534
Views
2
CrossRef citations to date
0
Altmetric
Articles

Acoustic multi-parameter full waveform inversion based on the wavelet method

Pages 220-247 | Received 06 Mar 2020, Accepted 12 Jun 2020, Published online: 26 Jun 2020

References

  • Lailly P. The seismic inverse problem as a sequence of before stack migrations. Conference on Inverse Scattering, Theory and Applications. Philadelphia (PA): SIAM; 1983. p. 206–220.
  • Tarantola A. Inversion of seismic reflection data in the acoustic approximation. Geophysics. 1984;49(8):1259–1266.
  • Mora P. Nonlinear two-dimensional elastic inversion of multioffset seismic data. Geophysics. 1987;52(9):1211–1228.
  • Tarantola A. A strategy for nonlinear elastic inversion of seismic reflection data. Geophysics. 1986;51(10):1893–1903.
  • Pratt RG, Worthington MH. Inverse theory applied to multi-source cross-hole tomography, part 1: acoustic wave equation method. Geophys Prospect. 1990;38(3):287–310.
  • Pratt RG. Inverse theory applied to multi-source cross-hole tomography, part 2: elastic wave equation method. Geophys Prospect. 1990;38(3):311–329.
  • Virieux J, Operto S. An overview of full-waveform inversion in exploration geophysics. Geophysics. 2009;74(6):WCC1–WCC26.
  • Shin C, Cha YH. Waveform inversion in the Laplace-Fourier domain. Geophys J Int. 2009;177(3):1067–1079.
  • Shin C, Cha YH. Waveform inversion in the Laplace domain. Geophys J Int. 2008;173(3):922–931.
  • Yang P, Brossier R, Métivier L, et al. A time-domain preconditioned truncated Newton approach to viso-acoostic multiparameter full waveform inversion. SIAM J Sci Comput. 2018;40(4):B1101–B1130.
  • Aghamiry HS, Gholami A, Operto S. ADMM-based multi-parameter wavefield reconstruction inversion in VTI acoustic media with TV regularization. Geophys J Int. 2019;219(2):1316–1333.
  • Métivier L, Brossier R, Operto S, et al. Full waveform inversion and the truncated Newton method. SIAM Rev. 2017;59(1):153–195.
  • Plessix RE. A review of the adjoint-state method for computing the gradient of a functional with geophysical applications. Geophys J Int. 2006;167(2):495–503.
  • Pratt RG, Shin C, Hicks GJ. Gauss-Newton and full Newton methods in frequency-space seismic waveform inversion. Geophys J Internat. 1998;133(2):341–362.
  • Epanomeritakis I, Akelik V, Ghattas O, et al. A Newton-CG method for large-scale three-dimensional elastic full waveform seismic inversion. Inverse Problems. 2008;24(3):1–26.
  • Engl H, Hanke M, Neubauer A. Regularization of inverse problems. Dordrecht: Kluwer Academic Publishers Group; 1996.
  • Guitton A. Blocky regularization schemes for full-waveform inversion. Geophys Prospect. 2012;60(5):870–884.
  • Lin Y, Huang L. Acoustic- and elastic-waveform inversion using a modified total-variation regularization scheme. Geophys J Int. 2015;200(1):489–502.
  • Bunks C, Saleck F, Zaleski S, et al. Multiscale seismic waveform inversion. Geophysics. 1995;60(5):1457–1473.
  • Engquist E, Froese BD. Application of the Wasserstein metric to seismic signals. Commun Math Sci. 2014;12(5):979–988.
  • Métivier L, Brossier R, Mérigot Q, et al. Measuring the misfit between seismograms using an optimal transport distance: application to full waveform inversion. Geophys J Int. 2016;205(1):345–377.
  • Virieux J. P-SV wave propagation in heterogeneous media: velocity-stress finite-difference method. Geophysics. 1986;51(4):889–901.
  • Zhang W, Tong L, Chung ET. A new high accuracy locally one-dimensional scheme for the wave equation. J Comput Appl Math. 2011;236(6):1343–1353.
  • Fornberg B. A practical guide to pseudospectral methods. Cambridge: Cambridge University Press; 1996.
  • Zhang W. Stability conditions for wave simulation in 3-D anisotropic media with the pseudospectral method. Commun Comput Phys. 2012;12(3):703–720.
  • Zhang W, Zhuang Y, Zhang L. A new high-order finite volume method for 3D elastic wave simulation on unstructured meshes. J Comput Phys. 2017;340:534–555.
  • Cohen G. Higher-order numerical methods for transient wave equations. Berlin: Springer-Verlag; 2002.
  • Zhang W, Chung ET, Wang C. Stability for imposing absorbing boundary conditions in the finite element simulation of acoustic wave propagation. J Comput Math. 2014;32(1):1–20.
  • Zhang W. Elastic full waveform inversion on unstructured meshes by the finite element method. Phys Scr. 2019;94: 115002.
  • Beylkin G, Keiser JM. On the adaptive numerical solution of nonlinear partial differential equations in wavelet bases. J Comput Phys. 1997;132(2):233–259.
  • Dahmen W. Wavelet and multiscale methods for operator equations. Acta Numer. 1997;6:55–228.
  • Fröhlich J, Schneider K. An adaptive wavelet-vaguelette algorithm for the solution of PDEs. J Comput Phys. 1997;130(2):174–190.
  • Hong TK, Kennett BLN. On a wavelet-based method for the numerical simulation of wave propagation. J Comput Phys. 2002;183(2):577–622.
  • Qian S, Weiss J. Wavelets and the numerical solution of partial differential equations. J Comput Phys. 1993;106(1):155–175.
  • Lions LJ, Magenes E. Non-homogeneous boundary value problems and application. Vol. 1. New York (NY): Springer-Verlag; 1972.
  • Chui C. Wavelets: a tutorial in theory and applications. San Diego (CA): Academic Press; 1992.
  • Daubechies I. Orthonormal bases of compactly supported wavelets. Commun Pure Appl Math. 1988;41:901–906.
  • Daubechies I. Ten lectures on wavelet. Philadelphia (PA): Society for Industrial and Applied Mathematics; 1992.
  • Mallat S. Multiresolution approximations and wavelet orthogonal bases of L2(R). Trans Amer Math Soc. 1989;315:69–88.
  • Clayton R, Engquist B. Absorbing boundary conditions for acoustic and elastic wave equations. Bull Seismol Soc Am. 1977;67(6):1529–1540.
  • Grote MJ, Keller JB. Exact nonreflecting boundary condition for elastic waves. SIAM J Appl Math. 2000;60(3):803–819.
  • Zhang W, Tong L, Chung ET. Exact nonreflecting boundary conditions for three dimensional poroelastic wave equations. Commun Math Sci. 2014;12(1):61–98.
  • Berenger JP. A perfectly matched layer for the absorption of electromagnetic waves. J Comput Phys. 1994;114(2):185–200.
  • Thomas JW. Numerical partial differential equations: finite difference methods. New York (NY): Springer Science Business Media; 1995.
  • Nocedal J, Wright ST. Numerical optimization. New York (NY): Springer Science Business Media; 1990.
  • Dembo RS, Steihaug T. Truncated Newton algorithms for large-scale unconstrained optimization. Math Program. 1983;26(2):190–212.
  • Klibanov MV. Global convexity in a three-dimensional inverse acoustic problem. SIAM J Math Anal. 1997;28(6):1371–1388.
  • Khoa VA, Klibanov MV, Nguyen LH. Convexification for a three-dimensional inverse scattering problem with the moving point source. SIAM J Imaging Sci. 2020;13(2):871–904.
  • Klibanov MV, Kolesov AE, Nguyen LH. Convexification method for an inverse scattering problem and its performance for experimental backscatter data fir buried targets. SIAM J Imaging Sci. 2019;12(1):576–603.
  • Martin GS, Wiley R, Marfurt KJ. Marmousi2: an elastic upgrade for Marmousi. Leading Edge. 2006;25:156–166.
  • Beylkin G. On the representation of operators in bases of compactly supported wavelet. SIAM J Numer Anal. 1992;29(6):1716–1740.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.