Acta Geophysica

, Volume 66, Issue 6, pp 1383–1396 | Cite as

Regularized inversion of amplitude-versus-incidence angle (AVA) based on a piecewise-smooth model

  • Zhiyong LiEmail author
  • Mantao Wang
  • Feng Xu
Research Article - Applied Geophysics


Different from the stacked seismic data, pre-stack data includes abundant information about shear wave and density. Through inversing the shear wave and density information from the pre-stack data, we can determine oil-bearing properties from different incident angles. The state-of-the-art inversion methods obtain either low vertical resolution or lateral discontinuities. However, the practical reservoir generally has sharp discontinuities between different layers in vertically direction and is horizontally smooth. Towards obtaining the practical model, we present an inversion method based on the regularized amplitude-versus-incidence angle (AVA) data to estimate the piecewise-smooth model from pre-stack seismic data. This method considers subsurface stratum as a combination of two parts: a piecewise smooth part and a constant part. To fix the ill-posedness in the inversion, we adopt four terms to define the AVA inversion misfit function: the data misfit itself, a total variation regularization term acting as a sparsing operator for the piecewise constant part, a Tikhonov regularization term acting as a smoothing operator for the smooth part, and the last term to smoothly incorporate a priori information for constraining the magnitude of the estimated model. The proposed method not only can incorporate structure information and a priori model constraint, but also is able to derive into a convex objective function that can be easily minimized using iterative approach. Compared with inversion results of TV and Tikhonov regularization methods, the inverted P-wave velocity, S-wave velocity and density of the proposed method can better delineate the piecewise-smooth characteristic of strata.


Pre-stack seismic inversion Unsuitability Multi-scale construction Regularization 



This research is financially supported by the National Natural Science Foundation of China (U1562218 and youth project 41604107) and Agricultural Information Engineering Key Laboratory of Sichuan Provincial Universities.


  1. Acar R, Vogel CR (1994) Analysis of bounded variation penalty methods for ill-posed problems. Inverse Prob 10(6):1219CrossRefGoogle Scholar
  2. Anagaw AY, Sacchi MD (2012) Edge-preserving seismic imaging using the total variation method. J Geophys Eng 9(2):138CrossRefGoogle Scholar
  3. Asnaashari A, Brossier R, Garambois S et al (2013) Regularized seismic full waveform inversion with prior model information. Geophysics 78(2):R25–R36CrossRefGoogle Scholar
  4. Bertete-Aguirre H, Cherkaev E, Oristaglio M (2002) Non-smooth gravity problem with total variation penalization functional. Geophys J Int 149(2):499–507CrossRefGoogle Scholar
  5. Bosch M, Mukerji T, Gonzalez EF (2010) Seismic inversion for reservoir properties combining statistical rock physics and geostatistics: a review. Geophysics 75(5):75A165–75A176CrossRefGoogle Scholar
  6. Bouchon M, Aki K (1977) Discrete wave-number representation of seismic-source wave fields. Bull Seismol Soc Am 67(2):259–277Google Scholar
  7. Fatti JL, Smith GC, Vail PJ et al (1994) Detection of gas in sandstone reservoirs using AVO analysis: a 3-D seismic case history using the Geostack technique. Geophysics 59(9):1362–1376CrossRefGoogle Scholar
  8. Fomel S (2007) Shaping regularization in geophysical-estimation problems. Geophysics 72(2):R29–R36CrossRefGoogle Scholar
  9. Gholami A, Hosseini SM (2013) A balanced combination of Tikhonov and total variation regularizations for reconstruction of piecewise-smooth signals. Sig Process 93(7):1945–1960CrossRefGoogle Scholar
  10. Guitton A, Symes WW (2003) Robust inversion of seismic data using the Huber norm. Geophysics 68(4):1310–1319CrossRefGoogle Scholar
  11. Hampson DP, Russell BH, Bankhead B (2005) Simultaneous inversion of pre-stack seismic data. SEG Techn Progr Expand Abstr 2005:1633–1637Google Scholar
  12. Li G, Zhang H, Wang Y et al (2014) Prestack AVO inversion using edge-preserving regularization with directional constraints. SEG Techn Progr Expand Abstr 2014:3080–3085Google Scholar
  13. Li Z, Hu G, Li Y et al (2016a) Regularized amplitude-versus-angle (AVA) inversion with traveltime information. SEG Techn Progr Expand Abstr 2016:548–552Google Scholar
  14. Li Z, Song B, Zhang J et al (2016b) Joint elastic and petrophysical inversion using prestack seismic and well log data. Explor Geophys 47(4):331–340CrossRefGoogle Scholar
  15. Li Z, Hu G, Zhang J (2017a) Adaptive mixed-norm seismic inversion for non-Gaussian errors. Explor Geophys 48(4):413–421CrossRefGoogle Scholar
  16. Li Z, Hu G, She B (2017b) A hybrid regularization approach for AVA inversion of the piecewise smooth model. SEG Techn Progr Expand Abstr 2017:793–797Google Scholar
  17. Lin Y, Huang L (2015) Acoustic-and elastic-waveform inversion using a modified total-variation regularization scheme. Geophys J Int 200(1):489–502CrossRefGoogle Scholar
  18. Moré JJ, Thuente DJ (1994) Line search algorithms with guaranteed sufficient decrease. ACM Trans Math Softw (TOMS) 20(3):286–307CrossRefGoogle Scholar
  19. Theune U, Jensås IØ, Eidsvik J (2010) Analysis of prior models for a blocky inversion of seismic AVA data. Geophysics 75(3):C25–C35CrossRefGoogle Scholar
  20. Tikhonov AN, Arsenin VIA (1977) Solutions of ill-posed problems. Winston, Washington DCGoogle Scholar
  21. Wang H, Fehler MC (2018a) The wavefield of acoustic logging in a cased hole with a single casing—part II: a dipole tool. Geophys J Int 212(2):1414–1428Google Scholar
  22. Wang H, Fehler MC (2018b) The wavefield of acoustic logging in a cased-hole with a single casing—part I: a monopole tool. Geophys J Int 212(1):612–626CrossRefGoogle Scholar
  23. Wang H, Tao G (2011) Wavefield simulation and data-acquisition-scheme analysis for LWD acoustic tools in very slow formations. Geophysics 76(3):E59–E68CrossRefGoogle Scholar
  24. Wang Y, Cao J, Yang C (2011) Recovery of seismic wavefields based on compressive sensing by an l1-norm constrained trust region method and the piecewise random subsampling. Geophys J Int 187(1):199–213CrossRefGoogle Scholar
  25. Wang H, Tao G, Zhang K (2013) Wavefield simulation and analysis with the finite-element method for acoustic logging while drilling in horizontal and deviated wells. Geophysics 78(6):D525–D543CrossRefGoogle Scholar
  26. Zhang X, Zhang J (2017) Model regularization for seismic travel time tomography with an edge-preserving smoothing operator. J Appl Geophys 138:143–153CrossRefGoogle Scholar
  27. Zhang J, Lv S, Liu Y et al (2013) AVO inversion based on generalized extreme value distribution with adaptive parameter estimation. J Appl Geophys 98:11–20CrossRefGoogle Scholar
  28. Zhang F, Dai R, Liu H (2014a) Seismic inversion based on L1-norm misfit function and total variation regularization. J Appl Geophys 109:111–118CrossRefGoogle Scholar
  29. Zhang H, Cao C, Shang Z (2014b) A nonlinear method of simultaneous inversion for pre-stack seismic data based on edge-preserving regularization. SEG Techn Program Expand Abstr 2014:3226–3230Google Scholar

Copyright information

© Institute of Geophysics, Polish Academy of Sciences & Polish Academy of Sciences 2018

Authors and Affiliations

  1. 1.College of Information Engineering, Sichuan Agricultural UniversityYa’anChina
  2. 2.Key Laboratory of Agricultural Information Engineering of Sichuan Province, Sichuan Agricultural UniversityYa’anChina
  3. 3.College of Geoscience and Technology, Southwest Petroleum UniversityChengduChina

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