<i>L</i>1−2 minimization for exact and stable seismic attenuation compensation

Wang, Yufeng; Ma, Xiong; Zhou, Hui; Chen, Yangkang

doi:10.1093/gji/ggy064

Cited by 62 publications

(17 citation statements)

References 91 publications

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“…; van der Baan ; Wang and Chen ; Wang et al . ). For a better expression of the method evaluated here, we transcribe some crucial formulae for the Q ‐filtered seismogram below.…”

Section: Theorymentioning

confidence: 99%

“…Lots of researchers have devoted to deriving the formulae that model the Q-filtered seismogram (e.g. Bickel and Natarajan 1985;Wang 2006;Margrave et al 2011;van der Baan 2012;Wang and Chen 2014;Wang et al 2018a). For a better expression of the method evaluated here, we transcribe some crucial formulae for the Q-filtered seismogram below.…”

Section: Modelling a Q-filtered Seismogrammentioning

confidence: 99%

“…Wang et al . () proposed

ℓ_{1 - 2}

minimization for stable absorption compensation, where the

ℓ_{1 - 2}

norm non‐convex penalty function is decomposed into two convex subproblems via difference of convex algorithm, and each subproblem is solved by an alternating direction method of multipliers.…”

Section: Introductionmentioning

confidence: 99%

“…Wang 2006;van der Baan 2012;Braga and Moraes 2013;Wang and Chen 2014;. The wavelet is additionally required for the methods described by Zhang and Ulrych (2007), van der Baan (2012), Oliveira and Lupinacci (2013), Chai et al (2014Chai et al ( , 2016Chai et al ( , 2018, and Wang et al (2018a).…”

mentioning

confidence: 99%

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Some remarks on Q‐compensated sparse deconvolution without knowing the quality factor Q

Chai

Peng

Tang

et al. 2019

Geophysical Prospecting

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The subsurface media are not perfectly elastic, thus anelastic absorption, attenuation and dispersion (aka Q filtering) effects occur during wave propagation, diminishing seismic resolution. Compensating for anelastic effects is imperative for resolution enhancement. Q values are required for most of conventional Q‐compensation methods, and the source wavelet is additionally required for some of them. Based on the previous work of non‐stationary sparse reflectivity inversion, we evaluate a series of methods for Q‐compensation with/without knowing Q and with/without knowing wavelet. We demonstrate that if Q‐compensation takes the wavelet into account, it generates better results for the severely attenuated components, benefiting from the sparsity promotion. We then evaluate a two‐phase Q‐compensation method in the frequency domain to eliminate Q requirement. In phase 1, the observed seismogram is disintegrated into the least number of Q‐filtered wavelets chosen from a dictionary by optimizing a basis pursuit denoising problem, where the dictionary is composed of the known wavelet with different propagation times, each filtered with a range of possible Q−1 values. The elements of the dictionary are weighted by the infinity norm of the corresponding column and further preconditioned to provide wavelets of different Q−1 values and different propagation times equal probability to entry into the solution space. In phase 2, we derive analytic solutions for estimates of reflectivity and Q and solve an over‐determined equation to obtain the final reflectivity series and Q values, where both the amplitude and phase information are utilized to estimate the Q values. The evaluated inversion‐based Q estimation method handles the wave‐interference effects better than conventional spectral‐ratio‐based methods. For Q‐compensation, we investigate why sparsity promoting does matter. Numerical and field data experiments indicate the feasibility of the evaluated method of Q‐compensation without knowing Q but with wavelet given.

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“…; van der Baan ; Wang and Chen ; Wang et al . ). For a better expression of the method evaluated here, we transcribe some crucial formulae for the Q ‐filtered seismogram below.…”

Section: Theorymentioning

confidence: 99%

Section: Modelling a Q-filtered Seismogrammentioning

confidence: 99%

“…Wang et al . () proposed

ℓ_{1 - 2}

minimization for stable absorption compensation, where the

ℓ_{1 - 2}

norm non‐convex penalty function is decomposed into two convex subproblems via difference of convex algorithm, and each subproblem is solved by an alternating direction method of multipliers.…”

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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Some remarks on Q‐compensated sparse deconvolution without knowing the quality factor Q

Chai

Peng

Tang

et al. 2019

Geophysical Prospecting

View full text Add to dashboard Cite

show abstract

“…To overcome the disadvantages of the conventional

ℓ_{1}

‐norm and

ℓ_{2}

‐norm likelihood functions, the logarithmic‐absolute‐norm metric is introduced to improve the robustness and stability. Besides, we introduce the

ℓ_{1 - 2}

‐norm metric as a penalty, defined as

{| | x | |}_{1 - 2} = {| | x | |}_{1} - {α | | x | |}_{2}

, which has been widely used as a sparse constraint in compressed sensing (Esser et al ., 2013; Lou et al ., 2015; Lou and Yan, 2016; Wang et al ., 2018; Qureshi and Inam, 2019).…”

Section: Introductionmentioning

confidence: 99%

Pre‐stack seismic inversion based on ‐norm regularized logarithmic absolute misfit function

Huang

Chen

Luo

et al. 2020

Geophysical Prospecting

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Ill‐posedness is one of the most common and intractable issues that arise when solving geophysical inverse problems. Ill‐posedness could be induced by various factors such as noise, band‐limited intrinsic property of seismic data and inappropriate forward operators. Regularization has been proven to be an effective method widely accepted for mitigating the adverse effects of ill‐posedness. Aiming to improve the stability and fidelity of the pre‐stack seismic inversion process, we implement the inversion in a Bayesian framework, with a logarithmic absolute criterion taken as a likelihood function, and an ℓ1−2‐norm metric as a priori constraint. Here, we exploit the linear approximation as the forward operator, and optimize the regularized misfit function by the alternating direction method of multipliers. Applications of the method to synthetic and real data sets yielded improved inversion results in terms of accuracy and resolution, and demonstrated the robustness of the method to noise.

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The Application of the Depth Residual Network Denoising Method in the Complex Mountainous Seismic Exploration

Qin

Zeng

Shou

et al. 2023

Springer Series in Geomechanics and Geoengineering

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L1−2 minimization for exact and stable seismic attenuation compensation

Cited by 62 publications

References 91 publications

Some remarks on Q‐compensated sparse deconvolution without knowing the quality factor Q

Some remarks on Q‐compensated sparse deconvolution without knowing the quality factor Q

Pre‐stack seismic inversion based on ‐norm regularized logarithmic absolute misfit function

The Application of the Depth Residual Network Denoising Method in the Complex Mountainous Seismic Exploration

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