Skip to main content
SpringerLink
Log in

Adaptive individual weight-gain AVO inversion with smooth nonconvex regularization

  • Research Article - Applied Geophysics
  • Published:
Acta Geophysica Aims and scope Submit manuscript

Abstract

Amplitude variation with offset (AVO) inversion is a widely used approach to obtain reliable estimates of elastic parameter in the fields of seismic exploration. However, the AVO inversion is an ill-posed problem because of the band-limited characteristic of seismic data. The regularization constraint plays an important role in improving inversion resolution. Total variation (TV) class regularization based on L\(_1\) norm has been introduced in seismic inversion. But, these methods may underestimate the high-amplitude components and obtain low-resolution results. To tackle these issues, we propose to combine a smooth nonconvex regularization approach with adaptive individual weight-gain. Compared with the L\(_1\) norm regularizers, the proposed smoothed nonconvex sparsity-inducing regularizers can lead to more accurate estimation for high-amplitude components. Different from previous regularization methods, the proposed approach also assigns different weight regularization parameters for different strata, which we call adaptive individual weight-gain strategy. To ensure sufficient minimization of the constructed objective function, a spectral Polak–Ribière–Polyak conjugate gradient method with line search step size is used. Further, we prove that the proposed algorithm converges to a stationary point. The synthetic data tests illustrate that our approach has improved performance compared with the conventional TV class regularization methods. Field data example further verifies the higher resolution of the proposed approach.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13

Similar content being viewed by others

References

  • Aki K, Richards PG (2002) Quantitative seismology. University Science Books

  • Anagaw AY, Sacchi MD (2012) Edge-preserving seismic imaging using the total variation method. J Geophys Eng 9(2):138–146

    Article  Google Scholar 

  • Bi C, Wang Y, Xie W, Sun W, Liu W (2020) Prestack avo inversion for brittleness index of shale based on bi\_zoeppritz equation and nsga ii. Acta Geophys 68(4):1067–1082

    Article  Google Scholar 

  • Bongajum E, Boisvert J, Sacchi M (2013) Bayesian linearized seismic inversion with locally varying spatial anisotropy. J Appl Geophys 88:31–41

    Article  Google Scholar 

  • Duttweiler DL (2000) Proportionate normalized least-mean-squares adaptation in echo cancelers. IEEE Trans Speech Audio Process 8(5):508–518

    Article  Google Scholar 

  • Engl H (1987) Discrepancy principles for tikhonov regularization of ill-posed problems leading to optimal convergence rates. J Optim Theory Appl 52(2):209–215

    Article  Google Scholar 

  • Epanomeritakis I, Akçelik V, Ghattas O, Bielak J (2008) A newton-cg method for large-scale three-dimensional elastic full-waveform seismic inversion. Inverse Probl 24(3):034015

    Article  Google Scholar 

  • Fan C, Song Y, Zhang Y, Jiang Z (2015) An amplitude-normalized pseudo well-log construction method and its application on avo inversion in a well-absent marine area. Acta Geophys 63(3):761–775

    Article  Google Scholar 

  • Fan J, Li R (2001) Variable selection via nonconcave penalized likelihood and its oracle properties. J Am Stat Assoc 96(456):1348–1360

    Article  Google Scholar 

  • Fu L, Symes WW (2017) A discrepancy-based penalty method for extended waveform inversion. Geophysics 82(5):R287–R298

    Article  Google Scholar 

  • Gholami A (2015) Nonlinear multichannel impedance inversion by total-variation regularization. Geophysics 80(5):R217–R224

    Article  Google Scholar 

  • Greenhalgh SA, Bing Z, Green A (2006) Solutions, algorithms and inter-relations for local minimization search geophysical inversion. J Geophys Eng 3(2):101–113

    Article  Google Scholar 

  • Gunning J, Sams M (2018) Joint facies and rock properties bayesian amplitude-versus-offset inversion using markov random fields. Geophys Prospect 66(5):904–919

    Article  Google Scholar 

  • Hamid H, Pidlisecky A (2015) Multitrace impedance inversion with lateral constraints. Geophysics 80(6):M101–M111

    Article  Google Scholar 

  • Hampson DP, Russell BH, Bankhead B (2005) Simultaneous inversion of pre-stack seismic data. In: SEG Technical Program Expanded Abstracts 2005, Society of Exploration Geophysicists, pp 1633–1637

  • Han L, Han L, Li Z (2012) Inverse spectral decomposition with the spgl1 algorithm. J Geophys Eng 9(4):423–427

    Article  Google Scholar 

  • Hansen PC, O’Leary DP (1993) The use of the l-curve in the regularization of discrete ill-posed problems. SIAM J Sci Comput 14(6):1487–1503

    Article  Google Scholar 

  • Li C, Zhang F (2017) Amplitude-versus-angle inversion based on the l 1-norm-based likelihood function and the total variation regularization constraint. Geophysics 82(3):R173–R182

    Article  Google Scholar 

  • Martin GS, Wiley R, Marfurt KJ (2006) Marmousi2: an elastic upgrade for marmousi. Lead Edge 25(2):156–166

    Article  Google Scholar 

  • Morozov VA (2012) Methods for solving incorrectly posed problems. Springer Science & Business Media

  • Nikolova M, Ng MK, Tam CP (2010) Fast nonconvex nonsmooth minimization methods for image restoration and reconstruction. IEEE Trans Image Process 19(12):3073–3088

    Article  Google Scholar 

  • Nocedal J, Wright S (2006) Numerical optimization. Springer Science & Business Media

  • Parekh A, Selesnick IW (2015) Convex denoising using non-convex tight frame regularization. IEEE Signal Process Lett 22(10):1786–1790

    Article  Google Scholar 

  • Polak E, Ribiere G (1969) Note sur la convergence de méthodes de directions conjuguées. ESAIM Mathematical Modelling and Numerical Analysis-Modélisation Mathématique et Analyse Numérique 3(R1):35–43

    Google Scholar 

  • Polyak BT (1969) The conjugate gradient method in extremal problems. USSR Comput Math Math Phys 9(4):94–112

    Article  Google Scholar 

  • Riedel M, Dosso SE, Beran L (2003) Uncertainty estimation for amplitude variation with offset (avo) inversion. Geophysics 68(5):1485–1496

    Article  Google Scholar 

  • Roy IG (2002) A robust descent type algorithm for geophysical inversion through adaptive regularization. Appl Math Modell 26(5):619–634

    Article  Google Scholar 

  • Roy IG (2005) Iteratively adaptive regularization in inverse modeling with bayesian outlook-application on geophysical data. Inverse Probl Sci Eng 13(6):655–670

    Article  Google Scholar 

  • Saraswat P, Sen MK (2012) Pre-stack inversion of angle gathers using a hybrid evolutionary algorithm. J Seism Explor 21(2):177–200

    Google Scholar 

  • Selesnick IW, Bayram I (2014) Sparse signal estimation by maximally sparse convex optimization. IEEE Trans Signal Process 62(5):1078–1092

    Article  Google Scholar 

  • Sen MK, Roy IG (2003) Computation of differential seismograms and iteration adaptive regularization in prestack waveform inversion. Geophysics 68(6):2026–2039

    Article  Google Scholar 

  • She B, Wang Y, Zhang J, Wang J, Hu G (2019) Avo inversion with high-order total variation regularization. J Appl Geophys 161:167–181

    Article  Google Scholar 

  • Tarantola A (2005) Inverse problem theory and methods for model parameter estimation, vol 89. SIAM, Philadelphia

  • Theune U, Jensås IØ, Eidsvik J (2010) Analysis of prior models for a blocky inversion of seismic ava data. Geophysics 75(3):C25–C35

    Article  Google Scholar 

  • Tihonov AN (1963) Solution of incorrectly formulated problems and the regularization method. Soviet Math 4:1035–1038

    Google Scholar 

  • Wahba G (1990) Spline models for observational data. CBMS-NSF Series in Applied Mathematics, vol 59. SIAM

  • Wan Z, Yang Z, Wang Y (2011) New spectral prp conjugate gradient method for unconstrained optimization. Appl Math Lett 24(1):16–22

    Article  Google Scholar 

  • Wang S, Selesnick I, Cai G, Feng Y, Sui X, Chen X (2018) Nonconvex sparse regularization and convex optimization for bearing fault diagnosis. IEEE Trans Ind Electron 65(9):7332–7342

    Article  Google Scholar 

  • Wang Z, Cao S, Pan X, Chen S, Liu W, Du X (2017) Seismic inversion via tv regularization and toeplitz-sparse matrix factorization. In: SEG Technical Program Expanded Abstracts 2017, Society of Exploration Geophysicists, pp 687–691

  • Wen F, Pei L, Yang Y, Yu W, Liu P (2017) Efficient and robust recovery of sparse signal and image using generalized nonconvex regularization. IEEE Trans Comput Imaging 3(4):566–579

    Article  Google Scholar 

  • Yilmaz Ö (2001) Seismic data analysis: Processing, inversion, and interpretation of seismic data. Society of exploration geophysicists

  • Yuan S, Wang S, Luo C, He Y (2015) Simultaneous multitrace impedance inversion with transform-domain sparsity promotion. Geophysics 80(2):R71–R80

    Article  Google Scholar 

  • Yuan S, Wang S, Luo C, Wang T (2018) Inversion-based 3-d seismic denoising for exploring spatial edges and spatio-temporal signal redundancy. IEEE Geosci Remote Sens Lett 15(11):1682–1686

    Article  Google Scholar 

  • Yuan S, Wang S, Luo Y, Wei W, Wang G (2019) Impedance inversion by using the low-frequency full-waveform inversion result as an a priori model. Geophysics 84(2):R149–R164

    Article  Google Scholar 

  • Zhang J, Lv S, Liu Y, Hu G (2013a) Avo inversion based on generalized extreme value distribution with adaptive parameter estimation. J Appl Geophys 98:11–20

    Article  Google Scholar 

  • Zhang Z, Yin X, Zong Z (2013b) A new frequency-dependent avo attribute and its application in fluid identification. In: 75th EAGE Conference & Exhibition incorporating SPE EUROPEC 2013, European Association of Geoscientists & Engineers, pp cp–348

  • Zhi L, Chen S, Song B, Li Xy (2018) Nonlinear pp and ps joint inversion based on the exact zoeppritz equations: a two-stage procedure. J Geophys Eng 15(2):397–410

    Article  Google Scholar 

  • Zong Z, Li K, Yin X, Zhu M, Du J, Chen W, Zhang W (2017) Broadband seismic amplitude variation with offset inversion. Geophysics 82(3):M43–M53

    Article  Google Scholar 

Download references

Acknowledgements

This work was supported by the National Nature Science Foundation of China (Grant: 62071396 and U1562218).

Author information

Authors and Affiliations

  1. Sichuan Province Key Lab of Signal and Information Processing, Southwest Jiaotong University, Chengdu, 610031, China

    Siyuan Du, Jiashu Zhang & Sheng Zhang

  2. School of Resources and Environments, Center for Information Geoscience, University of Electronic Science and Technology of China, Chengdu, 611731, China

    Guangmin Hu

Authors
  1. Siyuan Du
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jiashu Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Sheng Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Guangmin Hu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Siyuan Du.

Additional information

Communicated by Michal Malinowski (CO-EDITOR-IN-CHIEF)/Sanyi Yuan (ASSOCIATE EDITOR).

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Du, S., Zhang, J., Zhang, S. et al. Adaptive individual weight-gain AVO inversion with smooth nonconvex regularization. Acta Geophys. 69, 1199–1213 (2021). https://doi.org/10.1007/s11600-021-00574-w

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11600-021-00574-w

Keywords

Search

Navigation