Full‐waveform inversion for macro velocity model reconstruction in look‐ahead offset vertical seismic profile: numerical singular value decomposition‐based analysis

References

1. AlekseevA.S. and DobrinskiV.I.1975. The few points of practical application of dynamical inverse seismic problems. Mathematical Problems of Geophysics6(2), 7–33, (in Russian)
   [Google Scholar]
2. AssousF. and CollinoF.1990. A numerical method for the explanation of sensitivity: The case of the identification of the 2D stratified elastic medium. Inverse Problems6(4), 487.
   [Google Scholar]
3. BunksC., SaleckF.M., ZaleskiS. and ChaventG.1995. Multiscale seismic waveform inversion. Geophysics60(05), 1457–1473.
   [Google Scholar]
4. CheverdaV.A., ClementF., KhaidukovV.G. and KostinV.I.1998. Linearized inversion of data of multi‐offset data for vertically inhomogeneous background. Journal of Inverse and Ill‐posed Problems6(5), 453–484.
   [Google Scholar]
5. CheverdaV.A. and KostinV.I.1995. R‐pseudoinverses for compact operators in Hilbert spaces: Existence and stability. Journal of Inverse and Ill‐posed Problems3(2), 131–148.
   [Google Scholar]
6. DevaneyA.J. and OristaglioM.L.1983. Inversion procedure for inverse scattering within the distorted‐wave Born approximation. Physical Review Letters51, 237–240.
   [Google Scholar]
7. GauthierO., VirieuxJ. and TarantolaA.1986. Two‐dimensional non‐linear inversion of seismic waveforms – Numerical results. Geophysics51(07), 1387–1403.
   [Google Scholar]
8. GolubG.H. and Van LoanC.F.1994. Matrix Computation. 3rd Edition. Johns Hopkins University Press.
   [Google Scholar]
9. HansenP.C.1987. The truncated SVD as a method for regularization. BIT Numerical Mathematics27(4), 534–553.
   [Google Scholar]
10. HuW., AbubakarA. and HabashyT.2009. Simultaneous multifrequency inversion of full‐waveform seismic data. Geophysics74(2), R1–R14.
    [Google Scholar]
11. JannaneM., BeydounW., CraseE., CaoD., KorenZ., LandaE. et al. 1989. Wavelengths of earth structures that can be resolved from seismic reflection data (short note). Geophysics54(07), 906–910.
    [Google Scholar]
12. LaillyP.1983. The seismic inverse problem as a sequence of before stack migrations. Conference on Inverse Scattering: Theory and Application. SIAM. p. 206–220.
13. LebrunD., RichardV., MaceD. and CuerM.2001. SVD for multioffset linearized inversion: Resolution analysis in multicomponent acquisition. Geophysics66(3), 871–88.
    [Google Scholar]
14. MoraP.1988. Elastic wavefield inversion of reflection and transmission data. Geophysics53(06), 750–759.
    [Google Scholar]
15. NeklyudovD., SilvestrovI. and TcheverdaV.2010. A Helmholtz iterative solver with semianalytical preconditioner for the frequency‐domain full‐waveform inversion. SEG Technical Program Expanded Abstracts29(1), 1070–1074.
    [Google Scholar]
16. De NicolaoA., DrufucaG. and RoccaF.1993. Eigenvectors and eigenvalues of linearized elastic inversion. Geophysics58(05), 670–679.
    [Google Scholar]
17. PlessixR.E.2007. A Helmholtz iterative solver for 3D seismic imaging problems. Geophysics72(5), SM185–SM194.
    [Google Scholar]
18. PrattG., ShinC. and HicksG.J.1998. Gauss‐Newton and full Newton methods in frequency‐space seismic waveform inversion. Geophysical Journal International133(2), 341–362.
    [Google Scholar]
19. SilvestrovI. and TcheverdaV.2011. SVD analysis in application to full waveform inversion of multicomponent seismic data. Journal of Physics: Conference Series290012014.
    [Google Scholar]
20. SirgueL.2003. Inversion de la forme d'onde dans le domaine fréquentiel de données sismiques grand offset. PhD thesis, Université Paris and Queen's University.
    [Google Scholar]
21. SirgueL.2006. The importance of low frequency and large offset in waveform inversion. 68th Conference & Technical Exhibition, EAGE, Extended Abstracts, A037.
22. SirgueL. and PrattR.2004. Efficient waveform inversion and imaging: A strategy for selecting temporal frequencies. Geophysics69(1), 231–248.
    [Google Scholar]
23. SonneveldP. and Van GijzenM.B.2008. IDR(s): A Family of Simple and Fast Algorithms for Solving Large Nonsymmetric Systems of Linear Equations. SIAM Journal on Scientific Computing31(2), 1035–1062.
    [Google Scholar]
24. TarantolaA.1984. Inversion of seismic reflection data in the acoustic approximation. Geophysics49(08), 1259–1266.
    [Google Scholar]
25. ThompsonM., ArntsenB. and AmundsenL.2003. Acquisition geometry versus 4C image quality: A study from Gullfaks South. SEG Technical Program Expanded Abstracts22(1), 793–796.
    [Google Scholar]
26. VirieuxJ. and OpertoS.2009. An overview of full‐waveform inversion in exploration geophysics. Geophysics, 74(6), WCC1–WCC26.
    [Google Scholar]
27. WuR.S. and ToksözM.N.1987. Diffraction tomography and multisource holography applied to seismic imaging. Geophysics52(1), 11–25.
    [Google Scholar]