1887
Volume 65, Issue 5
  • E-ISSN: 1365-2478

Abstract

ABSTRACT

We present a new workflow for imaging damped three‐dimensional elastic wavefields in the Fourier domain. The workflow employs a multiscale imaging approach, in which offset lengths are laddered, where frequency content and damping of the data are changed cyclically. Thus, the inversion process is launched using short‐offset and low‐frequency data to recover the long spatial wavelength of the image at a shallow depth. Increasing frequency and offset length leads to the recovery of the fine‐scale features of the model at greater depths. For the fixed offset, we employ (in the imaging process) a few discrete frequencies with a set of Laplace damping parameters. The forward problem is solved with a finite‐difference frequency‐domain method based on a massively parallel iterative solver. The inversion code is based upon the solution of a least squares optimisation problem and is solved using a nonlinear gradient method. It is fully parallelised for distributed memory computational platforms. Our full‐waveform inversion workflow is applied to the 3D Marmousi‐2 and SEG/EAGE Salt models with long‐offset data. The maximum inverted frequencies are 6 Hz for the Marmousi model and 2 Hz for the SEG/EAGE Salt model. The detailed structures are imaged successfully up to the depth approximately equal to one‐third of the maximum offset length at a resolution consistent with the inverted frequencies.

Loading

Article metrics loading...

/content/journals/10.1111/1365-2478.12487
2017-01-20
2024-04-25
Loading full text...

Full text loading...

References

  1. AminzadehF., BracJ. and KunzT.1997. 3‐D salt and overthrust models. In: SEG/EAGE 3‐D Modeling Series No. 1. Tulsa, OK: Society of Exploration Geophysicists.
    [Google Scholar]
  2. Ben‐Hadj‐AliH., OpertoS. and VirieuxJ.2008. Velocity model‐building by 3D frequency‐domain, full waveform inversion of wide aperture seismic data. Geophysics73(5), VE101–VE117.
    [Google Scholar]
  3. BjorckA.1996. Numerical Methods for Least Squares Problems. Philadelphia, PA: SIAM.
    [Google Scholar]
  4. 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]
  5. BrossierR., OpertoS. and VirieuxJ.2015. Velocity model building from seismic reflection data by full‐waveform inversion. Geophysical Prospecting63, 354–367.
    [Google Scholar]
  6. BrownB.M., JaisM. and KnowlesI.W.2005. A variational approach to an elastic inverse problem. Inverse Problems21, 1953–1973.
    [Google Scholar]
  7. BühlmannP. and van de GeerS.2011. Statistics for High‐Dimensional Data: Methods, Theory and Applications. Springer.
    [Google Scholar]
  8. BunksC., SaleckF.M., ZaleskiS. and ChaventG.1995. Multiscale seismic waveform inversion. Geophysics60(5), 1457–1473.
    [Google Scholar]
  9. ButzerS., KurzmannA. and BohlenT.2013. 3D elastic full‐waveform inversion of small‐scale heterogeneities in transmission geometry. Geophysical Prospecting61, 1238–1251.
    [Google Scholar]
  10. CastellanosC., EtienneV., HuG., OpertoS., BrossierR. and VirieuxJ.2011. Algorithmic and methodological developments towards full waveform inversion in 3D elastic media. 81st annual international meeting, SEG, Expanded Abstracts, 2793–2797.
  11. ChoiY., MinD.‐J. and ShinC.2008. Frequency‐domain elastic full waveform inversion using the new pseudo‐Hessian matrix: experience of elastic Marmousi‐2 synthetic data. Bulletin of the Seismological Society of America98, 2402–2415.
    [Google Scholar]
  12. EpanomeritakisI., AkcelikV., GhattasO. and BielakJ.2008. A Newton‐CG method for large‐scale three‐dimensional elastic full‐waveform seismic inversion. Inverse Problems24, P26.
    [Google Scholar]
  13. ErlanggaY.A., VuikC. and OosterleeC.W.2004. On a class of preconditioners for solving the Helmholtz equation. Applied Numerical Mathematics50, 409–425.
    [Google Scholar]
  14. FichtnerA.2011. Full Seismic Waveform Modelling and Inversion. Springer.
    [Google Scholar]
  15. FletcherR. and ReevesC.M.1964. Function minimization by conjugate gradients. Computer Journal7, 149–154.
    [Google Scholar]
  16. ForstW. and HoffmannD.2010. Optimization—Theory and Practice. Springer Science+Business Media.
    [Google Scholar]
  17. GardnerG.H.F., GardnerL.W. and GregoryA.R.1974. Formation velocity and density—the diagnostic basics for stratigraphic traps. Geophysics39(6), 770–780.
    [Google Scholar]
  18. GillP.E., MurrayW. and WrightM.H.1981. Practical Optimization. Academic Press.
    [Google Scholar]
  19. GuaschL., WarnerM., NangooT., MorganJ., UmplebyA., SteklI.et al. 2012. Elastic 3D full‐waveform inversion. 82nd annual international meeting, SEG, Expanded Abstracts, 2465–2470.
  20. HaW. and ShinC.2012. Laplace‐domain full‐waveform inversion of seismic data lacking low‐frequency information. Geophysics77(5), R199–R206.
    [Google Scholar]
  21. HouseL., LarsenS. and BednarJ.B.2000. 3‐D elastic numerical modeling of a complex salt structure. 70th annual international meeting, SEG, Expanded Abstracts, 2201–2204.
  22. IkelleL.T.1995. Linearized inversion of 3‐D multi‐offset data: background reconstruction and AVO inversion. Geophysical Journal International123, 507–528.
    [Google Scholar]
  23. KapoorS., VighD., WiardaE. and AlwonS.2013. Full waveform inversion around the world, 75th EAGE Conference & Exhibition, SPE EUROPEC, Expanded Abstracts Extended Abstracts, London, UK.
  24. KöhnD., De NilD., KurzmannA., PrzebindowskaA. and BohlenT.2012. On the influence of model parametrization in elastic full‐waveform tomography. Geophysical Journal International191, 325–345.
    [Google Scholar]
  25. LasdonL.S.1970. Optimization Theory for Large Systems. Mineola, NY: Dover Publications, Inc.
    [Google Scholar]
  26. MaineR.E. and IliffK.W.1981. Formulation and implementation of a practical algorithm for parameter estimation with process and measurement noise. SIAM Journal on Applied Mathematics41(3), 558–579.
    [Google Scholar]
  27. MartinG.S., MarfurtK.J. and LarsenS.2002. Marmousi‐2: an updated model for the investigation of AVO in structurally complex areas. 72nd annual international meeting, SEG, Expanded Abstract, 1979–1982.
  28. NewmanG.A. and AlumbaughD.L.2000. Three‐dimensional magnetotelluric inversion using nonlinear conjugate gradients. Geophysical Journal International140, 410–424.
    [Google Scholar]
  29. OpertoS., VirieuxJ., AmestoyP., L'ExcellentJ.‐Y., GiraudL. and Ben‐Hadj‐AliH.2007. 3‐D finite‐difference modeling of visco‐acoustic wave propagation using a massively parallel direct solver: a feasibility study. Geophysics72(5), SM195–SM211.
    [Google Scholar]
  30. OpertoS., GholamiY., PrieuxV., RibodettiA., BrossierR., MetivierL.et al. 2013. A guided tour of multiparameter full‐waveform inversion with multicomponent data: from theory to practice. The Leading Edge32(9), 1040–1054.
    [Google Scholar]
  31. Perel'manI.I.1981. Methods for sound estimation of linear dynamic plant parameters and feasibility of their implementation on finite samples. Automation and Remote Control42(3), 309–313.
    [Google Scholar]
  32. PlessixR.E., BaetenG., de MaagJ.W., KlaasenM., RujieZ. and ZhifeiT.2010. Application of acoustic full‐waveform inversion to a low‐frequency large‐offset land data set. 80th annual international meeting, SEG, Expanded Abstracts, 930–934.
  33. PetrovP.V. and NewmanG.A.2012. 3D finite‐difference modeling of elastic wave propagation in the Laplace–Fourier domain. Geophysics77(4), T137–T155.
    [Google Scholar]
  34. PetrovP.V. and NewmanG.A.2014. Three‐dimensional inverse modelling of damped elastic wave propagation in the Fourier domain. Geophysical Journal International198, 1599–1617.
    [Google Scholar]
  35. PolyakE. and RibièreG.1969. Note sur la convergence des méthods conjugées. Revue Française d'Informatique et de Recherche Opérationnelle16, 35–43.
    [Google Scholar]
  36. PrattR.G., ShinC. and HicksG.J.1998. Gauss–Newton and full Newton method in frequency domain seismic waveform inversion. Geophysical Journal International133, 341–362.
    [Google Scholar]
  37. PrattR.G.1999. Seismic waveform inversion in the frequency domain. Part 1: Theory and verification in a physical scale model. Geophysics64(3), 888–901.
    [Google Scholar]
  38. RenZ. and LiuY.2016. A hierarchical elastic full‐waveform inversion scheme based on wavefield separation and the multistep‐length approach. Geophysics81(3), R99–R123.
    [Google Scholar]
  39. SearsT., SinghS. and BartonP.2008. Elastic full waveform inversion of multi‐component OBC seismic data. Geophysical Prospecting56, 843–862.
    [Google Scholar]
  40. SirgueL. and PrattR.G.2004. Efficient waveform inversion and imaging: a strategy for selecting temporal frequencies. Geophysics69(1), 231–248.
    [Google Scholar]
  41. 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]
  42. ShinC. and MinD.‐J.2006. Waveform inversion using a logarithmic wavefield. Geophysics71(3), R31–R42.
    [Google Scholar]
  43. ShinC. and HaW.2008. A comparison between the behavior of objective functions for waveform inversion in the frequency and Laplace domains. Geophysics73(5), VE119–VE133.
    [Google Scholar]
  44. ShinC. and ChaY.2009. Waveform inversion in the Laplace–Fourier domain. Geophysical Journal International177, 1067–1079.
    [Google Scholar]
  45. ShinC., KooN., ChaY.H. and ParkK.2010. Sequentially ordered single‐frequency 2‐D acoustic waveform inversion in the Laplace–Fourier domain. Geophysical Journal International181, 935–950.
    [Google Scholar]
  46. ShippR.M. and SinghS.C.2002. Two‐dimensional full wavefield inversion of wide‐aperture marine seismic streamer data. Geophysical Journal International151, 325–344.
    [Google Scholar]
  47. TarantolaA.1984. Inversion of seismic reflection data in the acoustic approximation. Geophysics49(8), 1259–1266.
    [Google Scholar]
  48. VighD., StarrB., KapoorJ. and LiH.2010. 3D full waveform inversion of Gulf of Mexico WAZ dataset. 80th annual international meeting, SEG, Expanded Abstracts, 957–961.
  49. VighD., KapoorJ. and LiH.2011. Full waveform inversion application in different geological settings. 81st annual international meeting, SEG, Expanded Abstracts, 2374–2378.
  50. VighD., MoldoveanuN., JiaoK., HuangW. and KapoorJ.2013. Ultralong‐offset data acquisition can complement full‐waveform inversion and lead to improved subsalt imaging. The Leading Edge32, 1116–1122.
    [Google Scholar]
  51. VirieuxJ.1986. P‐SV wave propagation in heterogeneous media: velocity‐stress finite‐difference method. Geophysics51(4), 889–901.
    [Google Scholar]
  52. VirieuxJ. and OpertoS.2009. An overview of full‐waveform inversion in exploration geophysics. Geophysics74(6), WCC127–WCC152.
    [Google Scholar]
  53. WangY. and RaoY.2009. Reflection seismic waveform tomography. Journal of Geophysical Research114(B3), B03304.
    [Google Scholar]
  54. WangS., de HoopM. and XiaJ.2012. Massively parallel structured multifrontal solver for time‐harmonic elastic waves in 3‐D anisotropic media. Geophysical Journal International191, 346–366.
    [Google Scholar]
  55. WarnerM., RatcliffeF., NangooT., MorganJ., UmplebyA., ShahN.et al. 2013. Anisotropic 3D full‐waveform inversion. Geophysics78(2), R59–R80.
    [Google Scholar]
  56. WarnerM.2014. Adaptive waveform inversion: theory. 84th annual international meeting, SEG, Expanded Abstracts, 1089–1093.
  57. XiongJ.L., LinY., AbubakarA. and HabashyT.M.2013. 2.5‐D forward and inverse modelling of full‐waveform elastic seismic survey. Geophysical Journal International193, 938–948.
    [Google Scholar]
http://instance.metastore.ingenta.com/content/journals/10.1111/1365-2478.12487
Loading
/content/journals/10.1111/1365-2478.12487
Loading

Data & Media loading...

  • Article Type: Research Article
Keyword(s): 3D full waveform inversion; Elastic attributes; Inversion workflow

Most Cited This Month Most Cited RSS feed

This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error