◽  
Hankel Matrix ◽  
Noise Attenuation ◽  
Rank Reduction ◽  
Data Set ◽  
Reduced Rank ◽  
Truncated Svd

Singular spectrum analysis (SSA) or Cadzow reduced-rank filtering is an efficient method for random noise attenuation. SSA starts by embedding the seismic data into a Hankel matrix. Rank reduction of this Hankel matrix followed by antidiagonal averaging is utilized to estimate an enhanced seismic signal. Rank reduction is often implemented via the singular value decomposition (SVD). The SVD is a nonrobust matrix factorization technique that leads to suboptimal results when the seismic data are contaminated by erratic noise. The term erratic noise designates non-Gaussian noise that consists of large isolated events with known or unknown distribution. We adopted a robust low-rank factorization that permitted use of the SSA filter in situations in which the data were contaminated by erratic noise. In our robust SSA method, we replaced the quadratic error criterion function that yielded the truncated SVD solution by a bisquare function. The Hankel matrix was then approximated by the product of two lower dimensional factor matrices. The iteratively reweighed least-squares method was used to approximately solve for the optimal robust factorization. Our algorithm was tested with synthetic and real data. In our synthetic examples, the data were contaminated with band-limited Gaussian noise and erratic noise. Then, denoising was carried out by means of [Formula: see text] deconvolution, the classical SSA method, and the proposed robust SSA method. The [Formula: see text] deconvolution and the classical SSA method failed to properly eliminate the noise and to preserve the desired signal. On the other hand, the robust SSA method was found to be immune to erratic noise and was able to preserve the desired signal. We also tested the robust SSA method with a data set from the Western Canadian Sedimentary Basin. The results with this data set revealed improved denoising performance in portions of data contaminated with erratic noise.

scholarly journals An Alternative Adaptive Method for Seismic Data Denoising and Interpolation

2020 ◽  
Vol 2020 ◽  
pp. 1-16
Author(s):  
Zilin Lu ◽  
Nuan Xia ◽  
Liang Sun ◽  
Wenxing Xu ◽  
Guangcheng Zhang ◽  
...  
Keyword(s):  
Seismic Data ◽  
Energy Intensity ◽  
Reduction Method ◽  
Random Noise ◽  
Complex Surface ◽  
Adaptive Method ◽  
Rank Reduction ◽  
Energy Entropy ◽  
The Difference ◽  
Field Area

Seismic data denoising and interpolation are generally essential steps for reflection processing and imaging workflow especially for the complex surface geologic conditions and the irregular acquisition field area. The rank-reduction method is a valid way for the attenuation of random noise and data interpolation by selecting the suitable threshold, i.e., the rank of the useful signals. However, it is difficult for the traditional rank-reduction method to select an appropriate threshold. In this paper, we propose an adaptive rank-reduction method based on the energy entropy to automatically estimate the rank as the threshold for seismic data processing and interpolation. This method considers the energy entropy into the traditional rank-reduction method. The energy entropy of signals can be used to indicate the energy intensity of a signal component in the total energy. The difference of the energy entropy between the useful signals and random noise is perceived as a measurement for selecting the appropriate threshold. Synthetic and field examples indicate that the proposed method can well achieve the attenuation of random noise and interpolation automatically without the estimation of the ranks and demonstrate the feasibility of the new adaptive method in seismic data denoising and interpolation.

Five-dimensional seismic data reconstruction using the optimally damped rank-reduction method

2020 ◽  
Vol 222 (3) ◽  
pp. 1824-1845 ◽  
Author(s):  
Yangkang Chen ◽  
Min Bai ◽  
Zhe Guan ◽  
Qingchen Zhang ◽  
Mi Zhang ◽  
...  
Keyword(s):  
Seismic Data ◽  
Reduction Method ◽  
Random Noise ◽  
Singular Values ◽  
Adaptive Method ◽  
Frobenius Norm ◽  
Damping Factor ◽  
Rank Reduction ◽  
Large Rank ◽  
Residual Noise

SUMMARY It is difficult to separate additive random noise from spatially coherent signal using a rank-reduction (RR) method that is based on the truncated singular value decomposition (TSVD) operation. This problem is due to the mixture of the signal and the noise subspaces after the TSVD operation. This drawback can be partially conquered using a damped RR (DRR) method, where the singular values corresponding to effective signals are adjusted via a carefully designed damping operator. The damping operator works most powerfully in the case of a small rank and a small damping factor. However, for complicated seismic data, e.g. multichannel reflection seismic data containing highly curved events, the rank should be large enough to preserve the details in the data, which makes the DRR method less effective. In this paper, we develop an optimal damping strategy for adjusting the singular values when a large rank parameter is selected so that the estimated signal can best approximate the exact signal. We first weight the singular values using optimally calculated weights. The weights are theoretically derived by solving an optimization problem that minimizes the Frobenius-norm difference between the approximated and the exact signal components. The damping operator is then derived based on the initial weighting operator to further reduce the residual noise after the optimal weighting. The resulted optimally damped rank-reduction method is nearly an adaptive method, i.e. insensitive to the rank parameter. We demonstrate the performance of the proposed method on a group of synthetic and real 5-D seismic data.

Simultaneous seismic data denoising and reconstruction via multichannel singular spectrum analysis

Geophysics ◽  
2011 ◽  
Vol 76 (3) ◽  
pp. V25-V32 ◽  
Author(s):  
Vicente Oropeza ◽  
Mauricio Sacchi
Keyword(s):  
Spectrum Analysis ◽  
Seismic Data ◽  
Field Data ◽  
Convex Sets ◽  
Singular Spectrum Analysis ◽  
Hankel Matrix ◽  
Reconstruction Method ◽  
Rank Reduction ◽  
Data Set ◽  
Singular Spectrum

We present a rank reduction algorithm that permits simultaneous reconstruction and random noise attenuation of seismic records. We based our technique on multichannel singular spectrum analysis (MSSA). The technique entails organizing spatial data at a given temporal frequency into a block Hankel matrix that in ideal conditions is a matrix of rank [Formula: see text], where [Formula: see text] is the number of plane waves in the window of analysis. Additive noise and missing samples will increase the rank of the block Hankel matrix of the data. Consequently, rank reduction is proposed as a means to attenuate noise and recover missing traces. We present an iterative algorithm that resembles seismic data reconstruction with the method of projection onto convex sets. In addition, we propose to adopt a randomized singular value decomposition to accelerate the rank reduction stage of the algorithm. We apply MSSA reconstruction to synthetic examples and a field data set. Synthetic examples were used to assess the performance of the method in two reconstruction scenarios: a noise-free case and data contaminated with noise. In both cases, we found extremely low reconstructions errors that are indicative of an optimal recovery. The field data example consists of a 2D prestack volume that depends on common midpoint and offset. We use the MSSA reconstruction method to complete missing offsets and, at the same time, increase the signal-to-noise ratio of the seismic volume.

Robust damped rank-reduction method for simultaneous denoising and reconstruction of 5-D seismic data

Geophysics ◽  
2020 ◽  
pp. 1-143
Author(s):  
Yapo Abolé Serge Innocent Oboué ◽  
Wei Chen ◽  
Hang Wang ◽  
Yangkang Chen
Keyword(s):  
Singular Value Decomposition ◽  
Seismic Data ◽  
Moving Average ◽  
Random Noise ◽  
Singular Value ◽  
Truncated Singular Value Decomposition ◽  
Rank Reduction ◽  
Residual Noise ◽  
Value Decomposition

We have developed a new method for simultaneous denoising and reconstruction of 5-D seismic data corrupted by random noise and missing traces. Several algorithms have been proposed for seismic data restoration based on rank-reduction methods. More recently, a damping operator has been introduced into the conventional truncated singular value decomposition (TSVD) formula to further remove residual noise, the presence of which disturbs the quality of the seismic results. Despite the success of the damped rank-reduction (DRR) method when the observed data have an extremely low signal-to-noise ratio (SNR), random noise is still a limiting factor for obtaining perfect quality of the result. Therefore, how to accurately solve the simultaneous denoising and reconstruction problem with high fidelity is still challenging. We assume that introducing only the damping operator into the TSVD formula is not enough to remove the random noise and restore the useful signal well. Here, by combining the soft thresholding operator and the moving-average filter, we first develop a new operator, which we call soft thresholding moving-average (STMA) operator. Then, by introducing the STMA operator into the DRR framework, we develop a new algorithm known as the robust damped rank-reduction (RDRR) method, which aims at mixing the advantages of the STMA operator and the damping operator. The STMA operator is applied to the Hankel matrix after damped truncated singular value decomposition (DTSVD) to better remove the residual noise. Examples of the proposed approach on synthetic and field 5-D seismic data demonstrate the better performance in terms of the visual examination and numerical test compared with the DRR approach. The proposed method aims at producing an effective low-rank filter and, thus, can perfectly enhance the SNR of the simultaneously denoised and reconstructed results with higher accuracy.

3D RECONSTRUCTION OF BREAST CANCER FROM MAMMOGRAMS USING VOLUME RENDERING TECHNIQUES

2015 ◽  
Vol 75 (2) ◽  
Author(s):  
Ho Wei Yong ◽  
Abdullah Bade ◽  
Rajesh Kumar Muniandy
Keyword(s):  
Breast Cancer ◽  
3D Reconstruction ◽  
Computational Cost ◽  
Reconstruction Method ◽  
Cancer Model ◽  
Volume Reconstruction ◽  
The Past ◽  
Breast Cancer Model ◽  
Reconstruction Software ◽  
To Come

Over the past thirty years, a number of researchers have investigated on 3D organ reconstruction from medical images and there are a few 3D reconstruction software available on the market. However, not many researcheshave focused on3D reconstruction of breast cancer’s tumours. Due to the method complexity, most 3D breast cancer’s tumours reconstruction were done based on MRI slices dataeven though mammogram is the current clinical practice for breast cancer screening. Therefore, this research will investigate the process of creating a method that will be able to reconstruct 3D breast cancer’s tumours from mammograms effectively.  Several steps were proposed for this research which includes data acquisition, volume reconstruction, andvolume rendering. The expected output from this research is the 3D breast cancer’s tumours model that is generated from correctly registered mammograms. The main purpose of this research is to come up with a 3D reconstruction method that can produce good breast cancer model from mammograms while using minimal computational cost.

Restricted model domain time Radon transforms

Geophysics ◽  
2016 ◽  
Vol 81 (6) ◽  
pp. A17-A21 ◽  
Author(s):  
Juan I. Sabbione ◽  
Mauricio D. Sacchi
Keyword(s):  
Inverse Problem ◽  
Seismic Data ◽  
Computational Cost ◽  
Synthetic Data ◽  
Model Space ◽  
Radon Transforms ◽  
Iterative Solver ◽  
Hard Thresholding ◽  
Restricted Model ◽  
Marine Data

The coefficients that synthesize seismic data via the hyperbolic Radon transform (HRT) are estimated by solving a linear-inverse problem. In the classical HRT, the computational cost of the inverse problem is proportional to the size of the data and the number of Radon coefficients. We have developed a strategy that significantly speeds up the implementation of time-domain HRTs. For this purpose, we have defined a restricted model space of coefficients applying hard thresholding to an initial low-resolution Radon gather. Then, an iterative solver that operated on the restricted model space was used to estimate the group of coefficients that synthesized the data. The method is illustrated with synthetic data and tested with a marine data example.

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

Application of complex-trace analysis to seismic data for random-noise suppression and temporal resolution improvement

Geophysics ◽  
2006 ◽  
Vol 71 (3) ◽  
pp. V79-V86 ◽  
Author(s):  
Hakan Karsli ◽  
Derman Dondurur ◽  
Günay Çifçi
Keyword(s):  
Seismic Data ◽  
Trace Analysis ◽  
Noise Suppression ◽  
Single Channel ◽  
Random Noise ◽  
Synthetic Data ◽  
Low Frequency ◽  
Bright Spot ◽  
Phase Information ◽  
Resolution Improvement

Time-dependent amplitude and phase information of stacked seismic data are processed independently using complex trace analysis in order to facilitate interpretation by improving resolution and decreasing random noise. We represent seismic traces using their envelopes and instantaneous phases obtained by the Hilbert transform. The proposed method reduces the amplitudes of the low-frequency components of the envelope, while preserving the phase information. Several tests are performed in order to investigate the behavior of the present method for resolution improvement and noise suppression. Applications on both 1D and 2D synthetic data show that the method is capable of reducing the amplitudes and temporal widths of the side lobes of the input wavelets, and hence, the spectral bandwidth of the input seismic data is enhanced, resulting in an improvement in the signal-to-noise ratio. The bright-spot anomalies observed on the stacked sections become clearer because the output seismic traces have a simplified appearance allowing an easier data interpretation. We recommend applying this simple signal processing for signal enhancement prior to interpretation, especially for single channel and low-fold seismic data.

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