Seismic inversion based on L1-norm misfit function and total variation regularization

Zhang, Fanchang; Dai, Ronghuo; Liu, Hanqing

doi:10.1016/j.jappgeo.2014.07.024

Cited by 72 publications

(27 citation statements)

References 16 publications

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“…So, a priori model regularization constraint (Dai et al . ; Zhang, Dai and Liu ; Dai, Zhang and Liu , ; Gholami ; Yin et al . ) is used to enhance the inversion stability, to make the low‐frequency information contained in inversion results more consistent with actual work area and to improve the lateral continuity of inversion results.…”

Section: Seismic Inversionmentioning

confidence: 99%

“…non-smooth. To solve the inverse problem based on L1-norm misfit function, many scholars used IRLS algorithm (Schlossmacher 1973;Holland and Welsch 1977;Yarlagadda, Bednar and Watt 1985;Scales, Gersztenkorn and Treitel 1988;Coleman and Li 1992;Huber 1996;Sacchi 1997;Youzwishen 2001;Thurber 2005, 2013;Bissantz et al 2009;Zhang, Dai and Liu 2014b). The details of iteratively re-weighted least square algorithm to solve equation (6) are shown in Appendix B.…”

Section: Objective Functionmentioning

confidence: 99%

“…The conventional post-stack inversion process is through the standard recursion formulas to obtain impedance data or other parameters in a single trace (Berteussen and Ursin 1983;Zhang, Dai and Liu 2014b;Zhang and Dai 2016). However, the inversion results obtained by these formulas are sensitive to noise in seismic data (Berteussen and Ursin 1983;Hamid and Pidlisecky 2015).…”

Section: Seismic Impedance Inversionmentioning

confidence: 99%

“…Aravkin, van Leeuwen and Herrmann (2011), Aravkin et al (2012), Kumar et al (2013) and van Leeuwen et al (2013) used the student's t penalty for the data misfit to perform robust seismic data processing and inversion. Zhang, Dai and Liu (2014b) proposed an inversion method based on the L1-norm misfit function and total variation regularization term in the presence of erratic data.…”

Section: Introductionmentioning

confidence: 99%

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Seismic deconvolution and inversion with erratic data

Dai

Chao

Yang

et al. 2018

Geophysical Prospecting

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If there are some erratic data (e.g. outliers), which may arise from measurement error, or other reasons, in seismic data, the seismic deconvolution and inversion need to be implemented in a way that minimizes their effects. However, the deconvolution and inversion methods based on L2‐norm misfit function are highly sensitive to these erratic seismic observations. As an alternative, L1‐norm misfit functions are more robust and erratic‐resistant. In order to find the solution of the inverse problem constrained by an L1‐norm misfit function, an iteratively re‐weighted least squares algorithm is used frequently. However, it is relatively time consuming. In this paper, we propose a new method based on the sparse signal representation theory. The overcomplete dictionary used for the sparse representation of seismic data with erratic data is composed of two bases: a wavelet basis used for representing the seismic data to implement deconvolution and a Dirac basis used for representing the erratic data. In addition, at the stage of seismic inversion after deconvolution, total variation and a priori model are used as the regularization constraint terms to estimate inversion results with a blocky and laterally continuous structure. The new method is successfully tested on the noisy synthetic seismic data with erratic data. Finally, the proposed method is performed on a real seismic data section, and the inversion results are reasonable, i.e. consistent with the geologic structure of the original seismic data. Compared to the conventional sparse deconvolution and inversion method, the proposed method not only eliminates the effect of outliers, but also has highly improved computational efficiency.

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Section: Seismic Inversionmentioning

confidence: 99%

Section: Objective Functionmentioning

confidence: 99%

Section: Seismic Impedance Inversionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Seismic deconvolution and inversion with erratic data

Dai

Chao

Yang

et al. 2018

Geophysical Prospecting

Self Cite

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“…With reflectivity coefficients of higher accuracy, so we get better inverted impedance results. Some researches on L1 norm regularization methods on impedance inversion have been done (Wang, 2010;Zhang et al, 2014). They stated the principle of regularization method and carried out a few tests to show the accuracy of L1 norm regularization inversion method.…”

Section: Introductionmentioning

confidence: 99%

Impedance inversion based on L1 norm regularization

Liu

Song

et al. 2015

Journal of Applied Geophysics

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AVA Inversion of PP Reflection in a VTI Medium using Proximal Splitting Algorithm

Zidan

Cheng

2022

Preprint

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Amplitude variation with offset (AVO) inversion, particularly for more than two model parameters, is a highly ill-posed problem and, hence, regularization is indispensable. Here, we propose a regularized inverse problem to mitigate the ill-posedness of the amplitude inversion. The regularization is added to measure the difference in information between the a priori probability density function and the predicted probability density of the inverted parameters. Information theory provides a collection of contrast functions which quantify the divergence from one probability distribution to another, such as the relative entropy. The a priori density is approximated by a Gaussian mixture model, obtained from well logs and rock physics model. The mixture model is a density estimator, providing the statistical properties of the model parameters of interest. The likelihood of the data and the divergence are combined in an augmented Lagrangian scheme, the alternating direction method of multipliers (ADMM), to obtain a unique solution that best generate the recorded seismic data and satisfy the geological constraints conveyed by the a priori probability density function. The proposed inversion scheme is then applied to the anisotropy AVO inversion, for estimating the elastic and seismic anisotropy parameters of shale formations.

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Seismic inversion based on L1-norm misfit function and total variation regularization

Cited by 72 publications

References 16 publications

Seismic deconvolution and inversion with erratic data

Seismic deconvolution and inversion with erratic data

Impedance inversion based on L1 norm regularization

AVA Inversion of PP Reflection in a VTI Medium using Proximal Splitting Algorithm

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