A nonstationary sparse spike deconvolution with anelastic attenuation

Geophysics ◽  
2019 ◽  
Vol 84 (2) ◽  
pp. R221-R234 ◽  
Author(s):  
Yuhan Sui ◽  
Jianwei Ma
Keyword(s):  
Seismic Data ◽  
Sparse Matrix ◽  
Estimation Error ◽  
Parameter Setting ◽  
Wavelet Estimation ◽  
Seismic Wavelet ◽  
Anelastic Attenuation ◽  
Extended Approach ◽  
Nonstationary Deconvolution ◽  
Sparse Matrix Factorization

Seismic wavelet estimation and deconvolution are essential for high-resolution seismic processing. Because of the influence of absorption and scattering, the frequency and phase of the seismic wavelet change with time during wave propagation, leading to a time-varying seismic wavelet. To obtain reflectivity coefficients with more accurate relative amplitudes, we should compute a nonstationary deconvolution of this seismogram, which might be difficult to solve. We have extended sparse spike deconvolution via Toeplitz-sparse matrix factorization to a nonstationary sparse spike deconvolution approach with anelastic attenuation. We do this by separating our model into subproblems in each of which the wavelet estimation problem is solved by the classic sparse optimization algorithms. We find numerical examples that illustrate the parameter setting, noisy seismogram, and the estimation error of the [Formula: see text] value to validate the effectiveness of our extended approach. More importantly, taking advantage of the high accuracy of the estimated [Formula: see text] value, we obtain better performance than with the stationary Toeplitz-sparse spike deconvolution approach in real seismic data.

scholarly journals Seismic sparse-spike deconvolution via Toeplitz-sparse matrix factorization

Geophysics ◽  
2016 ◽  
Vol 81 (3) ◽  
pp. V169-V182 ◽  
Author(s):  
Lingling Wang ◽  
Qian Zhao ◽  
Jinghuai Gao ◽  
Zongben Xu ◽  
Michael Fehler ◽  
...  
Keyword(s):  
Matrix Factorization ◽  
Seismic Data ◽  
Sparse Matrix ◽  
Estimation Error ◽  
Random Noise ◽  
Complex Structure ◽  
Wavelet Estimation ◽  
Convolution Model ◽  
Band Limited ◽  
Sparse Matrix Factorization

We have developed a new sparse-spike deconvolution (SSD) method based on Toeplitz-sparse matrix factorization (TSMF), a bilinear decomposition of a matrix into the product of a Toeplitz matrix and a sparse matrix, to address the problems of lateral continuity, effects of noise, and wavelet estimation error in SSD. Assuming the convolution model, a constant source wavelet, and the sparse reflectivity, a seismic profile can be considered as a matrix that is the product of a Toeplitz wavelet matrix and a sparse reflectivity matrix. Thus, we have developed an algorithm of TSMF to simultaneously deconvolve the seismic matrix into a wavelet matrix and a reflectivity matrix by alternatively solving two inversion subproblems related to the Toeplitz wavelet matrix and sparse reflectivity matrix, respectively. Because the seismic wavelet is usually compact and smooth, the fused Lasso was used to constrain the elements in the Toeplitz wavelet matrix. Moreover, due to the limitations of computer memory, large seismic data sets were divided into blocks, and the average of the source wavelets deconvolved from these blocks via TSMF-based SSD was used as the final estimation of the source wavelet for all blocks to deconvolve the reflectivity; thus, the lateral continuity of the seismic data can be maintained. The advantages of the proposed deconvolution method include using multiple traces to reduce the effect of random noise, tolerance to errors in the initial wavelet estimation, and the ability to preserve the complex structure of the seismic data without using any lateral constraints. Our tests on the synthetic seismic data from the Marmousi2 model and a section of field seismic data demonstrate that the proposed method can effectively derive the wavelet and reflectivity simultaneously from band-limited data with appropriate lateral coherence, even when the seismic data are contaminated by noise and the initial wavelet estimation is inaccurate.

TIME-VARYING SEISMIC WAVELET ESTIMATION FROM NONSTATIONARY SEISMIC DATA

2017 ◽  
Vol 60 (2) ◽  
pp. 191-202
Author(s):  
FENG Wei ◽  
HU Tian-Yue ◽  
YAO Feng-Chang ◽  
ZHANG Yan ◽  
Cui Yong-Fu ◽  
...  
Keyword(s):  
Seismic Data ◽  
Time Varying ◽  
Wavelet Estimation ◽  
Seismic Wavelet

Estimation of the depth-domain seismic wavelet based on velocity substitution and a generalized seismic wavelet model

Geophysics ◽  
2021 ◽  
pp. 1-50
Author(s):  
Jie Zhang ◽  
Xuehua Chen ◽  
Wei Jiang ◽  
Yunfei Liu ◽  
He Xu
Keyword(s):  
Least Squares ◽  
Seismic Data ◽  
Reservoir Characterization ◽  
Regularization Parameter ◽  
Estimation Method ◽  
Model Parameters ◽  
Wavelet Estimation ◽  
Seismic Wavelet ◽  
Hydrocarbon Reservoir ◽  
Convolution Model

Depth-domain seismic wavelet estimation is the essential foundation for depth-imaged data inversion, which is increasingly used for hydrocarbon reservoir characterization in geophysical prospecting. The seismic wavelet in the depth domain stretches with the medium velocity increase and compresses with the medium velocity decrease. The commonly used convolution model cannot be directly used to estimate depth-domain seismic wavelets due to velocity-dependent wavelet variations. We develop a separate parameter estimation method for estimating depth-domain seismic wavelets from poststack depth-domain seismic and well log data. This method is based on the velocity substitution and depth-domain generalized seismic wavelet model defined by the fractional derivative and reference wavenumber. Velocity substitution allows wavelet estimation with the convolution model in the constant-velocity depth domain. The depth-domain generalized seismic wavelet model allows for a simple workflow that estimates the depth-domain wavelet by estimating two wavelet model parameters. Additionally, this simple workflow does not need to perform searches for the optimal regularization parameter and wavelet length, which are time-consuming in least-squares-based methods. The limited numerical search ranges of the two wavelet model parameters can easily be calculated using the constant phase and peak wavenumber of the depth-domain seismic data. Our method is verified using synthetic and real seismic data and further compared with least-squares-based methods. The results indicate that the proposed method is effective and stable even for data with a low S/N.

Sparse reflectivity inversion for nonstationary seismic data with surface-related multiples: Numerical and field-data experiments

Geophysics ◽  
2017 ◽  
Vol 82 (3) ◽  
pp. R199-R217 ◽  
Author(s):  
Xintao Chai ◽  
Shangxu Wang ◽  
Genyang Tang
Keyword(s):  
Seismic Data ◽  
Resolution Enhancement ◽  
Synthetic Data ◽  
Data Sets ◽  
Data Set ◽  
Anelastic Attenuation ◽  
Seismic Resolution ◽  
Text Filtering ◽  
The Stability ◽  
Reflectivity Inversion

Seismic data are nonstationary due to subsurface anelastic attenuation and dispersion effects. These effects, also referred to as the earth’s [Formula: see text]-filtering effects, can diminish seismic resolution. We previously developed a method of nonstationary sparse reflectivity inversion (NSRI) for resolution enhancement, which avoids the intrinsic instability associated with inverse [Formula: see text] filtering and generates superior [Formula: see text] compensation results. Applying NSRI to data sets that contain multiples (addressing surface-related multiples only) requires a demultiple preprocessing step because NSRI cannot distinguish primaries from multiples and will treat them as interference convolved with incorrect [Formula: see text] values. However, multiples contain information about subsurface properties. To use information carried by multiples, with the feedback model and NSRI theory, we adapt NSRI to the context of nonstationary seismic data with surface-related multiples. Consequently, not only are the benefits of NSRI (e.g., circumventing the intrinsic instability associated with inverse [Formula: see text] filtering) extended, but also multiples are considered. Our method is limited to be a 1D implementation. Theoretical and numerical analyses verify that given a wavelet, the input [Formula: see text] values primarily affect the inverted reflectivities and exert little effect on the estimated multiples; i.e., multiple estimation need not consider [Formula: see text] filtering effects explicitly. However, there are benefits for NSRI considering multiples. The periodicity and amplitude of the multiples imply the position of the reflectivities and amplitude of the wavelet. Multiples assist in overcoming scaling and shifting ambiguities of conventional problems in which multiples are not considered. Experiments using a 1D algorithm on a synthetic data set, the publicly available Pluto 1.5 data set, and a marine data set support the aforementioned findings and reveal the stability, capabilities, and limitations of the proposed method.

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