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Volume 62, Issue 6
  • E-ISSN: 1365-2478

Abstract

ABSTRACT

Full waveform inversion is a powerful tool for quantitative seismic imaging from wide‐azimuth seismic data. The method is based on the minimization of the misfit between observed and simulated data. This amounts to the solution of a large‐scale nonlinear minimization problem. The inverse Hessian operator plays a crucial role in this reconstruction process. Accounting accurately for the effect of this operator within the minimization scheme should correct for illumination deficits, restore the amplitude of the subsurface parameters, and help to remove artefacts generated by energetic multiple reflections. Conventional minimization methods (nonlinear conjugate gradient, quasi‐Newton methods) only roughly approximate the effect of this operator. In this study, we are interested in the truncated Newton minimization method. These methods are based on the computation of the model update through a matrix‐free conjugate gradient solution of the Newton linear system. We present a feasible implementation of this method for the full waveform inversion problem, based on a second‐order adjoint state formulation for the computation of Hessian‐vector products. We compare this method with conventional methods within the context of 2D acoustic frequency full waveform inversion for the reconstruction of P‐wave velocity models. Two test cases are investigated. The first is the synthetic BP 2004 model, representative of the Gulf of Mexico geology with high velocity contrasts associated with the presence of salt structures. The second is a 2D real data‐set from the Valhall oil field in North sea. Although, from a computational cost point of view, the truncated Newton method appears to be more expensive than conventional optimization algorithms, the results emphasize its increased robustness. A better reconstruction of the P‐wave velocity model is provided when energetic multiple reflections make it difficult to interpret the seismic data. A better trade‐off between regularization and resolution is obtained when noise contamination of the data requires one to regularize the solution of the inverse problem.

Copyright © 2014 European Association of Geoscientists & Engineers © 2014 European Association of Geoscientists & Engineers
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2014-06-05
2024-04-25

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References

  1. AmestoyP., DuffI.S. and L'ExcellentJ.Y., 2000. Multifrontal parallel distributed symmetric and unsymmetric solvers. Computer Methods in Applied Mechanics and Engineering184(2‐4), 501–520.
     [Google Scholar]
  2. BekasC., KokiopoulouE. and SaadY.2007. An estimator for the diagonal of a matrix. Applied Numerical Mathematics57(11‐12), 1214–1229.
     [Google Scholar]
  3. BenziM.2002. Preconditioning techniques for large linear systems: a survey. Journal of Computational Physics182, 418–477.
     [Google Scholar]
  4. BérengerJ.‐P.1994. A perfectly matched layer for absorption of electromagnetic waves. Journal of Computational Physics114, 185–200.
     [Google Scholar]
  5. BilletteF.J. and Brandsberg‐DahlS.2004. The 2004 BP velocity benchmark. 67 th Annual EAGE Conference & Exhibition, Madrid, Spain, Extended Abstracts, B035.
  6. BonnansJ.F., GilbertJ.C., LemaréchalC. and SagastizábalC.A.2006. Numerical Optimization, Theoretical and Practical Aspects. Springer series. Universitext.
     [Google Scholar]
  7. BrossierR., OpertoS. and VirieuxJ.2009. Seismic imaging of complex onshore structures by 2D elastic frequency‐domain full‐waveform inversion. Geophysics74(6), WCC105–WCC118.
     [Google Scholar]
  8. BrossierR., OpertoS. and VirieuxJ.2010. Which data residual norm for robust elastic frequency‐domain full waveform inversion?Geophysics. 75(3), R37–R46.
     [Google Scholar]
  9. ByrdR.H., LuP. and NocedalJ.1995. A limited memory algorithm for bound constrained optimization. SIAM Journal on Scientific and Statistical Computing. 16, 1190–1208.
     [Google Scholar]
  10. ChaventG.1974. Identification of parameter distributed systems. in: Identification of function Parameters in Partial Differential Equations, (ed. R.Goodson and M.Polis ), American Society of Mechanical Engineers, pp. 31–48.
     [Google Scholar]
  11. ChiuJ. and DemanetL.2012. Matrix probing and its conditioning. SIAM Journal on Numerical Analysis50(1), 171–193.
     [Google Scholar]
  12. DaiY. and YuanY.1999. A nonlinear conjugate gradient method with a strong global convergence property. SIAM Journal on Optimization10, 177–182.
     [Google Scholar]
  13. EisenstatS.C. and WalkerH.F.1994. Choosing the forcing terms in an inexact Newton method. SIAM Journal on Scientific Computing17, 16–32.
     [Google Scholar]
  14. EpanomeritakisI., AkçelikV., GhattasO. and BielakJ.2008. A Newton‐CG method for large‐scale three‐dimensional elastic full waveform seismic inversion. Inverse Problems24, 1–26.
     [Google Scholar]
  15. EtienneV., HuG., OpertoS., VirieuxJ., BarkvedO.I. and KommedalJ.2012. Three‐dimensional acoustic full waveform inversion: algorithm and application to Valhall. 74 th Annual EAGE Conference & Exhibition, Copenhagen Denmark, Expanded Abstracts.
  16. FichtnerA. and TrampertJ.2011. Hessian kernels of seismic data functionals based upon adjoint techniques. Geophysical Journal International185(2), 775–798.
     [Google Scholar]
  17. GaoF., LevanderA.R., PrattR.G., ZeltC.A. and FradelizioG.L.2006. Waveform tomography at a groundwater contamination site: surface reflection data. Geophysics72(5), G45–G55.
     [Google Scholar]
  18. GauthierO., VirieuxJ. and TarantolaA.1986. Two‐dimensional nonlinear inversion of seismic waveforms: numerical results. Geophysics51(7), 1387–1403.
     [Google Scholar]
  19. GholamiY., BrossierR., OpertoS., PrieuxV., RibodettiA. and VirieuxJ.2013. Which parametrization is suitable for acoustic VTI full waveform inversion? Part 2: application to Valhall. Geophysics78(2), R107–R124.
     [Google Scholar]
  20. GrattonS., LaloyauxP., SartenaerA. and TshimangaJ.2011. A reduced and limited‐memory preconditioned approach for the 4d‐var data‐assimilation problem. uaterly Journal of the Royal J.R. Meteorological Society137, 452–466.
     [Google Scholar]
  21. HustedtB., OpertoS. and VirieuxJ.2004. Mixed‐grid and staggered‐grid finite difference methods for frequency domain acoustic wave modelling. Geophysical Journal International157, 1269–1296.
     [Google Scholar]
  22. KaltenbacherB., NeubauerA. and ScherzerO.2008. Iterative Regularization Methods for Nonlinear Problems. de Gruyter.
     [Google Scholar]
  23. KrebsJ., AndersonJ., HinkleyD., NeelamaniR., LeeS., BaumsteinA. and LacasseM.D.2009. Fast full‐wavefield seismic inversion using encoded sources. Geophysics74(6), WCC105–WCC116.
     [Google Scholar]
  24. LaillyP.1983. The seismic inverse problem as a sequence of before stack migrations. in: Conference on Inverse Scattering, Theory and Application, Society for Industrial and Applied Mathematics, Philadelphia (ed. R.Bednar and Weglein), pp. 206–220.
     [Google Scholar]
  25. LionsJ.L.1968. Contrôle optimal de systèmes gouvernés par des équations aux dérivées partielles. Dunod.
     [Google Scholar]
  26. MaY. and HaleD.2012. Quasi‐newton full‐waveform inversion with a projected Hessian matrix. Geophysics77(5), R207–R216.
     [Google Scholar]
  27. MétivierL.2011. Interlocked optimization and fast gradient algorithm for a seismic inverse problem. Journal of Computational Physics230(19), 7502–7518.
     [Google Scholar]
  28. MétivierL., BrossierR., VirieuxJ. and OpertoS.2012. Optimization schemes in FWI: the truncated Newton method. in: 2012 SEG Abstracts.
  29. MétivierL., BrossierR., VirieuxJ. and OpertoS.2013. Full waveform inversion and the truncated newton method. SIAM Journal On Scientific Computing35(2), B401–B437.
     [Google Scholar]
  30. NashS.G.2000. A survey of truncated Newton methods. Journal of Computational and Applied Mathematics124, 45–59.
     [Google Scholar]
  31. NocedalJ. and WrightS.J.2006. Numerical OptimizationSpringer, 2nd edn.
     [Google Scholar]
  32. OpertoS., RavautC., ImprotaL., VirieuxJ., HerreroA. and Dell'AversanaP.2004. Quantitative imaging of complex structures from dense wide‐aperture seismic data by multiscale traveltime and waveform inversions: a case study. Geophysical Prospecting52, 625–651.
     [Google Scholar]
  33. OpertoS., VirieuxJ. and DessaJ.X.2005. High‐resolution crustal seismic imaging from OBS data by full‐waveform inversion: application to the eastern‐Nankai trough. in: EOS Trans. AGU vol. 86. American Geophysical Union.
     [Google Scholar]
  34. OpertoS., VirieuxJ., DessaJ.X. and PascalG.2006. Crustal imaging from multifold ocean bottom seismometers data by frequency‐domain full‐waveform tomography: application to the eastern Nankai trough. Journal of Geophysical Research111(B09306), doi:10.1029/2005JB003835.
     [Google Scholar]
  35. OpertoS., VirieuxJ., RibodettiA. and AndersonJ.E.2009. Finite‐difference frequency‐domain modeling of visco‐acoustic wave propagation in two‐dimensional TTI media. Geophysics74 (5), T75–T95.
     [Google Scholar]
  36. OpertoS., BrossierR., GholamiY., MétivierL., PrieuxV., RibodettiA. and VirieuxJ.2013. A guided tour of multiparameter full waveform inversion for multicomponent data: from theory to practice. The Leading Edge, September (Special section Full Waveform Inversion), 1040–1054.
     [Google Scholar]
  37. PlessixR.E.2006. A review of the adjoint‐state method for computing the gradient of a functional with geophysical applications. Geophysical Journal International167(2), 495–503.
     [Google Scholar]
  38. PlessixR.E. and PerkinsC.2010. Full waveform inversion of a deep water ocean bottom seismometer dataset. First Break28, 71–78.
     [Google Scholar]
  39. PlessixR.‐E., BaetenG., de MaagJ.W. and ten KroodeF.2012. Full waveform inversion and distance separated simultaneous sweeping: a study with a land seismic data set. Geophysical Prospecting60, 733–747.
     [Google Scholar]
  40. PrattR.G.1990. Inverse theory applied to multi‐source cross‐hole tomography. part II : elastic wave‐equation method. Geophysical Prospecting38, 311–330.
     [Google Scholar]
  41. PrattR.G. and WorthingtonM.H.1990. Inverse theory applied to multi‐source cross‐hole tomography. Part I: acoustic wave‐equation method. Geophysical Prospecting38, 287–310.
     [Google Scholar]
  42. PrattR.G., ShinC. and HicksG.J.1998. Gauss‐Newton and full Newton methods in frequency‐space seismic waveform inversion. Geophysical Journal International133, 341–362.
     [Google Scholar]
  43. PrieuxV., BrossierR., GholamiY., OpertoS., VirieuxJ., BarkvedO.I. and KommedalJ.H.2011. On the footprint of anisotropy on isotropic full waveform inversion: the Valhall case study. Geophysical Journal International187, 1495–1515.
     [Google Scholar]
  44. PrieuxV., BrossierR., OpertoS. and VirieuxJ.2013. Multiparameter full waveform inversion of multicomponent OBC data from valhall. Part 1: imaging compressional wavespeed, density and attenuation. Geophysical Journal International194(3), 1640–1664.
     [Google Scholar]
  45. PrieuxV., BrossierR., OpertoS. and Virieux, J.2013. Multiparameter full waveform inversion of multicomponent OBC data from valhall. Part 2: imaging compressional and shear‐wave velocities. Geophysical Journal International194(3), 1665–1681.
     [Google Scholar]
  46. RavautC., OpertoS., ImprotaL., VirieuxJ., HerreroA. and dell'AversanaP.2004. Multi‐scale imaging of complex structures from multi‐fold wide‐aperture seismic data by frequency‐domain full‐wavefield inversions: application to a thrust belt. Geophysical Journal International159, 1032–1056.
     [Google Scholar]
  47. SaadY.2003. Iterative Methods for Sparse Linear Systems. SIAM,
     [Google Scholar]
  48. ShinC., JangS. and MinD.J.2001. Improved amplitude preservation for prestack depth migration by inverse scattering theory. Geophysical Prospecting49, 592–606.
     [Google Scholar]
  49. SirgueL., EtgenJ.T. and AlbertinU.2008. 3D Frequency Domain Waveform Inversion using Time Domain Finite Difference Methods. 70th EAGE, Conference and Exhibition, Roma, Italy, Expanded Abstracts, F022.
  50. SirgueL., BarkvedO.I., DellingerJ., EtgenJ., AlbertinU. and KommedalJ.H.2010. Full waveform inversion: the next leap forward in imaging at Valhall. First Break28, 65–70.
     [Google Scholar]
  51. TarantolaA.1984. Inversion of seismic reflection data in the acoustic approximation. Geophysics49(8), 1259–1266.
     [Google Scholar]
  52. TarantolaA.2005. Inverse Problem Theory and Methods for Model Parameter Estimation. Society for Industrial and Applied Mathematics.
     [Google Scholar]
  53. VighD., StarrB., KapoorJ. and LiH.2010. 3d full waveform inversion on a gulf of mexico waz data set. SEG Technical Program Expanded Abstracts29(1), 957–961.
     [Google Scholar]
  54. VirieuxJ. and OpertoS.2009. An overview of full waveform inversion in exploration geophysics. Geophysics74(6), WCC1–WCC26.
     [Google Scholar]
  55. WangZ., NavonI.M., DimetF.X. and ZouX.1992. The second order adjoint analysis: Theory and applications. Meteorology and Atmospheric Physics50(1‐3), 3–20.
     [Google Scholar]
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Full waveform inversion and the truncated Newton method: quantitative imaging of complex subsurface structures
Geophysical Prospecting 62, 1353 (2014); https://doi.org/10.1111/1365-2478.12136
/content/journals/10.1111/1365-2478.12136
/content/journals/10.1111/1365-2478.12136
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  • Article Type: Research Article
Keyword(s): Computing aspects; Full waveform; Imaging; Numerical study; Theory

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